UNIVERSITY  OF  CALIFORNIA 
SAN  FRANCISCO  LIBRARY 


(Fig.  575.) 
DOUBLE  PLATE  ELECTRICAL  MACHINE,  MADE  FOR  THE  UNIVERSITY  OF  MISSISSIPPI,  BY  RITCHIB.- 


PRINCIPLES 


OP 


PHYSICS, 


OR 


NATURAL    PHILOSOPHY; 


DESIGNED  FOR  THE 


to  0f  (Mkp  attfo  SrjjwrJs, 


BY 

BENJAMIN  J5ILLIMAN,  JR.,  M.  A.,  M.  D., 

PROFESSOR  OF  GENERAL  AND  APPLIED  CHEMISTRY  IN  YALE  COLLEGE. 

SECOND  EDITION, 

REVISED     AND     REWRITTEN. 


ttf)  %tim  ^uittajefc  an&  ^fojenta.-^too  ^llustx&tions. 


PUBLISHED      ¥  THEOi>RE      LISS  fe  OO 


Entered,  according  to  Act  of  Congress,  in  the  year  1860,  by 

H.  C.  PECK  &  THEO.  BLISS, 
in  the  Clerk's  Office  of  the  District  Court  of  the  Eastern  District  of  Pennsylvania. 


HEARS  *  DUSENBERY,  STEREOTYPERS.  0.  SHERMAN  &  SON,  PRINTERS. 


PKEFA.CE  TO  THE  SECOND  EDITION. 


MANY  important  changes  have  been  made  in  the  present  edition, 
designed  to  adapt  the  work  more  fully  to  the  wants  of  the  higher 
seminaries,  where  mathematical  demonstrations  are  required  of  the 
classes  in  Natural  Philosophy.  With  this  view,  the  two  first  Parts 
have  been  almost  wholly  rewritten,,  and  upon  a  different  plan  of 
arrangement.  Some  subjects  which  were  perhaps  too  fully  treated 
in  the  first  edition, — as,  for  example, -Crystallography, — have  been 
reduced,  while  others  have  been  expanded  to  meet  the  just  propor- 
tions of  a  harmonious  treatment.  These  remarks  apply  also  to  Part 
Third  (the  Physics  of  Imponderable  Agents),  and  especially  to 
Optics  and  Heat.  In  the  latter  chapter  some  topics  have  been 
omitted  which  are  more  appropriately  treated  in  Chemistry. 

The  mathematical  demonstrations,  while  they  are  designed  to  be 
as  simple  as  possible  consistent  with  exactness,  are  believed  to  be 
as  full  and  rigorous  as  are  demanded  in  institutions  where  only 
geometric  and  algebraic  methods  are  used.  Analytical  methods 
have  not  been  introduced,  as  the  book  was  not  designed  for  the 
comparatively  limited  number  of  colleges  where  the  higher  mathe- 
matics are  employed  in  teaching  Physics. 

The  questions  at  the  foot  of  the  pages  in  the  first  edition,  have 
been  omitted,  to  gain  space  for  a  considerable  number  of  practical 
problems  (mostly  original,)  designed  to  exercise  the  student  in  the 
application  of  the  principles  and  formulae  found  in  the  text.  To 
aid  in  the  solution  of  these,  and  to  assist  the  teacher  in  the  con- 
struction of  additional  problems,  numerous  physical  TABLES  have 
been  aided  in  the  APPENDIX. 

The  plan  of  using  two  kinds  of  type,  resorted  to  in  the  first 
'*  C5) 


vi  PREFACE    TO    THE    SECOND    EDITION. 

edition,  has  been  continued  with  more  particularity  in  this.  The 
book  is  thus  adapted  to  the  use  of  the  general  reader,  and  to  stu- 
dents who  seek  only  a  knowledge  of  general  principles. 

These  changes  and  additions,  the  author  believes,  entitle  this 
edition  more  fully  to  the  encomiums  bestowed  on  the  first  by  many 
of  the  ablest  physicists  and  most  experienced  teachers  in  this 
country.  By  the  liberality  of  the  publishers,  numerous  additions 
have  been  made  to  the  wood-cuts,  while  new  designs,  in  numerous 
cases,  replace  those  of  less  beauty  in  the  first  edition. 

The  design  has  been,  in  this  edition,  to  give  to  all  the  depart- 
ments of  physical  science  a  just  proportion  of  space,  in  harmony 
with  the  general  scope  of  the  book.  The  subject  of  Mechanics 
and  Machines  (upon  which  so  many  excellent  special  treatises 
exist)  has,  therefore,  been  condensed  into  a  smaller  proportionate 
space  than  it  usually  occupies  in  American  treatises  on  Natural 
Philosophy;  while  such  fundamental  subjects  as  Motion,  Force, 
Gravitation,  Elasticity,  Tenacity,  and  Strength  of  Materials,  are 
considered  at  more  length.  * 

The  author  has  freely  availed  himself  of  all  the  sources  of  infor 
mation  within  his  reach.  A  list  of  the  works  chiefly  used  in  the 
preparation  of  this  edition  is  appended — to  which  should  be  added 
the  chief  foreign  journals,  and  transactions  of  learned  societies — 
which  have  been  resorted  to  for  the  original  memoirs  quoted  on  a 
great  variety  of  topics.  He  is  also  particularly  indebted  for  good 
counsel  to  many  scientific  and  personal  friends,  the  influence  of 
whose  criticisms  on  the  first  edition  they  will  find  frequently  in 
the  present.  More  than  to  all  others  is  he  indebted  to  Dr.  M.  C. 
WHITE,  of  New  Haven,  for  his  constant  attention,  both  in  the 
preparation  of  new  matter  and  in  the  revision  of  the  press. 

He  also  takes  pleasure  in  again  acknowledging  his  obligations 
to  Prof.  C.  H.  PORTER,  of  Albany. 

For  a  final  revision  of  the  sheets,  and  the  detection  of  a  number 
of  errors  which  had  escaped  previous  proof-readers,  the  author 
is  indebted  to  Mr.  ARTHUR  W.  WRIGHT,  Assistant  Librarian  of 
Yale  College. 

Fuller  references  have  been  added,  especially  to  American  autho- 
rities }  and  the  author  hopes  no  apology  is  required  for  the  frequent 
references  to  the  American  Journal  of  Science,  which  is  supposed 


PREFACE    TO    THE    SECOND    EDITION.  Vll 

to  be  a  work  accessible  to  all  American  teachers,  while  the  Euro- 
pean journals  are  rarely  so;  and  references  to  these  would;  there- 
fore, be  of  little  practical  use  to  the  great  majority  of  readers  of 
such  a  treatise  as  this. 

As  no  table  of  errata  is  given  (all  errors  thus  far  discovered 
being  corrected),  the  author  will  esteem  it  a  great  favor  if  any 
person  using  the  book  will  communicate  to  him  direct  any  errors 
of  fact  or  figures  which  may  be  discovered. 

NEW  HAVEN,  October  15,  1860. 


LIST    OF   THE    PRINCIPAL    WORKS    USED   IN    PREPARING    THIS  EDITION. 

COOKE.     Chemical  Physios.     Boston,  1860. 

DAGUIN.  Traite  de  Physique,  torn.  I.,  II.,  and  III.  Paris  and 
Toulouse,  1855-1859. 

DE  LA  RIVE.  Treatise  on  Electricity,  3  volumes.  London,  1853- 
1858. 

GANOT.     TraitS  de  Physique.     Paris,  1859. 

GOODWIN.  A  Collection  of  Problems  and  Examples.  Cambridge, 
England,  1851. 

JAMIN.     Cours  de  Physique,  torn.  I.  and  II.     Paris,  1858-1859. 

KAHL.     Mathematische  Aufgaben  aus  der  Physik.     Leipzig,  1857. 

MILLER.     Chemical  Physics.     London,  1855. 

MULLER.  Lehrbuch  der  Physik  und  Meteorologie.  Braunschweig, 
1857. 

POTTER.  An  Elementary  Treatise  on  Optics,  2  Parts.  London, 
1851. 

POTTER.     An  Elementary  Treatise  on  Mechanics.     London,  1855. 

POTTER.     Physical  Optics.    London,  1856. 

WERNICKE.     Lehrbuch  der  Mechanik.    Braunschweig,  1858. 


FROM  PREFACE  TO  THE  FIRST  EDITION. 


THIS  hand-book  has  been  prepared  with  a  view  to  give  a  fair  exposi- 
tion of  the  present  condition  of  the  several  departments  of  Physics.  * 
*****  Accuracy  of  statement,  fullness  of  illustration, 
conciseness  of  expression,  and  a  record  of  the  latest  and  most  reliable 
progress  of  science  in  these  departments,  have  been  the  leading  objects 
in  its  preparation. 

Only  those  who  have  attempted  to  harmonize  and  present  in  due 
proportion  the  whole  of  so  vast  a  subject  as  this,  in  a  compendious 
form,  can  fully  appreciate  the  labor  and  difficulties  which  attend  it. 

Without  claiming  for  the  present  volume  any  credit  more  than 
belongs  to  a  faithful  digest  and  compilation  from  the  best  authorities 
in  modern  science,  it  is  hoped  that  it  will  be  found  suited  to  the  wants 
of  a  large  class  of  both  teachers  and  students.  No  pains  have  been 
wanting  to  secure  accuracy  both  in  fact  and  mechanical  execution. 
The  publishers  have  spared  no  expense  to  illustrate  the  book  with  a 
profusion  of  wood  cuts.  Many  of  these  are  original  designs,  or  are 
reduced  from  larger  drawings  by  photography — and  others  have  been 
selected  with  care  from  the  best  standard  authors.  *  *  *  *  *  * 
Whenever  it  was  possible,  reference  has  been  had  to  original  memoirs 
in  Journals  and  Transactions,  and  in  this  way  many  errors  current  in 
works  of  inferior  authority  have  been  corrected.  With  but  few  excep- 
tions, references  to  foreign  memoirs  have  been  omitted  in  the  text,  as 
their  insertion  could  profit  only  a  very  small  number  of  readers,  and 
might  seem  pedantic.  Not  so  with  respect  to  names  of  discoverers  of 
important  principles  and  phenomena.  A  great  number  of  names  of 
these  will  be  found  in  the  text,  in  their  proper  places,  and  not  unfre- 
quently  the  dates  of  birth,  or  death,  or  both,  are  given. 

Every  teacher  must  have  observed  that  an  abstract  principle  is 
often  fixed  in  the  memory  by  the  power  of  associated  ideas,  when  it  is 
connected  with  a  date  or  item  of  personal  interest,  as  the  attention  is 

(9) 


X  PREFACE   TO   THE   FIRST  EDITION: 

awakened  by  the  dramatic  far  more  than  by  the  didactic.  Hence  it 
has  been  thought  judicious  to  introduce  numerous  important  dates  in 
the  history  of  science. 

•*##•**•*•*# 
It  gives  me  great  pleasure  to  acknowledge  many  obligations  to  Prof. 
CHARLES  H.  PORTER,  M.  A.,  M.  D.,  of  Albany  (some  years  my  assistant), 
for  his  constant  and  most  important  assistance  in  the  compilation  and 
editing  of  this  book.  Preoccupied  as  my  own  time  has  been,  I  should 
not  at  times  have  found  it  possible  to  proceed  without  his  valuable 
assistance  and  excellent  judgment.  Dr.  M.  C.  WnriE,  of  this  town,  haa 
also  rendered  me  important  aid,  especially  in  OPTICS,  and  in  the  revi- 
sion of  the  press. 

******** 

NEW  HAVEN,  CONN.,  Oct.  15,  1858. 


CONTENTS. 

PART  FIRST. 

PHYSICS    OF    SOLIDS    AND    FLUIDS. 


CHAPTER  I. 

INTRODUCTION. 

Matter — Observation  and  experiment,  1 — Law,  theory  vand  hypothesis — Induc- 
tive philosophy — Force,  2 — The  properties  of  matter  are  general,  or  specific — 
The  changes  in  matter  are  physical,  or  chemical,  3 — Physical  and  chemical 
properties  of  matter — Physics  and  chemistry — Vitality,  4 — Light,  heat,  and 
electricity,  5. 

CHAPTER  II. 

GENERAL    PRINCIPLES. 

§  1.  Definitions  arid  General  Properties  of  Matter— I.  ESSENTIAL 
PROPERTIES — The  essential  properties  of  matter— Magnitude  or  extension,  5 
— Impenetrability — The  three  states  of  matter — II.  ENGLISH  AND  FRENCH 
SYSTEMS  OF  MEASURES — Units  of  measure,  6 — English  units  of  length — The 
French  system  of  measures,  7 — III.  ACCESSORY  PROPERTIES  OF  MATTER — 
Divisibility,  8 — Minute  division  in  the  animal  and  vegetable  kingdoms,  9 — 
Atoms,  molecules — Compressibility,  10 — Expansibility — Physical  pores,  11 — 
Sensible  pores — Mobility,  12 — Inertia — Action  and  reaction,  13. 

§  2.  Of  Motion  and  Force — I.  MOTION — Varieties  of  motion,  13 — Time 
and  velocity — Uniform  motion — Variable  motion,  14 — Motion  uniformly 
varied,  15 — Compound  motion-,  16 — Parallelogram  of  velocities — II.  OF 
FORCES — Definition  of  force — Forces  are  definite  quantities — Weight — Unit 
of  force— Dynamometers,  17 — Equilibrium — Statical  and  dynamical  forces — 
Direction  of  force,  19 — Measure  of  forces — Mass — Propositions  in  regard  to 
forces,  20 — Momentum,  21 — III.  COMPOSITION  OF  FORCES — System  of  forces 

(xi) 


Xii  CONTENTS. 

— Components  and  resultant — The  parallelogram  of  forces,  22 — Examples  of 
the  composition  of  motion  and  force — Parallel  forces — Resultant  of  unequal 
parallel  forces,  25— Resultant  of  two  parallel  forces  acting  in  opposite  direc- 
tions— Couples,  26 — Two  forces  not  parallel  and  applied  to  different  points — 
The  resolution  of  forces — Example  of  the  resolution  of  force,  27 — IV.  CURVI- 
LINEAR MOTION — CENTRAL  FORCES — Of  curvilinear  motion — Centrifugal  and 
centripetal  forces,  28 — Examples  of  the  action  of  centrifugal  force — Experi- 
mental demonstration  of  the  effects  of  centrifugal  force,  29 — The  centrifugal 
drying  machine  for  laundries,  31 — Analysis  of  the  motion  produced  by  central 
forces,  32 — Bohnenberger's  apparatus — Parallelogram  of  rotations,  33 — The 
gyroscope,  or  rotascope,  35 — Problems  on  weights  and  measures — Problems 
on  motion,  37. 

CHAPTER  III. 

GRAVITATION. 

§  1.  Direction  and  Centre  of  Gravity— Definition— Law  of  universal 
gravitation,  38 — Direction  of  terrestrial  attraction — Centre  of  gravity,  39 — 
Point  of  application  of  terrestrial  attraction,  40 — Centre  of  gravity — Corolla- 
ries, 41 — Centre  of  gravity  of  regular  figures,  42 — Centre  of  gravity  lying 
without  the  body — Equilibrium  of  solids  supported  by  an  axis — Equilibrium 
of  solids  placed  upon  a  horizontal  surface,  43 — Centre  of  gravity  in  bodies  of 
unequal  density  in  different  parts — Equilibrium  of  bodies  supported  in  moro 
than  one  point,  44. 

§  2.  Laws  of  Falling  Bodies — Gravity  is  a  source  of  motion — The  laws 
of  falling  bodies  are  five,  45 — Whole  space  described  by  a  falling  body,  47 — 
Verification  of  the  lav^  of  falling  bodies — Atwood's  apparatus,  48 — Morin's 
apparatus — Application  of  the  laws  of  falling  bodies,  50 — Descent  of  bodies 
on  inclined  planes,  51 — Descent  of  bodies  on  curves — Brachystochrone,  or 
curve  of  swiftest  descent— Action  and  reaction  of  a  falling  body,  52. 

g  3.  Measure  of  the  Intensity  of  Gravity— I.  PENDULUM— The  pendulum 
— Properties  of  the  simple  pendulum,  53 — Isochronism  of  the  pendulum,  54— 
Formulae  for  the  pendulum — Propositions  respecting  the  simple  pendulum,  55 
— The  physical  or  compound  pendulum — Centre  of  oscillation,  56 — Application 
of  the  pendulum  to  the  measurement  of  time,  57 — Cycloidal  pendulum — Physical 
demonstration  of  the  rotation  of  the  earth  by  means  of  the  pendulum,  58 — The 
pendulum  applied  to  the  study  of  gravity,  59 — Use  of  the  pendulum  for  mea- 
suring the  force  of  gravity — Value  of  g  in  these  experiments,  60 — Seconds  pen- 
dulum— II.  MODIFICATIONS  OF  TERRESTRIAL  GRAVITY  AND  THEIR  CAUSES. — The 
intensity  of  gravity  varies  with  the  latitude,  61 — Influence  of  the  earth's  figure 
upon  gravity,  62 — Exact  dimensions  of  the  earth — Sensible  weight  varies  in 
different  localities — Effect  of  the  earth's  rotation  on  gravity,  64 — Demonstra- 
tion, 65 — Variation  of  gravity  above  the  earth  and  below  its  surface — Below 
the  earth's  surface,  66. 

§  4.  Mass  and  "Weight— Mass— Weight— Density— Specific  weight,  67— 
French  system  of  weights,  68 — English  and  American  system  of  weights — 
Estimation  of  the  density  of  the  earth  by  experiment,  69— The  inference,  71. 

I  5.  Motion  of  Projectiles— Projectiles,  71— The  ballistic  pendulum- 
Problems — Falling  bodies,  73 — Descent  of  bodies  on  inclined  planes — Central 
forces — Pendulum  and  Gravity,  74 — Flight  of  Projectiles,  75. 


CONTENTS.  Xlll 

CHAPTER  IV. 

• 

THEORY    OP    MACHINERY. 

1.  Machines — Principle  of  virtual  velocities,  75 — Machine,  power,  weight 
— Equilibrium   of  machines,    76 — Utility   of    machines — Relation    of  power 
to   weight,  77 — Adaptation  of  the  power  to  the  weight  in  machinery — Vis 
viva,  or  living  force,  78 — Illustrations  of  vis  viva — Impact  and  its  results — 
Impact  considered  with  reference  to  momentum,  80 — Impact  considered  with 
reference  to  vis  viva,  81 — Pressure  produced  by  impact — Destructive  effects 
of  impact,  82. 

2.  Mechanical  Powers — The  lever,  83 — Conditions  of  equilibrium  in  the 
lever — Compound  levers — Application  of  the  lever,  84 — The  scale  beam — The 
steelyard,  85 — Examples  of  compound  levers,  86 — Roberval's  counter  platform 
balance,  87— The  wheel  and  axle,  88— Trains  of  wheel-work,  89 — Analysis  of 
a  train  of  wheel-work,  90 — The  pulley — Fixed  pulley — Movable  pulley — Com- 
pound pulleys,  91 — The  inclined  plane — Application  of  the  power  parallel  to  the 
length  of  the  inclined  plane,  93 — Application  of  the  power  parallel  to  the 
base  of  the  inclined  plane,  94 — Application  of  the  power  in  some  direction 
not  parallel  to  any  side  of  the  plane — The  wedge — Application  of  the  wedge, 
95 — The  screw,  96 — Mechanical  efficiency  and  applications  of  the  screw — The 
endless  screw,  97. 

3.  Strength  and   Power — Animal  strength — Strength  of  men — Horse- 
power machines,  98 — Table  of  the  comparative  strength  of  men  and  other 
animals — Steam-power,  99 — Perpetual  motion,  100. 

4.  Impediments    to    Motion — Passive  resistances — Sliding  .friction — 
Starting   friction — Friction    during   motion,    101 — Coulomb's    apparatus    for 
determining  starting  friction — Results  of  Coulomb's  experiments  on  starting 
friction,  102 — Rolling  friction — Coulomb's  apparatus  for  determining  rolling 
friction — Results    of  Coulomb's    experiments    on   rolling   friction,    104 — Mr. 
Babbage's  experiment — Advantages  derived  from  friction — Rigidity  of  ropes — 
Resistances  of  fluids,  105 — Actual  and  theoretical  velocities — Ballistic  curve, 
106— PROBLEMS— Vis  viva— The  lever— Wheel  and  axle,  107-  -The  pulley- 
Inclined  plane — The  screw — Resistance,  108. 

2 


CONTENTS. 

PART   SECOND. 

THE    THREE    STATES    OF    MATTER. 


CHAPTER  I. 

MOLECULAR    FORCES. 

Cohesion  and  repulsion — Repulsion,  109 — Examples  of  cohesion  among  sclids, 
1 10 — Cohesion  in  liquids  and  between  liquid  gases  and  solids,  111 — Between 
gases  and  solids,  112. 

CHAPTER  II. 

OP    SOLIDS. — MOLECULAR   FORCES    ACTING  BETWEEN    PARTICLES    OF    LIKE    KINDS. 

$  1.  Properties  of  Solids — The  characteristic  properties  of  solids — Struc- 
ture of  solids,  113. 

\  2.  Crystallography — Conditions  of  crystallization,  114 — Amorphism — 
Crystalline  forms — Definitions,  115 — Systems  of  crystals,  118 — Modified  forms, 
120 — Compound  crystals,  121 — Cleavage — Determination  of  crystalline  forms, 
122. 

\  3.  Elasticity — Elasticity  of  solids,  122 — Elasticity  of  tension  and  compres- 
sion, 123— Coefficient  of  elasticity,  124— Elasticity  of  flexure,  125— Applica- 
tions— M.  Bourdon's  metallic  barometer,  127 — The  Aneroid  barometer — 
Elasticity  of  torsion,  128 — Coulomb's  laws  of  torsion,  129 — Torsion  of  rigid 
bars — Limit  of  elasticity,  130 — Change  of  density  produced  by  tension,  131. 

§  4.  Strength  of  Materials— Laws  of  tenacity,  131— Johnson's  results- 
Tenacity  of  vegetable  and  animal  substances — Resistance  to  pressure  in 
columns,  132 — The  lateral  or  transverse  strength  of  materials,  133 — Practical 
applications,  134 — General  estimate  of  the  strength  of  beams — The  Britannia 
Tubular  Bridge,  136 — The  Victoria  Tubular  Bridge — Limits  of  magnitude,  137. 

\  5.  Properties  of  Solids  depending  on  a  permanent  displace- 
ment of  their  Molecules — Malleability — Ductility — Hardness,  138 — 
Brittleness— Hardening,  Temper,  Annealing,  139— Colors  of  tempered  steel — 
Tempering  by  a  bath — Temper  of  glass — Prince  Rupert's  Drops,  140 — Tem- 
pering copper  and  bronze — Hammering,  141 — Changes  of  structure  affecting 
the  mechanical  properties  of  metals,  142. 

$  6.  Collision  of  Solid  Bodies — Motion  communicated  by  collision,  142 
—Direct  impact  of  elastic  bodies — Modulus  of  elasticity,  143 — Velocity  of 
elastic  bodies  after  direct  impact,  144 — Scholium,  145 — Transmission  of  shock 
through  a  series  of  elastic  balls — Experimental  illustration  of  elasticity — 


CONTENTS.  XV 

PROBLEMS — Elasticity  of  tension — Elasticity  of  flexure — Tenacity — Transverse 
strength,  146 — Impact  of  elastic  bodies,  147. 

CHAPTER   III. 

OF    FLUIDS. — HYDRODYNAMICS. 

g  1.  Hydrostatics — I.  DISTINGUISHING  PROPERTIES  OF  LIQUIDS — Definitions 
— Fluids — Hydrodynamics — Mechanical  condition  of  liquids — Elasticity  of 
liquids — Compressibility,  148 — Elasticity — Consequences,  350 — II.  TRANS- 
MISSION OF  PRESSURE  IN  LIQUIDS — Liquids  transmit  pressure  equally  in  all 
directions,  151 — The  Bramah  hydrostatic  press,  152 — Uses  in  the  arts — Pres- 
sure of  a  liquid  on  the  bottom  of  a  vessel,  153 — Upward  pressure,  154 — Pres- 
sure on  the  sides  of  a  vessel — Pascal's  experiment  with  a  cask,  155 — The  water 
bellows,  or  hydrostatic  paradox — Total  pressure  on  the  walls,  156 — Total  pres- 
sure on  the  bottom  and  sides  of  a  vessel,  157— The  centre  of  pressure,  158 — 
Pressures  vary  as  the  specific  gravities  of  liquids — III.  EQUILIBRIUM  OF 
LIQUIDS — The  conditions  of  equilibrium  in  liquids,  159 — Equilibrium  of 
liquids  when  freed  from  the  influence  of  gravity — The  experiment  of  Plateau 
— Equilibrium  of  a  liquid  in  communicating  vessels,  160 — Equilibrium  of 
liquids  of  different  densities  in  communicating  vessels — Demonstration — The 
spirit  level,  161 — Artesian  wells — IV.  BUOYANCY  OF  LIQUIDS — Theorem  of 
Archimedes,  162 — Another  demonstration  of  A'rchimedes'  principle — Floating 
bodies,  164 — Examples — Equilibrium  of  floating  bodies,  165 — Neutral  equi- 
librium— Unstable  equilibrium,  166 — Stable  equilibrium — The  metacentre,  167 
— V.  DETERMINATION  OF  SPECIFIC  GRAVITY — The  problem  stated — Methods — 
Specific  gravity  by  the  hydrostatic  balance,  168— Examples,  169,  170— Spe- 
cific gravity  bottles,  170 — Example — Specific  gravities  by  hydrometers  or 
areometers — Nicholson's  hydrometer  or  areometer,  171 — Gay  Lussac's  and 
Beaume's  hydrometers,  172. 

$  2.  Hydraulics — I.  MOTION  OF  LIQUIDS-"— Definition — Pressure  of  liquids 
upon  the  containing  vessel,  173 — Appearance  of  the  surface  during  a  discharge 
— Theoretical  and  actual  flow,  174 — Reaction  of  the  escaping  vein — Barker's 
mill,  175— Flow— Theorem  of  Torricelli— Deductions  from  the  Torricellian 
theorem,  176 — Demonstration  of  the  theorem  of  Torricelli,  177 — The  inch  of 
water — Constitution  of  liquid  veins,  178 — Escape  of  liquids  through  short 
tubes — Escape  of  liquids  through  long  tubes — Formulae,  180 — Jets  of  water — 
Pressure  exerted  by  liquids  in  motion,  181 — Velocity  of  rivers  and  streams — 
Stream  measurers,  182 — II.  WATER-POWER  AND  WATER-WHEELS — Water- 
wheels — The  overshot  wheel — The  undershot  wheel,  183 — The  breast-wheel — 
Boyden's  American  turbine,  184. 

^MOLECULAR   FORCES    ACTING    BETWEEN    PARTJCLES    OF   UNLIKE    KINDS. 

T.  CAPILLARITY — Observation — Definition,  187 — General  facts  in  capillarity, 
188 — Form  of  the  surface — Cause  of  the  curve  of  liquid  surfaces  by  the 
contact  of  solids,  189 — Experimental  illustrations,  190 — Influence  of  the 
curve  on  capillary  phenomena,  191 — Law  of  the  elevation  and  depression 
of  liquids  in  capillary  tubes,  192 — Depression  of  mercury  in  capillary  tubes 
— Ascent  of  liquids  in  capillary  tubes,  193 — Laws  of  the  equilibrium  of 
liquids  between  parallel  or  inclined  laminae,  194 — Movement  of  drops  of 
liquid  in  con'cal  tubes  or  between  laminae — Attraction  and  repulsion  of 
light  floating  bodies,  195 — Escape  of  liquids  from  capillary  tubes—  Flow 


XVI  CONTENTS. 

of  liquids  from  capillary  tubes — II.  OSMOSE  OR  OSMOTIC  FORCE — Osmose,  exo?- 
mose,  endosmose,  196 — Endosmometer — Necessary  conditions — Materials  for 
septum,  197 — Direction  of  the  current — Organic  solutions — Inorganic  solu- 
tions— Endosmose  of  gases — Theories  of  endosmose,  198 — PROBLEMS  ON  HY- 
DRODYNAMICS— 'Elasticity  of  liquids — Hydrostatic  pressure,  199 — Buoyancy 
of  liquids—Floating  bodies,  200— Motion  of  liquids— Capillarity,  201. 

CHAPTER   IV. 

OF  ELASTIC  FLUIDS,  OR  GASES. 

Pneumatics — I.  DISTINGUISHING  PROPERTIES  OF  GASES — Definitions — Pneu- 
matics— Gases — Vapors — Tension — Expansion  of  gases,  202 — Mechanical  con- 
dition of  gases — II.  PROPERTIES  COMMON  TO  BOTH  LIQUIDS  AND  GASES — Gases 
transmit  pressure  equally  in  all  directions,  203 — The  atmosphere,  204 — Atmo- 
spheric pressure,  205 — Buoyancy  of  air,  206 — Impenetrability  of  air — Inertia 
of  air — III.  BAROMETERS  AND  BALLOONS — Torricellian  vacuum — Measure  of 
atmospheric  pressure,  207 — Pascal's  experiments,  208 — Construction  of  baro- 
meters— Apparatus  illustrating  the  principle  of  the  barometer,  209 — Height 
of  the  barometric  column  at  different  elevations — Cistern  barometer — Fortin's 
barometer,  210 — The  syphon  barometer,  211 — Wheel  barometer — Causes  of 
error — Correction  for  capillarity,  212 — Correction  for  temperature — Varia- 
tions of  the  barometric  height,  213 — Variations  observed  in  barometers  are 
of  two  kinds — Relation  between  barometric  changes  and  the  weather,  214 
— Rules  by  which  coming  changes  are  indicated — Measure  of  heights  by 
the  barometer,  215 — Balloons,  216 — Construction  and  filling  of  balloons, 
217 — Parachute — IV.  COMPRESSIBILITY  OF  GASES — Mariotte's  law,  218 — 
Experimental  verification  of  Mariotte's  law,  219 — Experiments  of  Despretz 
— Experiments  of  Regnault,  220 — Results  obtained  by  Regnault — General 
conclusions  on  the  compressibility  of  gases,  221 — V.  INSTRUMENTS  DEPENDING 
ON  THE  PROPERTIES  OF  GASES — Manometers — Manometer  with  free  air — Ma- 
nometer with  compressed  air,  222 — Bellows — Bellows  with  a  continuous  blast, 
223 — Furnace  blowers — Escape  of  compressed  gases,  224 — Pneumatic  ink- 
bottle — The  syphon,  225 — Intermittent  syphon — Tantalus'  vase — Intermittent 
springs,  226 — Intermittent  fountain — Air-pump,  227 — Degree  of  exhaustion 
— Compressing  machine — Water-pumps — Suction-pumps,  229 — Suction  and 
lifting  pump— Forcing-pump,  230— Rotary  pump— Fire-engine,  231— Hiero's 
fountain — Hydraulic  ram,  232 — Chain-pump — Archimedes'  screw,  233 — PRO- 
BLEMS ON  PNEUMATICS — Atmospheric  pressure,  234 — Barometer  and  balloons 
—Mariotte's  law,  235. 

CHAPTER   V. 

• 

OF    UNDULATIONS. 

|  1.  Theory  of  Undulations— Origin  of  undulations— Progressive  undu- 
lations, 236 — Mechanical  illustration  of  undulations — Stationary  undulations 
— Isochronous  vibrations — Phases  of  undulations,  237 — Nodal  points,  238. 

\  2.  Undulation's  of  Solids— Solid  bodies— Forms  of  vibration,  238-- 
Vibration  of  cords — Laws  of  the  vibration  of  cords,  239 — Vibrations  of  rods 
—Paths  of  vibration,  240— Vibration  of  elastic  plates— Nodal  lines— Determi- 
nation of  the  position  of  the  nodal  lines,  241— Laws  of  the  vibration  of  planes 


CONTENTS.  X«ii 

— Method  of  delineating  nodal  lines — Nodal  figures,  242 — Vibration  of  mem- 
branes, 243. 

§3.  Undulations  of  Liquids — Production  of  waves — Progressive  undula- 
tions in  liquids,  244 — Stationary  waves,  245 — Depth  to  which  waves  extend — 
Reflection  of  waves — Waves  propagated  from  the  foci  of  an  ellipse — Waves 
propagated  from  the  focus  of  a  parabola,  246 — Circular  waves  reflected  from 
a  plane,  247 — Combination  of  waves — Interference  in  an  ellipse — Undulations 
of  the  waters  of  the  globe,  248. 

g  4.  Undulations  of  Elastic  Fluids — Waves  of  condensation  and  rare- 
faction— Undulations  of  a  sphere  of  air,  249 — Mechanical  illustration — Velo- 
city and  intensity  of  aerial  waves,  250 — Interference  of  waves  of  air — Intensity 
of  waves  of  air  expanding  freely — PROBLEMS  ON  THE  LAWS  OF  VIBRATIONS, 
251. 

CHAPTER   VI. 

ACOUSTICS. 

§  1.  Production  and  Propagation  of  Sound — Acoustics — Sound — 
Sound  a  sensation — Key-note  of  nature — Noise — Musical  sounds,  252 — All 
bodies  producing  sound  are  in  vibration,  253 — Sound  propagated  by  waves 
— Co-existence  of  sound-waves — Sound  is  not  propagated  in  a  vacuum, 
254 — Sound  is  propagated  in  all  elastic  bodies — Hearing — Time  is  required 
for  the  transmission  of  sound — The  velocity  of  all  sounds  is  the  same,  255 — 
Velocity  of  sound  in  air,  256 — Velocity  of  sound  in  different  gases  and  vapors 
— Calculation  of  distances  by  sound — Velocity  of  sounds  in  liquids — Velocity 
of  sounds  in  solids,  257 — Interference  of  sound — Acoustic  shadow,  258 — Dis- 
tance to  which  sound  may  be  propagated,  259 — Reflection  of  sound — Echo,  260 
— Repeated  echoes — Change  of  tone  by  echo,  261 — Whispering  galleries — 
Refraction  of  sound,  262 — The  speaking-trumpet,  263 — Ear-trumpet — The 
siren,  2&1 — Savart's  toothed  wheel — Music  halls,  2G6. 

g  2.  Physical  Theory  of  Music— Qualities  of  musical  sounds— Tone  or 
pitch — Intensity  or  loudness — Quality — Unison — Melody — Harmony,  267 — 
Musical  scale — Gamut,  268 — The  sonometer  or  inonochord — Relative  number 
of  vibrations  corresponding  to  each  note,  269 — Absolute  number  of  vibrations 
corresponding  to  each  note,  270 — Length  of  sonorous  waves — Interval,  271 — 
Compound  chords — Perfect  concord — A  new  musical  scale,  272 — Transposition 
— Temperament,  274— Beating — Diapason,  tuning-fork,  275 — Sensibility  of 
the  ear,  276. 

$  3.  Vibration  of  Air  contained  in  Tubes — Sonorous  tubes — Mode 
of  vibrating,  276 — Mouth-pipes — Reed-pipes,  277 — Gas  jet — Musical  instru- 
ments, 278 — Vibration  of  air  in  tubes — Laws  of  Bernoulli — Demonstration, 
279 — Construction  of  musical  instruments,  280 — Vibrating  dams,  281. 

$  4.  Vocal  and  Auditory  Apparatus — I.  OP  VOICE  AND  SPEECH — Voice 
and  speech — The  vocal  apparatus  of  man,  281 — The  larynx — The  glottis,  282 
— Mechanism  of  the  voice — Range  of  the  human  voice,  283 — Ventriloquism, 
stuttering,  <fcc.,284 — Production  of  sounds  by  inferior  animals — Birds — Insects 
— II.  THE  EAR — HEARING — Auditory  apparatus  of  man — The  external  ear, 
285 — The  middle  ear,  tympanum,  or  tympanic  cavity,  286 — The  internal  ear, 
287 — Functions  of  the  different  parts  of  the  ear — Natural  diapason,  288 — 
Organs  of  hearing  in  the  lower  animals — PROBLEMS  IN  ACOUSTICS — Velocity 
of  sound,  289—  Physical  theory  of  Music,  290. 
2* 


xyiii  CONTENTS. 

PART   THIRD. 

PHYSICS  OF  IMPONDERABLE  AGENTS. 

LIGHT,    HEAT,    AND    ELECTRICITY. 


CHAPTER  I. 

LIGHT,    OR   OPTICS. 

g  1.  General  Properties  of  Light — Optics — Light— Nature  of  light — 
Theories,  291 — Sources  of  light — Phosphorescence,  292 — Relation  of  different 
bodies  to  light — Rays,  pencils,  and  beams  of  light — Visible  bodies  emit  light 
from  every  point,  293 — Propagation  of  light  in  a  homogeneous  medium — Ve- 
locity of  light — Foucault's  apparatus  for  measuring  the  velocity  of  light,  294 
— Fizeau's  method — Results — No  theory  of  light  is  entirely  satisfactory — 
Properties  of  light,  296 — Amount  of  light  reflected  at  different  angles  of  inci- 
dence, 298— Internal  reflection— Total  reflection,  299— Irregular  reflection- 
Diffused  light — Umbra  and  penumbra,  300 — Images  produced  by  light  trans- 
mitted through  small  apertures — Intensity  of  light  at  different  distances — 
Photometers,  301 — Bunsen's  photometer— Rumford's  photometer — Silliman's 
photometer,  302. 

§  2.  Catoptrics,  or  Reflection  by  Regular  Surfaces — I.  MIRRORS 
AND  SPECULA — Mirrors— Specula  are  metallic  reflectors — Forms  of  mirrors — 
II.  REFLECTION  AT  PLANE  SURFACES — Reflection  by  plane  mirrors,  303 — 
Images  formed  by  plane  mirrors,  304 — Images  multiplied  by  two  surfaces  of 
a  glass  mirror — Images  formed  by  light  reflected  by  two  plane  mirrors,  305 — 
Multiplicity  of  images  seen  by  means  of  inclined  mirrors — Deviation  of  light 
reflected  by  two  mirrors,  306 — Kaleidoscope,  307 — Hadley's  sextant — III. 
REFLECTION  AT  CURVED  SURFACES — Concave  and  convex  spherical  mirrors, 
308 — Foci  of  concave  mirrors  for  parallel  rays — Foci  of  diverging  rays,  309 — 
Converging  rays — Virtual  focus — Secondary  axes — Oblique  pencils — Rule  for 
conjugate  foci  of  concave  mirrors — Convex  spherical  mirrors,  311 — Images 
formed  by  concave  mirrors,  312 — Virtual  images — Formation  of  images  by 
convex  mirrors,  313 — General  rule  for  constructing  images  formed  by  mirrors 
Spherical  aberration  of  mirrors — Caustics,  314. 

g  3.  Dioptrics,  or  Refraction  at  Regular  Surfaces— I.  DEFINITIONS— 
Prisms  and  lenses,  314—11.  REFRACTION  AT  PLANE  SURFACES — Refraction  by 
prisms,  315 — Method  of  determining  the  index  of  refraction,  316 — Plane  glass 
— Light  passing  through  parallel  strata  of  different  media,  317 — Pencils  of 
light  refracted  at  plane  surfaces,  318— Pencils  of  light  transmitted  through 
plane  glass — III.  REFRACTION  AT  CURVED  SURFACES — Principles  determining 
the  foci  of  lenses,  320— Small  pencils  of  light  refracted  at  a  spherical  surface, 
321 — Refraction  at  a  concave  surface,  322 — Action  of  a  double  convex  lena 
upon  small  pencils  of  light,  323— Conclusions  deduced— Analysis,  324— Action 


CONTENTS.  XIX 

of  a  double  concave  lens  upon  small  pencils  of  light — Conclusions  deduced 
from  analysis,  326 — Rules  for  determining  the  foci  of  lenses — Combined  lenses, 
327 — Oblique  pencils — The  optical  centre  of  a  lens,  328 — Images  formed  by 
lenses — Spherical  aberration  of  lenses,  329 — Accurate  estimate  of  spherical 
aberration,  330 — Aberration  of  sphericity  ;  distortion  of  images,  331. 

4.  Chromatics — Analysis  of  light — Spectrum — Primary  colors — Recompo- 
sition  of  white  light — Analysis  of  colors  by  absorption,  332 — Complementary 
colors — Properties  of  the  solar  spectrum,  333 — Fraunhofer's  dark  lines  in  the 
solar  spectrum,  334 — Lines  in  light  from  different  sources,  335 — Fixed  lines 
in  the  spectra  from  various  colored  flames — Intensity  of  luminous,  calorific, 
and  chemical  rays — Refraction  and  dispersion  of  the  solar  spectrum — Kaly- 
chromatics,    336 — Chromatic    aberration — Achromatism,    337 — Formulae    for 
achromatism,  338. 

5.  Vision — Structure  of  the  human  eye,  339 — Action  of  the  eye  upon  light, 
340 — Inversion  of  the  image  formed  in  the  eye — Optic  axis — Optic  angle — 
Visual  angle,  341 — The  brightness  of  the  ocular  image — Conditions  of  distinct 
vision — Background,  342 — Sufficiency  of  illumination — Distance  of  distinct 
vision — Visual  rays  nearly  parallel,  343 — Adaptation  of  the  eye  to  different 
distances — Appreciation  of  distance  and  magnitude — Aerial  perspective,  344 
— Single  vision  with  two  eyes — Double  vision— Binocular  vision,  345 — Near- 
sightedness — Long-sightedness,  346 — Duration   of  the  impression  upon   the 
retina — Optical  toys — Thaumatrope — Time  required  to  produce  visual  impres- 
sions— Appreciation  of  colors — Color  blindness,  347 — Chevreul's  classification 
of  colors,  and  chromatic  diagram,  348 — Examples — The  study  of  colors,  349. 

6.  Optical    Instruments— Magnifying   glasses,   349 — The   magnifying 
power  of  a  lens,  350 — The  simple  microscope — Raspail's  dissecting  micro- 
scope— The  compound  microscope,  351 — The  telescope — The  telescope  used  by 
Galileo,  352 — The  opera-glass — Night-glasses — The  astronomical  telescope — 
— Eye-pieces — The  positive  eye-piece — The  negative  eye-piece,  353— The  ter- 
restrial eye-piece — Reflecting  telescopes — Sir  William  Herschel's  telescope,  354 
— Lord  Rosse's  telescope — Achromatic  telescopes,  355 — Equatorial  mountings 
for  telescopes,  356 — The  Cambridge  telescope  with  equatorial  mountings,  357 — 
The  visual  power  of  telescopes,  358 — Achromatic  object-glasses  for  microscopes 
• — Lister's  aplanatic  foci,  and  compound  objectives,  359 — Aberration  of  glass 
cover  corrected — The  compound  achromatic  microscope,  361 — Solid  eye-piece 
— Visual  power  of  the  achromatic  microscope,  362 — The  mechanical  arrange- 
ment of  the  microscope,  363 — The  magic  lantern — The  solar  microscope,  364 
— The  camera  obscura — Wollaston's  camera  lucida,  365 — Photography — Rail- 
way illumination,  366 — The  Fresnel  lens — Sea-lights,  367 — Revolving  lights, 
368 — The  telestereoscope,  369 — The  stereoscope,  370 — The  stereomonoscope, 
372. 

7.  Physical  Optics — I.  INTERFERENCE,  DIFFRACTION,  FLUORESCENCE,  &c. 
Interference  of  light,  373 — Facts  at  variance  with  theory — Interference  colors 
of  thin  plates,  374 — Newton's  rings — Length  of  luminous  waves  or  vibrations, 
375 — Diffraction,  376— Fluorescence — Epipolic  dispersion — Phosphorescence, 
377 — Colors  of  grooved  plates — II.  OPTICAL  PHENOMENA  OF  THE  ATMOSPHERE 
— The  rainbow,   378 — A  secondary   rainbow,  380 — Spurious    rainbow — Fog- 
bows — Halos — Coronas — Parhelia — Atmospheric    refraction — Looming — The 
mirage,  381 — III.  POLARIZATION  OF  LIGHT — Direction  of  luminous  vibrations 
— Transmission  of  luminous  vibrations,  382 — Change  produced  by  polarization 
of  light — Resolution  of  vibrations,  383 — Light  polarized  by  absorption — Po- 


XX  CONTENTS. 

larization  by  reflection,  384 — Polarization  by  metallic  reflection — Polarization 
by  refraction — Polarization  by  successive  refractions,  385 — Partial  polariza- 
tion— Double  refraction,  386 — Positive  and  negative  crystals — Polarization  by 
double  refraction — Nicol's  single  image  prism,  387 — Polarizing  instruments 
— Colored  polarization,  388 — Rotary  polarization — Arago's  chromatic  polari- 
scope,  389 — Colored  rings  in  crystals — Polarization  by  heat,  and  by  compres- 
sion, 390 — Magnetic  rotary  polarization — Atmospheric  polarization  of  light — 
The  eye  a  polariscope,  391 — The  practical  applications  of  polarized  light — 
PROBLEMS  IN  OPTICS — Velocity  and  intensity  of  light,  392 — Reflection  of  light 
— Refraction  of  light,  393 — Optical  Instruments — Polarization  of  light,  394. 


CHAPTER  II. 


\  1.  Nature  of  Heat — Heat — Its  nature — Temperature — Heat  and  cold,  395 
— Action  of  heat  on  matter,  396. 

§  2.  Measurement  of  Temperature — I.  THERMOMETERS — Thermometers 
— Construction  of  mercurial  thermometers — Thermometer  tubes,  396 — Filling 
the  tube  with  mercury — Standard  points  in  the  thermometer — Graduation,  397 
— Freezing  point — Boiling  point,  398 — Different  thermometric  scales — Fah- 
renheit's scale — Centigrade  scale,  399 — Reaumur's  scale — Comparison  and 
conversion  of  thermometric  scales — House  thermometers,  400 — Tests  of  a  good 
thermometer — Sensibility  of  thermometers — Displacement  of  the  zero  point, 
401 — Limits  of  the  mercurial  thermometer — Spirit  thermometers — Other  liquid 
thermometers,  402 — Defects  inherent  in  mercurial  thermometers,  403 — Stand- 
ard thermometer,  405 — II.  SELF-REGISTERING  THERMOMETERS — Maximum  and 
minimum  thermometers,  406 — Rutherford's  maximum  and  minimum  thermo- 
meter— Negretti  and  Zambra's  maximum  thermometer,  407 — Walferdin's 
maximum  thermometer — Metastatic  thermometer,  408 — III.  METALLIC  THER- 
MOMETERS AND  PYROMETERS — Breguet's  metallic  thermometer — Saxton's  deep- 
sea  metallic  thermometer,  409 — Saxton's  reflecting  pyrometer — Wedgewood's 
pyrometer — Daniell's  pyrometer,  410 — Draper's  pyrometer — Estimation  of  very 
high  temperatures — IV.  THERMOSCOPES — Thermoscopes — Air  thermometers, 
411 — Leslie's  differential  thermometer — Howard's  differential  thermometer — 
Rumford's  thermoscope — Thermo-multiplier,  412. 

§  3.  Expansion — I.  EXPANSION  OF  SOLIDS — Linear  expansion — Pyrometers 
— Cubical  expansion,  413 — Relation  between  cubical  and  linear  expansion — 
Expansion  of  crystals — Coefficient  of  expansion,  414 — The  capacity  of  hollow 
vessels  is  increased  by  the  expansion  of  their  walls — The  amount  of  expansion 
in  solids,  415 — The  ratio  of  expansion  increases  with  the  temperature — Amount 
of  force  exerted  by  expansion,  416 — Common  phenomena  produced  by  the 
expansion  of  solids,  417 — Fire  regulators — Unequal  expansion  of  solids,  418 
— Compensating  pendulums — Harrison's  gridiron  compensating  pendulum — 
Graham's  compensating  pendulum,  419 — Mr.  Henri  Roberts'  compensating 
pendulum — Martin's  compensating  pendulum — Compensating  balance  wheels 
of  watches  and  chronometers,  420 — II.  EXPANSION  OF  LIQUIDS — General  state- 
ment— Apparent  and  absolute  expansion,  421 — Correction  of  the  observed 
height  of  the  barometer  for  temperature — Apparent  expansion  of  mercury, 
422 — Amount  of  expansion  of  liquids,  423 — Expansion  of  liquids  above  their 
boiling  points — Curves  of  expansion  of  liquids—  The  amount  of  force  exerted 


CONTENTS.  XXI 

in  the  expansion  of  liquids,  424 — Expansion  of  water — Maximum  density  of 
water,  425 — Effects  of  the  unequal  expansion  of  water — Maximum  density  of 
different  aqueous  solutions,  426 — The  volume  of  water  at  different  tempera- 
tures— III.  EXPANSION  OF  GASES — General  statement — Gay  Lussac's  laws 
for  the  expansion  of  gases  by  heat — Result  of  Regnault's  experiments  upon 
the  expansion  of  gases,  427 — Formulae  for  computing  changes  of  volume  in 
gases,  428 — Formulae  expressing  general  relation  between  volume,  tempera- 
ture, and  pressure — Relation  between  expansibility  and  compressibility — 
Density  of  gases,  429. 

§  4.  Communication  of  Heat — I.  CONDUCTION — Modes  in  which  heat  is 
communicated — Conduction  of  heat,  430 — Determination  of  the  conductibility 
of  solids,  431 — Conductibility  of  metals,  &c. — Conductibility  of  crystals — 
Conductibility  of  wood,  432 — Vibrations  produced  by  conduction  of  heat — 
Conductibility  of  liquids — Conductibility  of  gases,  433 — Relative  conducti- 
bility of  solids,  liquids,  and  gases — Examples  and  illustrations  of  the  different 
conductibility  of  solids — Examples  drawn  from  the  animal  and  vegetable 
kingdoms,  434 — The  conducting  power  of  substances  in  a  pulverized  or  fibrous 
state — Clothing,  435 — II.  CONVECTION — Convection — Convection  in  liquids — 
Currents  in  the  ocean,  436 — III.  RADIATION — Radiation  of  heat — Radiant 
heat  is  but  partially  absorbed  by  the  media  through  which  it  passes,  437 — 
Intensity  of  radiant  heat — Law  of  cooling  by  radiation,  438 — Universal  radia- 
tion of  heat — Apparent  radiation  of  cold,  439. 

§  5.  Action  of  different  Bodies  upon  Heat— I.  SURFACE  ACTION— 
Reflection  of  heat — Conjugate  mirrors — Determination  of  reflective  power,  440 
— Absorptive  power — Emissive  or  radiating  power,  441 — Causes  which  modify 
the  emissive,  absorbent,  and  reflective  powers  of  bodies — Applications  of  the 
powers  of  reflection,  absorption,  and  radiation,  442 — II.  DIATHERMANCY — 
Transmission  of  radiant  heat — Melloni's  apparatus,  443 — Influence  of  the 
substance  of  screens,  444 — Influence  of  the  material  and  nature  of  the  source 
— Other  causes  which  modify  the  diathermanic  power  of  bodies,  445 — Thermo- 
chrosy — Applications  of  the  diathermancy  of  bodies — Refraction  of  heat,  446 
— Polarization  of  heat,  447. 

§  G.  Calorimetry— Calorimetry— Unit  of  heat,  447— Specific  heat— Method 
of  mixture — Method  by  fusion  of  ice,  448 — The  method  of  cooling — Specific 
heat  affected  by  change  of  state — Specific  heat  of  gases,  449 — Specific  heat  of 
gases  under  a  constant  volume,  450 — Specific  heat  determined  by  the  laws  of 
acoustics,  451 — Relation  between  the  specific  heat  and  atomic  weight  of  ele- 
ments and  compounds,  452. 

$  7.  Liquefaction  and  Solidification — Latent  heat,  452 — Liquefaction 
and  congelation  are  always  gradual — Freezing  mixtures,  453 — Laws  of 
fusion  and  latent  heat  of  fusion — Peculiarities  in  the  fusion  of  certain  solids, 
---Refractory  bodies — Solution — Saturation,  454 — Laws  of  solidification — Ele- 
vation of  temperature  during  solidification — Change  of  volume  during  solidi- 
fication, and  its  effects,  455 — Freezing  of  water — Absolute  zero,  456. 

§  8.  Vaporization  and  Condensation — Vaporization,  456 — Formation 
of  vapors  in  a  vacuum,  457— Saturated  space  or  maximum  tension  of  vapors 
— Dalton's  law  of  the  tension  of  vapors — The  tension  of  vapors  in  communi- 
cating vessels  unequally  heated — Temperature  and  limits  of  vaporization,  458 
— Circumstances  influencing  evaporation — Dew-point — Ebullition,  459 — Cir- 
cumstances influencing  the  boiling  point,  460 — The  culinary  paradox — Frank- 


CONTENTS. 

lin's  pulse  glass — Useful  applications  in  the  arts — Measurement  of  heights  by 
the  boiling  point — Hypsometer,  461 — High,  pressure  steam — Production  of 
cold  by  evaporation,  462 — Twining's  ice  machine — Latent  heat  of  steam,  463 
-Latent  and  sensible  heat  of  steam  at  different  temperatures — Mechanical 
force  developed  during  evaporation,  464 — Liquefaction — Distillation — Distil- 
ling apparatus — Physical  identity  of  gases  and  vapors — Theory  of  the  lique- 
faction and  solidification  of  gases,  465 — Methods  of  reducing  gases  to  liquids 
— Later  researches  of  Faraday — Thilorier's  and  Bianchi's  apparatus  for  con- 
densation of  gases,  466 — Properties  of  liquid  and  solid  gases — Latour's  law, 
467 — Density  of  vapors,  468. 

|  9.  Spheroidal  condition  of  Liquids— Spheroidal  state— Illustration 
of  the  spheroidal  state — Noticeable  phenomena  connected  with  the  spheroidal 
state,  468 — Spheroidal  state  produced  upon  the  surface  of  liquids — A  liquid 
in  a  spheroidal  state  is  not  in  contact  with  the  heated  surface  beneath,  469 — 
A  repulsive  action  is  exerted  between  the  spheroid  and  the  heated  surface — 
The  causes  which  produce  the  spheroidal  form,  470 — Freezing  water  and 
mercury  in  red-hot  crucibles — Remarkable  phenomena  connected  with  the 
spheroidal  state — Explosions  produced  by  the  spheroidal  state,  471 — Steam 
boiler  explosions — Familiar  illustrations  of  the  spheroidal  state,  472. 

\  10.  The  Steam-Engine — Historical — The  eolipile — First  steamboat — 
Savary's  engine,  473 — Papin's  steam  cylinder — Newcomen's  engine,  474 — The 
atmospheric  engine — Watt's  improvements  in  the  steam-engine,  475 — The  low 
pressure  or  condensing  engine,  476 — The  high  pressure  engine — The  cut  off, 
477 — Steam  boilers — Mechanical  power  of  steam — Horse-power,  478 — Evapo- 
rating power  and  value  of  fuel,  479. 

§  11.  Ventilation  and  Warming — I.  VENTILATION — Currents  in  air  and 
gases,  480 — Draught  in  chimneys,  481 — Reversed  draughts  and  smoky  chimneys 
— Products  of  respiration  and  combustion,  and  necessity  for  ventilation,  482 
— The  quantity  of  vapor  given  off  by  the  body— The  quantity  of  air  required 
for  good  ventilation — Products  of  gas  illumination,  483 — The  actual  ventila- 
tion of  buildings  is  a  practical  problem — Stone's  ventilating  shaft,  484 — Cold 
currents  produced  by  ice — Refrigerators — Cowls — Emerson's  ventilators,  485 
— The  supply  of  fresh  air  in  dwellings — II.  WARMING — The  artificial  tempe- 
ratures demanded  in  cold  climates — The  open  fire,  486 — Hot  air  furnaces,  487 
— Heating  by  hot  water — Perkins'  high  pressure  hot  water  apparatus,  488 
— Gold's  steam  heaters — The  radiators,  489 — The  boiler  of  Gold's  steam 
heater,  490. 

$  12.  Sources  of  Heat — Sources  of  heat — I.  MECHANICAL  SOURCES  OP  HEAT 
— Friction,  490 — Quantity  of  heat  produced  by  friction — Circumstances  which 
vary  the  quantity  of  heat  developed  by  friction — Illustrations  and  application 
of  the  heat  developed  by  friction,  491 — Compression — Percussion — Capillarity, 
492 — II.  PHYSICAL  SOURCES  OF  HEAT — The  sun — Quantity  of  heat  emitted  by 
the  sun — Extremes  of  natural  temperature,  493 — Terrestrial  radiation — Origin 
of  terrestrial  heat — Atmospheric  electricity,  494 — III.  CHEMICAL  SOURCES  OP 
HEAT — Chemical  combination — Combustion — On  the  cause  of  the  heat  gene- 
rated by  combustion — The  amount  of  heat  developed  by  chemical  action,  495 
— The  pyrometrical  heating  effect  of  a  substance,  496 — Relative  value  of  fuel 
— Combinations  in  the  humid  way — Animal  heat;  warm  and  cold-blooded 
animals,  497 — The  cause  of  animal  heat — Temperature  of  vegetables,  498. 

g  13.  Correlation  of  Physical  Forces— I.  MECHANICAL  EQUIVALENT  OF 


CONTENTS.  XX111 

HEAT — Relations  of  heat  and  force,  498 — Unit  of  measurement,  the  foot-pound 
— Determination  of  the  mechanical  equivalent  of  heat — Results  of  Joule's 
experiments,  499 — Conclusions  deduced  from  Joule's  experiments. — II.  DY- 
NAMICAL THEORY  OF  HEAT — The  dynamical  theory  of  heat — Motions  of  the 
molecules — Changes  in  the  state  or  volume  of  bodies,  500 — III.  ANALOGY  OF 
LIGHT  AND  HEAT — Vibrations  producing  heat  and  light — Impressions  of  light 
and  heat,  501 — Bodies  become  luminous  by  incandescence,  502 — Heat  and  light 
produced  by  chemical  and  mechanical  action — Dilatation  and  change  of  state, 
503 — Change  of  state  produced  by  heat — Quality  of  heat  changed  by  absorp- 
tion and  radiation,  504 — Difference  between  quantity  and  intensity  of  heat — 
Conclusion,  505 — PROBLEMS  ON  HEAT — Thermometers,  506— Expansion — 
Specific  heat,  507 — Tension  of  vauors — Ventilation  and  warming,  508. 


CHAPTER  III. 

ELECTRICITY. 

General  statement       ..........     509 

§  1.  Magnetic  Electricity— I.  PROPERTIES  OF  MAGNTSTS— Lodestone— 
Natural  magnets — Artificial  magnets,  509 — Magnetic  needles — Distribution 
of  the  magnetic  force — Polarity,  510 — Magnetic  phantom — Magnetic  curves — 
Magnetic  figures,  511 — Anomalous  magnets — Attraction  and  repulsion — Mag- 
netism by  contact,  512 — Magnetism  in  bodies  not  ferruginous — II.  MAG- 
NETIC INDUCTION  OR  INFLUENCE — Induction,  513 — Theoretical  considerations 
— Theory  of  two  fluids,  514 — Coercitive  force — III.  TERRESTRIAL  MAGNETISM 
— Magnetic  needle — Directive  tendency,  515 — The  mariner's  compass,  516 — 
The  astatic  needle — Magnetic  meridian — Declination  or  variation,  517 — Varia- 
tion chart — Isogonal  lines,  518 — Daily  variations  of  the  magnetic  needle — The 
annual  variation — Dip  or  inclination,  520 — The  action  of  the  earth's  magnetism 
— Dipping  needle,  521 — Inclination  map,  or  isoclinal  lines,  522 — Magnetic 
intensity,  523 — Isodynamic  lines,  524- — The  inductive  power  of  the  earth's 
magnetism — System  of  simultaneous  magnetic  observations,  525 — Lines  of 
magnetic  force — Atmospheric  magnetism,  526 — Notions  of  the  origin  of  the 
earth's  magnetism — IV.  PRODUCTION  OF  MAGNETS — Artificial  magnets,  527 — 
The  circumstances  affecting  the  value  of  magnets — Magnets  by  touch,  528 — 
Horse-shoe  magnets,  529 — Magnets  by  electro-magnetism — Compound  mag- 
nets, 530 — Magnetism  of  steel  by  the  sun's  rays — To  deprive  a  magnet  of  its 
power,  531. 

\  2.  Statical  or  Frictional  Electricity — I.  ELECTRICAL  PHENOMENA — 
Definitions,  531 — The  chief  sources  of  electrical  excitement — Electrical  effects 
— Attraction  and  repulsion,  532 — Vitreous  and  resinous,  or  positive  and  nega- 
tive electricities — Electroscopes,  533 — Conductors  of  electricity — Good  con- 
ductors— Bad  conductors — Insulation,  534 — The  earth  is  the  great  common 
reservoir — Theories  of  electricity,  or  electrical  hypothesis — Franklin's  single- 
fluid  hypothesis,  535 — The  hypothesis  of  Symmer,  or  Du  Fay,  536 — Electrical 
tension — Electrical  currents  are  either  momentary  or  permanent — Path  and 
velocity  of  electric  currents,  537 — II.  LAWS  OF  ELECTRICAL  FORCES  AND  DIS- 
TRIBUTION OF  ELECTRICITY  UPON  THE  SURFACE  OF  BODIES — Coulomb's  laWS — 

Torsion  electrometer,  538 — Demonstration  of  the  first  law — Demonstration  of 
the  second  law — Sir  Wm.   S.   Harris — Proof-plane,  539 — Electricity  resides 


CONTENTS. 

only  on  the  outer  surfaces  of  excited  bodies,  540 — Distribution  of  electricity-— 
The  power  of  points  541 — The  loss  of  electricity  in  excited  bodies — III.  IN- 
DUCTION OF  ELECTRICITY — Electrical  influence  or  induction,  542 — The  laws  of 
induction — Induction  is  an  act  of  contiguous  particles,  543 — The  attractions 
and  repulsions  of  light  bodies,  544 — Electrometers — Cavallo's,  Volte's,  and 
Bennett's — IV.  ELECTRICAL  MACHINES — The  electrophorus,  545 — The  cylinder 
electrical  machine,  546 — Amalgam — Ramsden's  plate  machine,  547 — The  Ame- 
rican plate  electrical  machine — Large  electrical  machine — Ritchie's  double 
plate  machine,  548 — The  Tylerian  machine,  549 — Care  and  management  of 
electrical  machines — Electricity  from  steam,  550 — Other  sources  of  electrical 
excitement,  551 — Theory  of  the  electrical  machine — Experimental  illustrations 
of  electrical  attractions  and  repulsions — The  insulating  stool,  552 — Henly's 
electroscope—Electrical  bells — Volta's  hail-storm — The  electrical  wheel — By 
a  candle  flame,  553 — V.  ACCUMULATED  ELECTRICITY  AND  ITS  EFFECTS — Dis- 
guised or  latent  electricity — The  condenser  of  JEpinus,  554 — The  discharge  of 
the  condenser — Volta's  condensing  electroscope,  556 — Dr.  Hare's  single  gold- 
leaf  electrometer — The  Leyden  jar,  557 — Electricity  in  the  Lcyden  jar  resides 
on  the  glass,  558 — The  electric  Battery — Discharge  in  cascade,  559 — The  uni- 
versal discharger — The  electric  spark,  560 — Kinnersley's  thermometer — The 
color  of  the  electrical  spark — The  electrical  discharge  in  a  vacuum,  561 — Dif- 
ference between  the  positive  and  negative  spark — The  diamond  jar — Scintil- 
lating tube  and  magic  squares,  562 — Effects  of  the  electric  discharge — Physio- 
logical effects,  563 — Inflammation  of  combustibles — Chemical  union  effected 
by  electricity,  564 — Volta's  electrical  lamp — The  mechanical  effects  of  the 
electrical  discharge,  565 — The  chemical  effects — Ozone — VI.  ATMOSPHERIC 
ELECTRICITY — Franklin's  kite,  566 — Free  electricity  in  the  atmosphere,  567. 
3.  Dynamical  Electricity — I.  GALVANISM  AND  VOLTAISM — Discovery 
of  galvanism,  568 — The  galvanic  fluid — Origin  of  Volta's  discovery — Contact 
theory,  569— Volta's  pile,  or  the  Voltaic  battery,  570— Distinction  between 
voltaism  and  galvanism,  571 — Quantity  and  intensity — Simple  voltaic  couple, 
572 — Electro-positive  and  electro-negative — Amalgamation,  573 — II.  BAT- 
T*ERIES  WITH  ONE  FLUID — Voltaic  batteries — Trough  batteries — Hare's  calori- 
motor,  574 — The  deflagrators  of  Dr.  Hare — Smee's  battery,  575 — The  sulphate  of 
copper  battery — III.  DRY  PILES — Dry  piles  of  Zamboni  and  De  Luc,  576 — Boh- 
nenberger's  electroscope — IV.  BATTERIES  WITH  TWO  FLUIDS — Daniell's  con- 
stantbattery,  577 — Grove's  nitric  acid  battery,  578 — Carbon  battery,  579 — Other 
forms  of  voltaic  battery — V.  POLARITY,  RETARDING  POWER,  AND  NOMENCLA- 
TURE OF  THE  VOLTAIC  PILE — Polarity  of  the  compound  circuit,  580 — Grouping 
the  elements  of  a  pile — Electrical  retarding  power  of  the  battery — Ohm's  law, 
581 — Formulae  of  electric  piles,  582 — Intensity  given  by  many  couples,  583 — 
Effect  of  increasing  the  number  of  couples  in  a  battery — Effect  of  enlarging 
the  plates  of  a  battery,  584 — Effect  of  enlarging  the  couples  and  increasing 
their  number — Faraday's  nomenclature,  585 — VI.  THE  EFFECTS  OF  THE  VOL- 
TAIC PILE — 1.  Physical  effects — The  voltaic  spark  and  arch,  586 — Regulators 
of  the  electric  light,  587 — Dubosq's  photo-electric  lantern — Properties  of  the 
electric  light,  588 — Heat  of  the  voltaic  arch — Deflagration,  589 — Measurement 
of  the  heat  of  the  voltaic  current — 2.  Chemical  effects  of  the  pile — Historical, 
590— Electrolysis  of  water— Voltameter,  591— Laws  of  electrolysis— Electro- 
lysis of  salts,  592— Electro-metallurgy — The  electrotype,  593 — Crystallization 
from  the  action  of  feeble  currents,  594 — Examples — Deposit  of  metallic  oxyds 
and  Nobili's  rings,  595 — 3.  Physiological  effects  of  the  pile — The  physiological 


CONTENTS.  XXV 

effects  of  the  voltaic  pile — The  magnetic  effects  of  the  pile — VII.  THEORY  oi 
THE  PILE — Three  views,  596 — Volta's  contact  theory,  697 — The  chemical 
theory — Laws  of  the  disengagement  of  electricity  by  chemical  action — The 
quantity  of  electricity  required  to  produce  chemical  action,  598 — Polarization 
and  transfer  of  the  elements  of  a  liquid — Chemical  affinity  and  molecular 
attraction  distinguished — Peschel's  molecular  theory  of  the  pile,  599. 

g  4.  Electro-Dynamics— I.  ELECTRO-MAGNETISM— General  laws,  600— 
(Ersted's  discovery,  601 — The  electric  magnetic  current  moves  at  right  angles 
to  the  course  of  the  conjunctive  wire — Galvanometers  or  multipliers,  602 — 
The  tangents  or  sine  compass  galvanometer — Rheostat,  604 — Ampere's  electro- 
magnetic discoveries  and  theory — Mutual  action  of  electric  currents,  605 — 
De  La  Rive's  floating  current — Roget's  oscillating  spiral — Helix,  solenoid,  or 
electro-dynamic  spiral,  606 — Directive  action  of  the  earth — Magnetizing  by 
the  helix,  608 — Arago's  original  experiment — Electro-magnets,  609 — Page's 
revolving  electro-magnet,  610 — Power  of  electro-magnets,  611 — Vibrations  and 
musical  tones  from  induced  magnetism — Electro-magnetic  motions  and  me- 
chanical power,  612 — Conversion  of  magnetism  into  heat — II.  DIAMAGNETISM 
— Action  of  magnetism  on  light,  614 — Diamagnetism,  615 — III.  ELECTRIC 
TELEGRAPH — Historical,  616 — The  earth  circuit,  618 — Varieties  of  electro-tele- 
graphic communication — The  electro-mechanical  form — The  electro-chemical 
telegraphs — Morse's  recording  telegraph,  619 — House's  electro-printing  tele- 
graph, 620 — The  electro-chemical  telegraph,  621 — Autograph  telegraphic  mes- 
sages— Submarine  telegraphs — The  Atlantic  cable,  622 — Electrical  clocks  and 
astronomical  records — Fire-alarm,  623. 

\  5.  Electro- dynamic  Induction — I.  INDUCED  CURRENTS — Currents  in- 
duced from  other  currents — Volta-electric  induction,  623 — Induced  currents 
of  different  orders,  625 — Extra-current,  or  the  induction  of  a  current  on  itself 
— Page's  vibrating  armature  and  electrotome,  626 — Induced  currents  from  the 
earth's  magnetism — Conversion  of  dynamic  into  static  electricity — The  induc- 
tion coil,  627 — Effects  of  the  induction  coil — The  luminous  effects,  629 — The 
chemical  effects — Light  of  these  currents  in  a  vacuum — Gassiot's  cascade  in 
vacuo,  630 — Rotation  of  the  electric  light  about  a  magnet — Applications,  631 
— II.  MAGNETO-ELECTRICITY — Currents  induced  by  magnets,  632 — Clark's 
magneto-electric  apparatus,  633 — Identity  of  electricity  from  whatever  source, 
634. 

§6.  Other  Sources  of  Electrical  Excitement — Universality  of  elec- 
trical excitement,  634 — I.  THERMO-ELECTRICITY — Thermo-electricity,  635 — 
Thermo-electric  motions — Cold  produced  by  electrical  currents — Melloni's 
thermo-multiplier — II.  ANIMAL  ELECTRICITY — The  galvanic  current,  636 — 
Ele-itrioal  animals — Electricity  of  plants,  638. 
3 


XXVI  CONTENTS. 


APPENDIX. 


CHAPTER  I. 

METEOROLOGY. 

§  1.  Climatology — Climates,  seasons — Influence  of  the  sun,  639 — Meteoro- 
logical observations — Mean  temperature,  640 — Variations  of  temperature  in 
latitude — Variations  of  temperature  in  altitude,  641 — Limit  of  perpetual  snow 
— Isothermal  lines,  642. 

g  2.  Aerial  Phenomena — General  consideration  of  winds — Propagation  of 
winds — Anemoscopes,  643 — Anemometers — The  velocity  of  winds — Formulae, 
644 — Regular  winds — Periodical  winds,  545 — Variable  winds — General  di- 
rection of  winds  in  the  higher  latitudes,  646 — Physical  properties  of  winds 
— Hot  winds — Hurricanes,  or  cyclones,  647 — Tornadoes  or  whirlwinds — 
Water-spouts,  649 — General  laws  of  storms,  650. 

g  3.  Aqueous  Phenomena— Humidity  of  the  air— Absolute  humidity- 
Relative  humidity,  651 — Hygrometers — Saussure's  hygrometer — Daniell's  hy- 
grometer— August's  psychrometer  or  hygrometer  of  evaporation,  652 — Fogs 
or  mists — Dew — Cause  of  dew — Circumstances  influencing  the  production  of 
dew,  653 — Substances  upon  which  dew  falls — Frost,  654 — Clouds — Classifica- 
tion of  clouds,  655 — Rain,  656 — Distribution  of  rain — Days  of  rain,  657 — 
Annual  depth  of  rain — Snow — Colored  snow,  658 — Hail,  659. 

\  4.  Electrical  Phenomena — Free  electricity  of  air — Thunder-storms,  659 
— The  geographical  distribution  of  thunder-storms — The  origin  of  thunder- 
clouds— Thunder,  660 — Lightning — Classes  of  lightning — Zigzag  or  chain 
lightning — Sheet  lightning — Heat  lightning — Ball  lightning,  661 — Volcanic 
Jghtning— Return  stroke— Lightning-rods,  662— Protective  power— Aurora 
borealis — Appearance  of  auroras — Remarkable  auroras,  663 — Height  of  au- 
roras, 664 — Frequency  of  auroras — Geographical  distribution  of  auroras,  665 
— Magnetic  disturbances  during  auroral  displays — Effect  of  the  aurora  on 
telegraphic  wires,  666 — Reversal  of  polarity  in  the  auroral  current — PROBLEMS 

ON  ELECTRICITY,  667. 

Addenda— Note  to  g  369  :  Uniform  musical  pitch— Note  to  §  343  :  The  velo- 
city of  all  sounds  not  the  same — Note  to  §  392 :  Sounds  produced  by  insects, 
668. 

CHAPTER  II. 

PHYSICAL    TABLES. 

TABLE  L— Measures  and  weights  (Cooke)     .         .         .     .'.  V    ;>    PAGE  669 

II. — For  converting  French   decimal   measures  and  weights   into 

English  measures  and  weights  (Gmelin)    ....     672 

III. — Expansion  of  solids          .......          674 

IV. — Expansion  of  liquids  .          .          .          .'.'••        .     675 


CONTENTS.  XXV11 

TABLE  V. — Expansion  of  gases  (Regnault)        ....         PAGE  676 

VI. — Radiating  power  according  to  Provostaye,  Desains,  and  Melloni  676 

VII. — Conducting  power  of  metals  and  building  materials  .          .  677 

VIII. — Absorptive  power  of  different  bodies  (Provostaye  &  Desains)  678 

IX. — Absorptive  power  for  heat  from  different  sources  (Melloni)  678 

X. — Diathermancy  of  different  liquids  (Melloni)            .          .          .  679 

XI.— Specific  heat  (Regnault  and  others)          ....  679 

XIL— Freezing  mixtures 680 

XIII. — Diathermancy  of  different  solids  (Melloni)         .          .          .  681 
XIV. — Tension  of  vapors  at  equal  distances  above  and  below  the 

boiling  point  of  their  respective  liquids          .          .          .  681 

XV.— Melting  points  and  latent  heat  of  fusion  of  different  bodies     .  682 

XVI. — Boiling  point  of  water  under  different  pressures  (Regnault)  682 

XVII. — Boiling  points  of  liquids  (Kopp  &  Pierre)     ....  683 

XVIII. — Boiling  point  of  water  at  different  places  and  their  elevation 

above  the  sea         ........  683 

XIX. — Boiling  point  of  water  at  different  atmospheric  pressures  (Reg- 
nault)   684 

XX. — Liquefaction  and  solidification  of  gases  (Faraday)          .          .  684 
XXI. — Aqueous  vapor  in  a  cubic  foot  of  saturated  air  at  different 

temperatures  (Guyot,condensed)     .....  685 

XXII.— Latent  and  sensible  heat  of  steam  (Regnault)  ...  686 

XXIII. — Specific  gravity  of  solids  and  liquids  .....  686 

XXIV.— Volume  and  density  of  water  (Kopp)        ....  687 

XXV. — Comparison  of  the  degrees  of  Baume's  hydrometer,  with  the 

real  specific  gravity  .......  688 

XXVI. — Tension,  volume,  and  density  of  aqueous  vapor  (Regnault, 

Peclet)     .          . 689 

ANSWERS  TO  PROBLEMS .  691 

INDEX                                                                                     ...  698 


PART   FIRST. 

PHYSICS  OF  SOLIDS  AND  FLUIDS. 
CHAPTER  I. 

INTRODUCTION. 

1,  Matter. — Matter  is  that  which  occupies  space,  and  is  the  object 
of  sense.     Our  knowledge  of  the  material  world  is  founded  upon  expe- 
rience, or  the  evidence  of  our  senses ;  and  the  conviction  that  the  same 
causes  will  always  produce  the  same  effects. 

A  definite  and  limited  portion  of  matter,  whether  it  be  a  particle  of 
dust  or  a  planet,  is  called  a  body.  The  different  kinds  of  matter,  as 
water,  marble,  gold,  or  diamond,  are  called  substances.  Numberless  as 
are  the  various  substances  known  to  man,  they  are  all  composed  of 
a  limited  number  of  simple  bodies  called  elements. 

2.  Observation   and   experiment. — By   observation   we   become 
acquainted  with  those,  changes,  in  the  condition  and  relations  of  bodies, 
which  occur  spontaneously  in  the  ordinary  course  of  nature ;  but  the 
knowledge  thus  acquired  is  limited  when  compared  with  the  results 
of  experiment.     By  the  use  of  proper  apparatus  we  can  repeat  natural 
phenomena  under  varied  conditions ;   and,   among  all  the  attendant 
circumstances,  we  can  determine  what  are  accidental,  and  what  are 
essential  to  any  given  effect. 

Phenomena. — A  phenomenon,  in  the  sense  in  which  this  word  is 
used  in  science,  is  any  event  taking  place  in  the  ordinary  course  of 
nature.  Thus  the  changes  of  the  seasons,  the  fall  of  rain  or  dew,  the 
burning  of  a  fire,  and  the  death  of  an  animal,  are  more  truly  pheno- 
mena of  nature  than  those  more  rare  or  alarming  events  to  which  in  a 
vulgar  sense  this  word  is  usually  confined. 

8*  (1) 


2  PHYSICS    OP    SOLIDS    AND    FLUIDS. 

3.  Law,  Theory,  and  Hypothesis. — In  conducting  an  experiment, 
we  are  taught  to  trace  with  certainty  the  connection  between  different 
phenomena ;  to  classify  effects  of  the  same  kind  and  refer  them  to  their 
common  cause ;  in  fine,  to  deduce  from  many  experiments  the  govern- 
ing principle,  or  law  of  nature,  in  obedience  to  which  they  are  produced, 
and  to  unite  both  facts  and  principles  into  a  theory,  or  comprehensive 
view  of  the  whole  subject.     Such  theories  are  a  fruitful  source  of  new 
experiments  and  new  discoveries. 

The  terms  law,  theory,  and  hypothesis  are  often  used  interchangeably, 
and  are  all  designed  to  express  the  various  degrees  of  perfection  attained 
in  any  department  of  human  knowledge,  towards  the  understanding  of 
the  thoughts  of  God  as  expressed  in  the  phenomena  of  the  physical 
world.  An  hypothesis  is  a  guess  or  assumption,  designed  to  aid  further 
investigation,  and  bears  the  same  relation  to  a  theory  or  law  as  the 
scaffolding  bears  to  the  perfect  building.  A  theory  is  the  most  perfect 
expression  of  physical  truth,  and  is  deduced  from  both  laws  and  prin- 
ciples that  have  been  established  on  independent  testimony. 

That  a  theory  should  rise  to  the  highest  expression  of  the  laws  of 
nature,  it  must  account  not  only  for  all  known  phenomena  falling 
under  it,  but  for  all  possible  cases  with  their  irregularities  and  varia- 
tions. Thus  the  law  of  gravitation,  as  developed  by  Newton  from 
terrestrial  phenomena,  has  been  found  strictly  universal  in  its  applica- 
tion;  not  only  meeting  all  known  facts  in  celestial  mechanics,  but, 
outstripping  observation,  it  has  foretold  events  which  have  been  subse- 
quently confirmed,  or  which  it  still  requires  centuries  of  years  to 
verify. 

4.  Inductive    Philosophy. — When  individual   experience   is  en- 
larged by  the  experience  of  other  inquirers  and  other  times,  and  the 
combined  knowledge  of  many  is -so  arranged  as  to  be  comprehended  by 
one,  the  system  becomes  a  science  or  philosophy  of  nature.     Because 
its  principles  are  founded  upon  a  comparison  and  analysis  of  facts,  a 
system  of  this  kind  is  also  called  Inductive  Philosophy. 

Inductive  philosophy  is  of  modern  origin.  Galileo  (born  in  1564)  was  the 
first  to  commence  a  course  of  experimental  researches ;  and  Bacon  (born  in 
1561),  in  his  immortal  work,  Novum  Organum,  showed  that  this  was  the  only 
road  to  an  accurate  knowledge  of  nature.  The  ancients  were  ignorant  of  the 
principles  and  methods  of  inductive  science.  Their  explanations  of  natural 
phenomena  were  based  on  assumed  causes ;  they  are  therefore  confused  and 
contradictory,  and  often  in  direct  opposition  to  experience. 

5.  Force. — From  the  axiom  that  every  event  must  have  a  cause, 
the  mind  naturally  passes  to  the  recognition  of  certain  powers  or  forces 
in  nature  adequate  to  account  for  the  observed  phenomena.     Thus  we 


INTRODUCTION.  3 

refer  the  fall  of  bodies  to  the  earth  to  the  force  of  gravitation — the 
strength  of  materials  to  the  force  of  cohesive  attraction — the  directive 
power  of  the  compass-needle  to  the  earth's  magnetism — the  evaporation 
of  water  to  the  action  of  heat — the  combustion  of  a  tire  to  the  action 
of  oxygen  on  the  elements  of  the  fuel,  or  to  the  force  of  chemical 
affinity. 

Man  exercising  his  volition  walks,  or  strikes  a  blow — examples  of  the 
mysterious  connection  between  spirit  and  matter,  of  the  conscious  exer- 
cise of  mechanical  force.  By  the  use  of  a  lever  or  screw  he  transmits 
or  multiplies  his  force  at  will — by  experiment  he  learns  that  he  can 
also,  by  suitable  appliances,  call  into  action,  where  he  pleases,  certain 
other  forces,  otherwise  dormant,  which  he  calls  chemical,  or  physical, 
according  as  they  do,  or  do  not,  involve  an  essential  change  in  the 
nature  of  the  materials  employed.  Both  his  consciousness  and  expe- 
rience inform  him  that  all  these  manifestations  of  force  result  from  the 
voluntary  but  mysterious  action  of  mind  upon  matter.  He  is  thus  led 
to  the  unavoidable  conclusion  that  those  great  phenomena  of  nature, 
ov,er  which  he  has  no  control,  must  have  their  origin  also  in  the  volitions 
of  a  SUPREME  RULER.  FORCE  and  WILL  thus  become  related  terms,  and 
we  are  compelled  to  regard  the  forces  of  nature,  as  they  are  usually 
styled,  as  only  the  outward  and  visible  manifestations  of  the  mind  of 
GOD. 

In  Physics  the  term  force  is  often  used  for  the  unknown  cause  of  a 
known  effect. 

6.  The  properties   of  matter  are  general,    or  specific. — The 
attentive  consideration   of  any  sort  of  matter  will  show  us   the   ex- 
istence of  two  sorts   of  properties  in  it — namely,  general  properties 
and  specific  properties.     Gold,  for  example,  occupies  space  and  pos- 
sesses weight,  but  so  also  does  all  matter,  whether  solid,  liquid,  or 
gaseous  ;  these  properties  are  general.     But  gold  has  a  peculiar  color 
and  lustre,  is  unchangeable  by  the  action  of  causes  which  destroy  the 
identity  of  nearly  all  other  sorts  of  matter,  has  a  definite  and  peculiar 
crystalline  form,  and  weighs    about  nineteen  times  as  much  as  a  like 
bulk  of  water.     These  are  qualities  peculiar  to  gold,  and  by  which  we 
always  recognize  it.     They  are  its  specific  properties. 

7.  The  changes  in  matter  are  physical,  or  chemical. — Water 
is  changed  by  heat  to  steam  or  vapor,  by  loss  of  heat  (cold)  it  is 
reduced  to  a  solid.     By  the  ceaseless  action  of  these  natural  causes,  it 
perpetually  changes  its  place  and  condition.     It  returns  to  the  earth, 
from  its  distillation  in  the  great  alembic  of  the  atmosphere,  as  dew, 
mist,  rain,  hail,  or  snow,  and  by  gravity  seeks  to  gain  a  place  of  rest 
in  tho  great  ocean.     But  in  all  its  changes  of  state  and  position  it  is 


i  PHYSICS    OP    SOLIDS    AND    FLUIDS. 

still  the  same  substance.  A  bar  of  iron,  by  contact  with  a  lodestone, 
acquires  new  properties,  which  we  call  magnetic,  but  its  color,  form, 
and  weight  remain  unchanged.  A  glass  tube  or  plate  of  resin  rubbed 
by  dry  silk  or  fur  becomes  electrical,  in  virtue  of  which  property  it 
will  attract  or  repel  light  bodies.  These  changes,  which  do  no4*  destroy 
the  specific  identity  of  the  substance,  are  termed  physical  changes. 

But  in  a  damp  atmosphere  the  iron  bar  is  soon  covered  with  rust, 
from  the  action  of  oxygen  (one  of  the  gases  of  the  air)  upon  the  iron. 
The  same  change  follows  the  action  of  water  alone.  In  this  latter  case 
the  water  is  decomposed,  and  with  great  activity  if  a  dilute  acid  is 
present.  The  oxygen  of  the  water  combines  with  the  iron,  while  the 
hydrogen  escapes  as  a  gas,  and  thus  the  specific  identity  of  both  sub- 
stances is  destroyed.  Such  changes,  destructive  of  specific  identity,  are 
called  chemical  changes. 

8.  Physical  and  chemical  properties  of  matter. — The  changes 
of  matter  just  noticed  correspond  to  its  physical  and  chemical  proper- 
ties.    Gold  possesses  certain  specific  properties,  depending  solely  on  its 
physical  qualities ;  its  density,  lustre,  color,  form,  malleability,  and  its 
high  point  of  fusion,  are  all  qualities  of  gold  which  can  never  be  lost 
without  an  essential  change  of  its  nature,  and  are  therefore  termed 
physical  properties.     Exposed  however  to  the  action  of  chlorine  and 
certain  other  agents,  gold  loses  its  specific  "identity,  and  becomes,  as  it 
were,  a  new  substance,  while  the  same  change  passes  equally  upon  the 
agent  by  whose  efficiency  the  transmutation  is  effected.     Such  changes 
of  matter,  involving  an  essential  loss  of  specific  identity,  depend  on  the 
chemical  properties  of  matter. 

9.  Physics   and   Chemistry. — It  is   plain   that  the   distinctions 
just  pointed  out  are  fundamental,  in  the  nature  of  things,  and  that  out 
of  them  spring  two  entirely  distinct,  although  nearly  related,  branches 
of  human  knowledge,  namely,  PHYSICS  and  CHEMISTRY;  the  former  is 
more  frequently  called,  in  this  country,  Natural  Philosophy ;  a  term 
too  comprehensive  in  its  general  significance  for  an  exact  definition. 
Now  as  all  substances  possess  both  physical  and  chemical  properties, 
it  is  plain  that  a  thorough  knowledge  of  either  branch  involves  some 
familiarity  with  the  other.     But  the  natural  order  of  knowledge  con- 
sists in  obtaining  first  a  familiarity  with  the  general  properties  and 
laws  of  matter,  and  subsequently  the  specific  properties.     Physical 
knowledge  therefore  naturally  precedes  chemical. 

10.  Vitality,   or  the  principle  of  life,  is  recognized  as  a  distinct 
force  in  nature,  controlling  both  physical  and  chemical  forces ;  by  its 
action  inanimate  or  unorganized  matter  is  transformed  into  animate 
and  organized  existences.     Thus,  out  of  air,  water,  and  a  few  mineral 


GENERAL  PROPERTIES  OF  MATTER.  5 

substances,  all  living  forms,  both  animal  and  vegetable,  are  built  up 
by  the  chemistry  of  life.  After  a  life  of  definite  duration,  they  die, 
and  their  structures  dissolve  again  into  the  inanimate  bodies  out  of 
which  they  grew.  They  are  subject  to  the  general  laws  of  matter,  but 
these  laws  are  often  modified,  and  sometimes  directly  opposed  by  the 
action  of  that  unknown  power  which  we  call  the  principle  of  life.  The 
description  of  organized  bodies  constitutes  the  science  of  Natural 
History. 

11.  Light,  Heat,  and  Electricity  are  terms  employed  to  dis- 
tinguish certain  phenomena,  or  forces  in  nature,  connected  with,  or 
growing  out  of  the  changes  of  matter,  physical  or  chemical,  or  both. 
They  are  supposed  by  most  physicists  to  be  dependent  on  the  existence 
of  certain  hypothetical  fluids,  or  on  the  vibrations  of  an  assumed 
ethereal  medium.  As  these  fluids,  or  forces,  are  without  weight  or 
other  sensible  properties  of  ordinary  matter,  they  are  termed,  by  many 
writers,  the  imponderable  agents,  or  simply  imponderables.  What 
the  spirit  is  to  the  animal  body  these  mysterious  agents  are  to  lifeless 
matter. 


CHAPTER  II. 

GENERAL    PRINCIPLES. 
§  1.  Definitions  and  General  Properties  of  Matter. 

I.    ESSENTIAL    PROPERTIES. 

12.  The  essential  properties  of  matter  are  (1)  magnitude,  or 
extension,  (2)  impenetrability.     We  cannot  conceive  of  matter  with- 
out magnitude,  and  it  is  equally  clear  that  the  space  occupied  by  any 
given  particle  of  matter  cannot,  at  the  same  time,  be  occupied  by  any 
other  particle. 

All  the  other  general  properties  of  matter,  however  universal  they 
may  be,  have  been  made  known  to  us  by  observation  and  experiment, 
and  are  not  essential  to  the  fundamental  notion  of  the  existence  of 
matter.  The  accessory  or  non-essential  properties  of  matter  are,  1, 
Divisibility,  2,  Compressibility,  3,  Expansibility,  4,  Porosity,  5,  Mo- 
bility, and,  6,  Inertia.  • 

13.  Magnitude  or  extension. — Extension  is  the  property  which 


6  PHYSICS    OF    SOLIDS    AND   FLUIDS. 

every  body  possesses  of  occupying  a  portion  of  space.  The  amount  of 
space  so  occupied  by  a  body  is  called  its  volume. 

Every  body  has  three  dimensions,  length,  breadth,  and  thickness, 
the  external  boundaries  of  which  are  surfaces  and  lines.  The  exact 
measurement  of  these  three  dimensions  is  the  foundation  of  all  exact 
knowledge  in  experimental  science,  and  demands  the  adoption  of  cer- 
tain arbitrary  units  of  comparison. 

14.  Impenetrability. — The  power  of  a  body  to  exclude  all  other 
bodies  from  the  space  occupied  by  itself  is  called  impenetrability.  This 
property  is  possessed  by  all  forms  of  matter.  Air  may  be  compressed 
indefinitely,  perhaps,  but  the  mechanical  force  required  for  its  com- 
pression is  at  once  the  evidence  and  the  measure  of  its  impenetrability. 

A  stone  dropped  into  the  water  displaces  its  own  bulk  of  the  fluid, 
but  does  not  penetrate  its  particles.  A  nail  driven  into  a  board  only 
displaces  certain  particles  of  the  wood,  whose  resistance  or  elasticity 
imparts  to  the  nail  its  power  of  adhesion. 

The  union  of  these  two  properties,  extension  and  impenetrability 
gives  exactness  to  our  fundamental  notion  of  matter.  Neither  alone 
will  suffice  to  produce  a  body.  The  image  in  a  mirror  is  not  a  body, 
for  behind  the  mirror,  where  the  image  appears,  is  the  wall,  or  perhaps 
another  body.  The  shadow  of  any  object  in  the  sunlight  has  exten- 
sion, but,  as  it  is  not  impenetrable,  it  is  not  a  body. 

15.  The   three  states   of  matter. — Matter  is  presented   to  our 
senses  in  three  unlike  physical  states,  viz.,  solid,  liquid,  and  gaseous. 
The  last  two  states  are  more  comprehensively  called  fluids.     These 
three  physical  conditions  of  matter  represent  the  opposite  action  of  the 
forces  of  attraction  and  repulsion.     But  as  these  interesting  relations, 
and  the  physical  laws  governing  them,  are  fully  discussed  under  their 
appropriate  heads,  it  is  needless  to  do  more  than  refer  to  them  here. 
(146.) 

11.    ENGLISH    AND    FRENCH    SYSTEMS  OF   MEASURES. 

16.  Units   of    measure. — In  order   to   determine   with   accuracy 
the  volume  of  solids  and  the  area  of  surfaces  or  the  length  of  lines, 
some   arbitrary   unit  of  extension  must    be   adopted.    Of  the   three 
geometric  degrees  of  extension  the  unit  of  length  is  the  only  one  which 
need  be  arbitrary,  since  by  squaring  it  we  may  measure  surfaces,  and 
by  cubing  it  we  can  measure  solids.     In  early  times  the  weight  of 
grains  of  wheat,  ("thirty-two  of  which,  from  the  midst  of  the  ear, 
were,  A.  D.  1266,  declared  to  be  equal  to  an  English  penny,  called  a 
sterling,")  or  the  length  of  "  barley  corns"  (three  to  an  inch)  gave  the 
rude  basis  of  legal  units  of  weight  and  measure  in  England,  and,  long 
after,  by  adoption  in  the  United  States.  * 


GENERAL  PROPERTIES  OP  MATTER.  7 

17.  English  units  of  length. — The  yard  is  the  English  unit  of 
length,  adopted  both  in  Great  Britain  and  America.     It  appears  to 
have  had  its  origin  about  A.  D.  1120,  in  the  reign  of  Henry  the  First, 
"  who  ordered  that  the  ulna,  or  ancient  ell  (which  corresponds  to  the 
modern  yard)  should  be  made  of  the  exact  length  of  his  own  arm,  and 
that  the  other  measures  of  length  should  be  based  upon  it."     The  yard 
is  divided  into  thirty-six  inches. 

In  1824  it  was  enacted  by  the  English  Parliament,  that  if  at  any 
time  the  standard  yard  should  be  lost,  defaced,  or  otherwise  injured,  it 
should  be  restored  by  making  a  new  standard  yard,  bearing  the  same 
proportion  to  a  pendulum  vibrating  seconds  of  mean  time  in  the  lati- 
tude of  London,  in  a  vacuum  and  at  the  level  of  the  sea,  as  36  inches 
bears  to  39.1393  inches,  the  latter  being  the  length  of  the  pendulum 
vibrating  seconds  at  London. 

In  1834  the  Parliament  House  was  destroyed  by  fire,  and  with  it  the 
standard  yard.  The  measurement  of  the  seconds'  pendulum,  as  given 
above,  was  subsequently  found  to  be  incorrect,  and  the  commissioners 
appointed  to  consider  the  steps  to  be  taken  to  restore  the  lost  standard, 
recommended  the  construction  of  four  standard  yards  from  the  best 
authenticated  copies  of  the  old  standard.  These  duplicates  (a  copy  of 
which  exists  in  the  U.  S.  Mint)  are  the  basis  of  English  and  American 
standards  of  length. 

The  subdivisions  and  multiples  of  the  yard  are  given  in  Table  I.,  at 
the  end  of  this  volume. 

Nearly  all  the  English  units  of  surface  are  squares  whose  sides  are 
equal  to  the  units  of  length.  The  square  and  cubic  inch  are  the  units 
most  frequently  employed  for  scientific  purposes. 

The  measures  of  capacity  are  related  to  those  of  length,  by  the  deter- 
mination that  a  gallon  contains  277.274  cubic  inches.  ($  101.) 

Where  volume  can  be  calculated  from  linear  measurements,  it  is 
usual  to  estimate  it  in  cubic  yards,  cubic  feet,  or  cubic  inches.  In  this 
way  earth-work  and  masonry  are  measured. 

18.  The  French  system  of  measures  originated  with  the  great 
revolution  in  France,  when  all   regard  for  ancient   institutions  was 
repudiated.    A  commission  of  the  members  of  the  Academy  of  Sciences 
was  appointed,  who  developed  a  decimal  system,  which  was  at  once 
adopted.     They  proposed  that  the  ten-millionth  part  of  the  quadrant 
^f  a  meridian  of  the  globe  should  be  assumed  as  the  basis  of  a  new 
metrical  system.     This  was  called  a  metre,  and  subdivisions  and  mul- 
tiples of  this  unit  were  made  on  the  decimal  system.     The  metre  is 
equivalent    to    39.37079   English   inches,    or    39.36850535    American 
inches.     Later   determinations   have    shown    that   the    length   of    the 


8  PHYSICS   OP   SOLIDS   AND   FLUIDS, 

standard  metre  is  not  precisely  the  one  ten-millionth  part  of  a  quad- 
rant. Thus  it  appears  that  the  metre  of  France  is  a  standard  of 
measure  not  less  arbitrary  than  the  English  yard. 

The  French  metre  is  subdivided  into  tenths,  called  decimetres ;  hun- 
dredths,  or  centimetres;  and  thousandths,  or  millimetres.*  The  names 
of  the  multiples  are  as  follows :  the  decametre,  ten  metres  ;  the  hecto- 
metre, one  hundred  metres ;  and  the  kilometre,  one  thousand  metres. 
This  last  length  is  equal  to  about  two-thirds  of  an  English  mile,  and 
it  is  the  ordinary  road-measure  in  France. 

The  French  units  of  surface  are  squares,  whose  sides  are  equal  to 
the  units  of  length.  The  common  French  measure  of  land  is  the 
square  decimetre,  which  is  called  an  are. 

The  measures  of  capacity  are  connected  with  those  of  length  by 
means  of  the  litre,  which  is  a  cubic  decimetre,  (or  a  cube  measuring 
3.937  English  inches  on  the  side).  It  is  equal  to  1.765  Imperial  pints, 
or  somewhat  more  than  If  English  pints.  (See  Table  I.) 

The  cubic  metre  is  the  measure  of  bulky  articles,  and  has  received 
the  name  of  stere.  The  stere,  as  well  as  the  litre,  and  the  are,  have 
decimal  multiples  and  subdivisions,  named  like  those  of  the  metre. 

The  connection  of  the  system  of  weights  with  those  of  capacity  and  length  ia 
explained  in  §  100. 

III.     ACCESSORY  PROPERTIES  OF  MATTER. 

19.  Divisibility. — By  mechanical  means  matter  may  be  reduced  to 
an  extreme  degree  of  comminution.  By  chemical  means,  and  the  pro- 
cesses of  life,  this  subdivision  is  carried  very  much  farther.  A  few 
illustrations  of  each  of  these  kinds  of  divisibility  will  suffice. 

Gold  is  beaten  into  leaves  so  thin  that  one  million  of  leaves  measure 
less  than  an  inch  in  thickness.  A  bar  of  silver  may  be  gilded,  and 
then  drawn  into  wire  so  fine  that  the  gold,  covering  a  foot  of  such 
thread,  weighs  less  than  Q^Q  of  a  grain.  An  inch  of  this  wire,  con- 
taining TJ^^-Q  of  a  grain,  may  be  divided  into  100  equal  parts  dis- 
tinctly visible,  and  each  containing  TJ^Q^-Q-QQ  °f  a  grain  of  gold. 
Under  a  microscope  magnifying  500  times,  each  of  these  minute  pieces 
may  be  again  subdivided  500  times,  each  subdivision  having  to  the  eye 
the  same  apparent  magnitude  as  before,  and  the  gold  on  each,  with 
its  original  lustre,  color,  and  chemical  properties  unchanged,  repre- 
8ents  3,eff<J,W<J,o-<T<>  Part  of  the  original  quantity.  • 

Dr.  Wollaston,  by  a  very  ingenious  device,  obtained  platinum  wire 
for  the  micrometers  of  telescopes,  measuring  only  ^  }^  of  an  inch  in 
diameter.  Though  platinufh  is  nearly  the  heaviest  of  known  bodies,  a 

*  The  smaller  measures  are  named  by  Latin,  the  larger  by  Greek  numbers. 


GENERAL  PROPERTIES  OF  MATTER.  9 

mile  of  such  wire  would  weigh  only  a  grain,  and  150  strands  of  it 
would  together  form  a  thread  only  as  thick  as  a  filament  of  raw  silk. 

A  grain  of  copper  dissolved  in  nitric  acid,  to  which  is  afterwards 
added  water  of  ammonia,  will  give  a  decided  blue  color  to  392  cubic 
inches  of  water.  Now  each  cubic  inch  of  the  water  may  be  divided 
into  a  million  particles,  each  distinctly  visible  under  the  microscope, 
and  therefore  the  grain  of  copper  must  have  been  divided  into  392 
million  parts. 

One  hundred  cubic  inches  of  a  solution  of  common  salt  will  be  ren- 
dered milky  by  a  cube  of  silver,  O001  of  an  inch  on  each  side,  dissolved 
in  nitric  acid,  and  the  magnitude  of  each  particle  of  silver  thus  repre- 
sents the  one-hundred  billionth  part  of  an  inch  in  size.  To  aid  the 
student  in  forming  an  adequate  conception  of  so  vast  a  number  as  a 
billion,  it  may  be  added  that  to  count  a  billion  from  a  clock  beating 
seconds,  would  require  31,688  years  continuous  counting,  day  and 
night. 

Minute  division  in  the  animal  and  vegetable  kingdoms. — The 
blood  of  animals  is  not  a  uniform  red  liquid,  as  it  appears  to  the  naked 
eye,  but  consists  of  a  transparent  colorless  fluid,  in  which  float  an  innu- 
merable multitude  of  red  corpuscles,  which,  in  animals  that  suckle  their 
young,  are  flat  circular  discs,  doubly  concave,  like  the  spectacle  glasses 
of  near-sighted  persons.  In  man,  the  diameter  of  these  corpuscles  is 
the  3500th  of  an  inch,  and  in  the  musk-deer,  only  the  12,000th  of  an 
inch,  and  therefore  a  drop  of  human  blood,  such  as  would  remain  sus- 
pended from  the  point  of  a  cambric  needle,  will  contain  about  3,000,000 
of  corpuscles,  and  about  120,000,000  might  float  in  a  similar  drop  drawn 
from  the  musk-deer. 

But  these  instances  of  the  divisibility  of  matter  are  far  surpassed 
by  the  minuteness  of  animalcules,  for  whose  natural  history  we  are 
indebted  chiefly  to  the  researches  of  the  renowned  Prussian  naturalist, 
Ehrenberg.  He  has  shown  that  there  are  many  species  of  these  crea- 
tures, so  small  that  millions  together  would  not  equal  the  bulk  of  a 
grain  of  sand,  and  thousands  might  swim  at  once  through  the  eye  of  a 
needle.  These  infinitesimal  animals  are  as  well  adapted  to  life  as  the 
largest  beasts,  and  their  motions  display  all  the  phenomena  of  life, 
sense,  and  instinct.  Their  actions  are  not  fortuitous,  but  are  evidently 
governed  by  choice,  and  directed  to  gratify  their  appetites  and  avoid 
the  dangers  of  their  miniature  world.  The  stagnant  waters  of  the 
earth  (and  sometimes  the  atmosphere)  everywhere  are  populous  with 
them,  to  an  extent  beyond  the  power  of  the  imagination  to  conceive 
their  numbers.  Their  silicious  skeletons  are  found  in  a  fossil  state, 
forming  the  entire  mass  of  rocky  strata,  many  feet  in  thickness  and 
4 


10  PHYSICS   OF   SOLIDS   AND    FLUIDS. 

hundreds  of  square  miles  in  extent.  The  polishing-slate  near  Biliu, 
in  Bohemia,  contains  in  every  cubic  inch  about  41,000  millions  of  these 
animals.  Since  a  cubic  inch  of  this  slate  weighs  220  grains,  there  must 
be  in  a  single  grain  187  millions  of  skeletons,  and  one  of  them  would, 
therefore,  weigh  about  the  one  187-millionth  of  a  grain.  The  city  of 
Richmond,  Va.,  has  been  shown  by  Prof.  Bailey  to  rest  on  a  similar 
deposit  of  silicious  animalcules  of  exquisite  form.  It  is  impossible  to 
form  a  conception  of  the  minute  dimensions  of  these  organic  structures, 
and  yet  each  separate  organ  of  every  animalcule  is  a  compound  of 
several  organic  substances,  each  in  its  turn  comprising  numberless 
atoms  of  carbon,  oxygen,  and  hydrogen.  It  is  plain  from  these  exam- 
ples that  the  actual  magnitude  of  the  ultimate  molecules  of  any  body 
is  something  completely  beyond  the  reach  equally  of  our  senses  to  per- 
ceive, or  of  our  intellects  to  comprehend. 

20.  Atoms,  Molecules. — The  ultimate  constitution  of  matter  has 
divided  the  opinions  of  philosophers  from  the  earliest  period  of  science. 
Two  hypotheses  have  prevailed  ;  the  one,  that  matter  is  composed  of 
irregular  particles  without  fixed  size  or  weight,  and  divisible  without 
limit ;  the  other,  that  "  matter  is  formed  of  solid,  massy,  impenetrable, 
movable  particles,  so  hard  as  never  to  wear  or  break  in  pieces"  (New- 
ton), and  which,  being  wholly  indivisible,  have  a  certain  definite  size, 
figure,  and  weight,  which  they  retain  unchangeably  through  all  their 
various  combinations.     These  ultimate  and  unchangeable  particles  are 
called  atoms  (meaning  that  which  cannot  be  subdivided). 

While  there  is  no  mathematical  objection  to  the  assumption  that 
matter  is  infinitely  divisible  (since  no  mass  can  be  conceived  of,  so  small 
that  it  cannot  be  mentally  subdivided),  physics  and  more  particularly 
chemistry  have  shown,  from  the  mutual  relations  of  bodies,  that  their 
constituent  particles  possess  definite  and  limited  magnitudes. 

The  term  molecule  (a  little  mass)  is  more  commonly  applied  to  what, 
in  chemistry,  are  sometimes  called  divisible  atoms ;  i.  e.,  to  a  group  of 
two  or  more  atoms,  e.  g.,  the  molecule  of  water  is  composed  of  at  least 
two  atoms,  one  of  hydrogen  and  one  of  oxygen,  forming  together  a 
chemical  compound".  The  phenomena  of  crystallization  show  us  that 
molecules  possess  different  properties  at  different  points  of  their  sur- 
faces. While  their  form  is  unknown,  it  is  assumed  that  they  touch 
each  other  not  at  all,  or  only  at  a  few  points,  leaving  spaces  between 
them  which  bear  a  large  ratio  to  their  own  bulk.  From  this  fact  result 
the  two  general  properties  of  compressibility  and  expansibility,  which 
are  next  to  be  considered. 

21.  Compressibility. — Diminution  of  volume  in  solids,  by  mecha- 
nical means,  and  by  loss  of  heat,  is  a  fact  long  familiar  to  all  who  are 


GENERAL  PROPERTIES  OF  MATTER. 


11 


conversant  with  constructions.  Even  columns  of  stone,  and  arches,  sup- 
porting heavy  loads,  are  found  to  diminish  sensibly  from  their  original 
dimensions  by  pressure  alone.  Metals  are  compressed  by  coining.  In 
liquids  it  was  long  believed  there  was  no  compressibility,  but  in  reality 
liquids  possess  this  property  to  a  greater  extent  than  solids. 

1  Saxton's  modification  of  Perkins's  original  apparatus  serves  to 

demonstrate  the  compressibility  of  water.  A  strong  metallic  ves- 
sel, C,  fig.  1,  is  filled  with  water,  and  closed  by  a  close  fitting 
screw  plug,  B,  fig.  2;  and  a  perfectly  polished  cylindrical  piston  of 
steel,  A,  passes  water-tight  through  the  steel  collar,  P.  When  the 
vessel  is  thus  prepared,  it  is  placed  in  a  larger  vessel  capable  of 
enduring  great  pressure,  which  is  also  filled  with  water. 

Pressure  to  any  extent  desired  is  then  applied  by  means  2 
of  a  hydraulic  press.  It  is  evident  that  if  the  water 
undergoes  diminution  of  volume  when  subjected  to  pres- 
sure, the  piston  A  must  be  forced  into  the  cylinder  to  a 
corresponding  extent.  The  index  T  having  been  placed  at 
0  of  the  scale  S,  if  it  is  found,  after  the  experiment,  above 
that  point,  as  in  fig.  2,  it  is  evidence  of  a  corresponding 
descent  of  the  piston,  due  to  compression  of  the  water 
contained  in  the  cylinder  C.  On  removing  the  pressure  T| 
the  elasticity  of  the  water  restores  the  original  bulk. 
Water  is  found,  by  this  experiment,  to  yield  about  fifty 
millionths  of  its  volume  for  each  atmosphere  of  pressure, 
i.  e.,  for  a  pressure  of  fifteen  pounds  to  a  square  inch. 

In  air  and  all  gases  we  see  the  property  of  com- 
pressibility very  apparent.     The  air  syringe  is  an 
instrument  in  which  a  portion  of  air  is  compressed 
before  a  solid  piston,  with  the  evolution  of  so  much  heat  as  to  set  fire 
to  tinder. 

The  return  of  gases  and  liquids  to  their  original  bulk  on  removal  of 
the  condensing  force  is  due  to  a  property  termed  elasticity.  This 
quality  exists  in  many  solids,  if  not  in  all,  and  its  consideration  will 
be  resumed  hereafter. 

22.  Expansibility. — The  expansion  and  contraction  of  all  bodies 
by  heat  and  cold  is  a  fact  sufficiently  familiar.     Upon  it  is  based  the 
construction  of  all  instruments  for  reading  changes  of  temperature,  for 
a  description  of  which  the  reader  is  referred  to  the  chapter  on  heat. 

23.  Physical  pores. — The  facts  connected  with  the  compressibility 
of  matter,    and   its   change  of  form   by   heat,    indicate  clearly   that 
the  atoms  of  matter  (assumed  to  be  unchangeable)  are  not  in  contact. 
The  spaces  existing  between  them  are  called  physical  pores,  on  the 
existence  of  which  depends  the  property  of  porosity.     Many  chemical 
phenomena  illustrate  the  existence  of  this  property.    If  equal  measures 
of  alcohol  and  water,  or  of  water  and  sulphuric  acid  are  mixed,  the 


12  PHYSICS   OP    SOLIDS    AND   FLUIDS. 

bulk  of  the  resulting  liquid  is  sensibly  less  than  the  sum  of  the  two 
liquids  before  they  were  mingled.  This  shrinkage  can  result  only  from 
the  insinuation  of  the  particles  of  one  substance  among  the  pores  of 
the  other. 

The  great  amount  of  heat  developed,  during  these  experiments,  is  a 
significant  fact.  These  molecular  or  physical  pores  of  bodies  are  no 
more  sensible  to  our  organs  than  the  atoms  themselves,  and  are  per- 
meable only  to  light,  heat,  and  electricity. 

24.  Sensible  pores. — It  is  important  to  distinguish  the  molecular 
porosity  just  described  from  those  sensible  openings  which  give  to  cer- 
tain substances  the  property  generally  known  as  porosity.     The  pores 
of  organic  bodies,  as  of  wood,  skin,  and  tissues,  are  only  capillary 
openings,  or  canals,  for  the  passage  of  fluids.     Nearly  all  animal  and 
vegetable  substances  present  these  sensible  pores.     The  familiar  pneu- 
matic experiment — the  mercurial  rain — is  an  illustration  of  the  porosity 
of  wood.     Many  minerals  and  rocks  are  porous.     Common  chalk  and 
clay  are  familiar  examples.     Hydrophane  is  a  kind  of  agate,  opaque 
when  dry,  but  translucent  when  wet  from  absorption  of  water.     Even 
gold,  and  other  metals,  under  great  pressure,  as  in  the  experiments  of 
the  Florentine  academicians  in  1661,  are  found  to  exude  water. 

25.  Mobility. — We  constantly  see  bodies  changing  their  place  by 
motion,  while  others  remain  in  a  state  of  rest.    The  capacity  of  change 
of  place,  or  of  being  set  in  motion,  constitutes  what  is  called  mobility. 

"We  recognize  motion  only  by  comparing  the  body  moving  with  some 
other  body  at  rest.  If  that  rest  is  real  then  the  motion  is  absolute,  but  if 
it  is  only  apparent  then  the  motion  is  only  relative.  Thus,  on  board  ship, 
or  on  a  rail  car,  the  passenger  appears  to  change  his  place  in  reference 
to  objects  about  him.  But  all  these  objects  are  equally  in  motion  with 
himself. 

All  motion  on  the  earth's  surface  is  relative,  because  the  globe  itself 
is  impelled  by  a  double  movement — of  revolution  on  its  own  axis,  and 
of  translation  about  the  sun. 

Rest  is  also  absolute  or  relative.  Absolute  when  the  body  occupies 
really  the  same  point  in  space — relative  when  it  preserves  the  same 
apparent  distance  from  surrounding  objects  regarded  as  fixed,  but 
which  are  not  in  reality  so.  A  ship  sailing  six  miles  an  hour  against 
a  current  of  the  same  velocity  appears  to  persons  on  her  deck  to  be 
advancing  with  reference  to  the  surrounding  waves  ;  but,  viewed  from 
the  shore,  or  by  comparison  with  objects  on  shore,  she  appears  at  rest. 
Absolute  rest  is  of  course  unknown  on  the  earth,  since  every  terrestrial 
object  partakes  of  the  double  motion  already  noticed,  and  it  is  doubtful 
if  any  part  of  the  universe  is  in  absolute  rest,  seeing  that  the  smi 


MOTION    AND    FORCE.  13 

itself  with  the  whole  solar  system  is  carried  around  with  a  rapid  motion 
of  translation  in  space  about  a  central  sun. 

26.  Inertia. — No   particle   of   matter   possesses   within   itself   the 
power  of  changing  its  existing  state  of  motion  or  rest.     Matter  has  no 
spontaneous  power  either  of  rest  or  motion,  but  is  equally  susceptible 
to  each,  according  as  it  may  be  acted  on  by  an  external  cause.     If  a 
body  is  at  rest,  a  force  is  necessary  to  put  it  in  motion  ;  and  conversely, 
it  cannot  change  from  motion  to  rest  without  the  agency  of  some  force. 
A  body  once  put  in  motion  will  continue  that  motion  in  an  unchang- 
ing direction  with  unchanging  velocity  until  its  course  is  arrested  by 
external   causes.     This  passive  property  of  matter  is  called  inertia. 
Descartes  first  gave  definite  expression  to  this  law  in  his  "  Principles." 

When  we  are  told  that  a  body  at  rest  will  for  ever  remain  so,  unless  it  receives 
an  impulse  from  some  external  power,  the  mind  at  once  assents  to  a  statement 
which  embodies  the  results  of  our  constant  experience.  But  it  requires  some 
reflection  in  one  who  for  the  first  time  considers  the  subject,  to  admit  that 
bodies  in  motion  will  continue  to  move  for  ever,  unless  arrested  by  external 
forces.  Casual  observation  seems  to  contradict  the  assertion.  On  the  earth's 
surface  we  know  of  no  motion  which  does  not  require  force  to  maintain  as  well 
as  produce  it. 

We  may  observe,  however,  that  all  such  moving  bodies  meet  with  constant 
obstruction  from  friction,  and  the  resistance  of  the  air  j  and  that  as  one  or  both 
of  these  are  diminished,  the  motion  becomes  prolonged  and  continuous. 

The  familiar  apparatus  called  the  wind-mill  in  vacuo  is  a  good  illustration  of 
the  tendency  to  continued  motion  due  to  inertia — the  usual  causes  of  arrest  of 
motion  being  here  greatly  diminished. 

The  planets  furnish  the  only  example  of  constant  motion.  These  celestial 
bodies,  removed  from  all  the  casual  resistances  and  obstructions  which  disturb 
our  experiments  at  the  earth's  surface,  roll  on  in  their  appointed  orbits  with 
faultless  regularity,  and  preserve  unchanged  the  direction  and  velocity  of  the 
motion  which  they  received  at  their  creation. 

27.  Action  and  reaction. — It  follows  as  a  necessary  consequence 
of  the   inertia   of  matter,   that  when   a  body,  M,  in  motion  strikes 
another  body,  M',  at  rest,  the  action  of  M  in  imparting  motion  to 
W  is  exactly  equaled  by  the  power  of  M/  to  destroy  motion  in  M. 
Hence  the  law  that  action  and  reaction  are  always  equal  and  opposite. 
It  is  here  assumed  that  the  bodies  impinging  are  entirely  devoid  of 
elasticity,  and  so  related  that  after  collision  they  shall  move  on  as 
one  body.     It  is  also  true  for  elastic  bodies.     See  §  181. 

§  2.  Of  Motion  and  Force. 

I.     MOTION. 

28.  Varieties  of  motion. — We  distinguish  the  following  varieties 
in  the  motion  of  a  body. 

4* 


14  PHYSICS   OF    SOLIDS   AND   FLUIDS. 

a — A  motion  of  translation,  or  direct  motion,  in  which  all  the  points 
of  a  body  move  parallel  to  each  other. 

6 — A  motion  of  rotation,  as  of  a  wheel  on  an  axis,  where  the  dif- 
ferent parts  of  a  body  move  at  the  same  time  in  different  directions. 
Oscillation  or  vibration,  as  in  a  pendulum,  is  only  a  particular  case  of 
rotation. 

c — A  combination  of  translation  and  rotation,  as  in  the  motions  of 
the  earth. 

The  direction  of  motion  is  represented  by  a  straight  line  drawn  from 
the  point  where  motion  commences,  to  the  point  towards  which  the 
body  is  propelled.  The  direction  is  rectilinear,  when  it  is  constantly 
the  same,  and  curvilinear,  when  it  varies  every  moment. 

29.  Time  and  velocity. — As  all  the  phenomena  of  nature  may 
be  referred  to  motion,  so  the  succession  of  natural  phenomena  gives 
us  the  idea  of  duration,  or  time.     Day  and  night,  months,  and  the 
order  of  the  seasons,  are  nature's  units  of  time;  but  in  physics  the 
invariable  unit  of  time  is  the  duration  of  a  single  oscillation  of  a  pen- 
dulum, called  a  seconds'  pendulum,  the  time  of  oscillation  being  a 
second.     The   length  of  such  a  pendulum   at    London  is  39*14056 
English  inches.     The  distance  passed  over  by  a  moving  body,  in  a 
unit  of  time,  is  its  velocity,  represented  by  V  in  physical  formulae. 
This  symbol  obviously  involves  both  time  and  velocity. 

30.  Uniform    motion. — A    body  moving   over   equal  spaces  in 
equal  times   is   said   to   have  uniform  motion.     It  follows   from   the 
property  of  inertia  that  a  body  in  motion,  if  left  to  itself,  will  continue 
its  motion  uniformly  both  in  time  and  direction. 

PROPOSITION  I.  The  distance  PASSED  over,  in  uniform  velocity,  is  pro- 
portioned to  the  time.  This  follows  directly  from  the  definition  of 
velocity.  Denoting  by  D  the  distance  passed  over,  and  by  T  the  num- 
ber of  seconds,  we  have 

V=VXT,     V=^    and  y=:-^-. 

The  first  expression  is  called  the  formula  for  uniform  motion,  and 
the  two  others  serve  to  calculate  the  velocity,  the  distance  and  time 
being  known  ;  or  the  time,  the  distance  and  velocity  being  given. 

It  follows  that  if  we  represent  T  by  one  of  the  longer  sides  (A  B)  of 
a  parallelogram,  A  B  C  D,  fig.  3,  and  V  by  one  of  3 

the  shorter   sides   (B  C)  of  the  same  parallelogram,  i!_ 
then  the  area  of  the  parallelogram  A  B  C  D  represents 
the  distance  passed  over  by  a  moving  body  in  the  num- 
ber of  seconds  denoted  by  T.  B  A 

31.  Variable  motion. — In  varying   motion   the  distances   passed 


MOTION   AND   FORCE.  15 

over  in  successive  seconds  are  unequal.  In  this  case,  the  velocity  at 
any  given  instant,  is  the  relation  between  the  distance  traversed  and 
the  time,  considering  the  time  infinitely  small;  or  the  distance  that 
would  be  traversed  in  a  unit  of  time,  supposing  the  motion  at  the  given 
instant  to  be  continued  uniform  for  the  unit  of  time. 

32.  Motion  uniformly  varied. — When  the  velocity  of  a  body 
increases  by  a  constant  quantity  in  a  given  time,  it  is  said  to  be  uni- 
formly accelerated.  The  increase  of  velocity  in  a  second  is  called  its 
acceleration,  which  will  be  represented  by  v.  Uniformly  retarded 
motion  is  where  the  velocity  of  the  body  diminishes  by  a  uniform 
quantity  in  each  second  of  time. 

PROPOSITION  II.  The  change  of  velocity  in  uniformly  varying  motion, 
at  the  end  of  any  given  time,  is  proportional  to  that  time. 

Let  u  be  the  initial  velocity,  that  is,  the  velocity  at  the  instant  from 
which  the  time  is  computed,  v  the  acceleration  and  V  the  velocity  at 
the  end  of  t  seconds,  then  F=  u  +  vt.  The  sign  4-  corresponds  to  the 
case  of  uniformly  accelerated  motion,  and  the  sign  —  to  that  of  uni- 
formly retarded  motion.  In  the  last  case  the  velocity  becomes  null 
when  u  =  vt,  that  is  at  the  end  of  a  number  of  seconds  represented 
by  |f.  The  above  formula  in  fact  involves  this  proposition.  If  we 
then  make  u  =  0,  that  is,  if  it  be  assumed  that  the  motion  starts 
from  a  state  of  repose,  we  shall  have  at  the  end  of  the  time  t,  F=  vt. 
This  is  what  we  announced  in  stating  that  the  velocity  acquired,  at  the 
end  of  a  given  time,  is  proportional  .to  that  time. 

PROPOSITION  III.  In  uniformly  accelerated  motion  the  distances  passed 
over,  by  a  body  starting  from  a  state  of  rest,  are  proportional  to  the 
squares  of  the  times  employed. 

Representing  the  time  by  the  line  A  B,  fig.  4,  and  the  velocity  at 
the  end  of  the  given  time  by  the  line  B  C,  4 

divide  the  time  A  B  into  minute  equal 
parts,  A-l,  1-2,  2-3,  3-4  - 
The  velocities  acquired  during  the  times  ^     ^mm^' 


represented  by  A  1,  A  2,  A  3,  A  4,  will  be   q;      JjiK 
represented  by  the  lengths  of  the  several 

lines,  1  a,  2  b,  3  c,  4d, which 

are  proportioned  to  these  times.  Suppose,  however,  that  during  each 
minute  portion  of  time  A-l,  1-2,  2-3,  3-4 ,  the  velocity  is  con- 
stant, and  equal  to  that  attained  at  the  end  of  each  interval ;  the  motiom 
being  uniform,  the  distances  passed  over  during  these  several  sub- 
divisions of  time  will  be  represented  (30)  by  the  areas  of  the  parallelo- 
grams 1  a/,  2  V,  3  c',  —  — ,  and  the  distance  passed  over  at  the 
end  of  the  time  J±  B,  by  the  sum  of  these  parallelograms.  This  sum 


16  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

differs  from  the  area  of  the  triangle  A  B  C  by  all  that  passes  the  line 
A  C.  It  is  evident  that  if  the  time  A  B  had  been  divided  into  a  larger 
number  (say  double)  of  equal  parts,  the  sum  of  the  parallelograms 
would  have  been  less  in  excess  of  the  triangle.  The  diminution  is 
indicated  by  the  areas  shaded  in  the  figure.  In  proportion  therefore 
as  the  subdivisions  of  the  time  A  B  are  more  numerous,  the  sum  of 
the  parallelograms  will  differ  less  from  the  area  of  the  triangle  ABC. 
Finally,  when  the  number  of  divisions  becomes  infinite,  that  is,  when 
the  velocity  varies  in  a  uniform  manner,  the  distance  passed  over 
during  the  time  A  B  will  be  represented  by  the  surface  of  the  triangle 
ABC. 

But  that  area  ==  £  A  B  X  B  C.  Substituting  A  B  =  t,  B  C  =  F, 
and  recalling  the  value  of  V=  vt,  we  have  for  the  distance  passed 
over  D  =  £ABXBC  or  D  —  $  vt2,  a  formula  involving  the  propo- 
sition stated  above.  This  elegant  demonstration  is  due  to  Galileo,  who 
discovered  the  laws  of  uniformly  varying  motion. 

COROLLARIES.  1st.  The  last  formula  shows  that  the  distance  passed 
over,  in  uniformly  accelerated  motion,  by  a  body  which  starts  from  a 
state  of  repose,  is  equal  to  the  distance  it  would  pass  over  with  a  uni- 
form mean  velocity.  2d.  It  follows  also,  from  the  same  formula,  if  we 
represent  by  a  the  distance  through  which  a  body  moves  in  the  first 
second,  we  can  easily  find  the  following  values  for  the  distances  it  will 
move  through  during  each  succeeding  second,  and  also  the  whole  dis- 
tance it  will  have  passed  through  at  the  end  of  each  second. 

Times,  1  2  3  4  5  n 

Successive  distances,      a          3a         5a         la         9a      (2,n-l}a 

"Whole  distances,  a          4a         9a       16a       25a        n2a. 

The  coefficients  in  the  last  series  are  as  the  squares  of  the  times,  while 
those  in  the  second  series  are  as  the  odd  numbers,  and  are  deduced 
from  the  last  series  by  subtracting  from  each  of  its  terms  the  one 
next  preceding  it.  3d.  The  distance  passed  over  during  a  given  time, 
in  uniformly  accelerated  motion,  is  equal  to  one  half  the  distance  which 
would  be  traversed  during  the  same  time  by  a  uniform  motion,  with 
the  velocity  acquired  at  the  end  of  the  given  time ;  that  is,  the  velocity 
at  the  end  of  the  time  t  is  equal  to  vt,  and  the  distance  which  it 
traverses  during  the  time  t  is  $vf*,  according  to  the  formula.  4th. 
To  determine  the  velocity  acquired  in  terms  of  the  distance  passed 
over,  it  is  necessary  to  eliminate  t  from  the  equations  V=  vt  and 
D=$vt\  which  gives  V=  j/2  v  D. 

The  velocity  is  said  to  be  due  to  the  distance,  (D,)  an  expression 
which  should  not  be  literally  interpreted. 

33.  Compound  motion. — A  body  moving  along  a  right  line  may 


MOTION   AND   FORCE.  17 

partake  of  two  or  more  motions,  in  which  case  its  path  will  be  the 
resultant  of  the  combination  of  these  motions.  Such  a  motion  is  called 
a  compound  motion.  Daily  observation  confirms  this  statement,  which 
will  be  sufficiently  illustrated  when  we  consider  the  results  uf  com- 
pound forces. 

34.  Parallelogram  of  velocities. — The  composition  and  resolution  of 
velocities  will  be  more  readily  explained  and  illustrated  when  considering  the 
forces  in  which  motion  has  its  origin,  as  they  follow  the  same  laws. 

II.    OF  FORCES, 

35.  Definition  of  force. — By  force,  as  used  in  mechanics,  we  mean 
any  cause  producing,  or  modifying,  motion.     All  known  forces,  under 
this  definition,  have  their  origin  in  three  causes ;  namely,  1st,  gravi- 
tation, or  the  mutual  attraction  of  bodies  for  each  other;   2d,  the 
unknown  cause  of  the  phenomena  of  light,  heat,  and  electricity ;  and 
3d,  life,  or  the  mysterious  agency  producing  the  motions  of  animals. 

The  study  of  forces  and  their  effects  constitutes  the  science  of 
mechanics. 

36.  Forces  are  definite  quantities. — As  we  readily  conceive  of 
one  force  as  greater  than  another,  so  we  understand  that  forces  are 
equal  when,  operating  in  opposite  directions,  they  mutually  balance 
each  and  produce  equilibrium.     The  same  may  be  true  of  the  action 
of  two,  three,  or  more  equal  forces,  forming,  by  their  union,  double, 
triple,  or  any  higher  combination  of  force. 

To  determine  a  force  with  precision  we  must  consider  three  things: 
1st,  the  point  of  application ;  2d,  the  direction ;  3d,  the  intensity,  or 
energy  with  which  the  force  acts. 

It  is  usual  to  represent  forces,  like  other  magnitudes,  by  lines  of 
definite  lengths.  Any  line  may  be  chosen  as  the  unit  of  force.  The 
direction  of  a  line  will  then  represent  the  direction  of  the  force,  starting 
from  the  point  of  application  ;  and  its  length  will  represent  the  magni- 
tude, or  intensity,  of  the  force,  expressed  by  the  number  of  times  that 
it  contains  the  unit  of  force.  A  force  is  therefore  defined  in  each  of 
its  three  elements  by  a  line,  being  thus  brought  within  the  limits 
of  number,  geometry,  and  mathematical  analysis. 

37.  Weight;  Unit  of  Force;   Dynamometers. — Where  a  body 
is  left  free  to  the  action  of  gravity,  but  is  held  immovably  by  some 
obstacle,  the  pressure  or  tension  which  it  exerts  on  the  point  of  support 
is  called  its  weight.     It  is  important  to  distinguish  carefully  between 
the  words  weight  and  gravity.     The  latter  signifies  the  general  cause 
which  produces  the  fall  of  all  bodies  to  the  earth,  while  the  former 


13 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


means  only  the  result  of  the  action  of  that  general  cause  in  the  case 
of  a  particular  body. 

The  common  unit  of  force  is  the  pound  avoirdupois. 

The  weight  of  a  body  may  be  rendered  sensible  by  the  use  of  an 
instrument  called  a  dynamometer,  or  measurer  of  force. 

One  of  the  most  simple  of  these  is  represented  in  fig.  5 ;  it  5 

consists  of  a  steel  spring,  a  C  b.  The  metallic  arc  a  d  is  fixed 
near  the  end  of  the  limb  G  a,  and  passes  freely  through  an 
opening  in  the  other  limb.  The  graduated  arc  b  e,  is  fixed,  in 
like  manner,  in  the  limb  C  b.  The  amount  of  the  force  ex- 
erted at  the  points  e  and  d,  determines  the  degree  to  which 
the  two  limbs  will  approach,  and  is  represented  on  the  gradu- 
ated arc  in  pounds  and  ounces,  the  graduation  of  the  arc 
being  the  result  of  actual  trial,  by  hanging  known  weights 
upon  the  hook,  and  observing  the  positions  marked  by  the 
index. 

Many  forms  of  dynamometer  exist,  of  which  the  spring  balance,  or 
Le  Roy's  dynamometer,  is  the  most  familiar. 

Le  Roy's  dynamometer,  or  spring  balance,  fig.  6,  consists  of  a  steel 
spring,  coiled  within  a  cylin- 
drical tube.  The  end  n  of  the 
spring  is  attached  to  a  rod  of 
metal,  graduated  in  pounds  and  ounces,  which  is  drawn  out  more,  as 
the  applied  force,  6,  is  greater. 

Reynier's  dynamometer,  fig.  7,  consists  of  a  steel  spring,  m  a  n  b, 
of  which  the  part  a  and  6  ap-  7 

proach  each  other,  when  a  force 
is  exerted  at  the  points  m  and  n. 
An  arc  graduated  in  Ibs.  is  at- 
tached to  the  spring  at  the  point 
a,  and  carries  a  needle,  r  o, 
worked  by  a  lever,  c.  The  posi- 
tion of  this  needle  upon  the  arc, 
indicates  the  amount  of  the  force 
exerted.  If  it  is  wished  to  de- 
termine the  strength  or  force 
exerted  by  any  animal  or  machine,  as  the  strength  exerted  by  a  horse 
in  drawing  a  plow  through  the  ground,  it  is  only  necessary  to  attach 
one  end  of  the  instrument,  as  n,  to  the  plow,  and  have  the  horse 
attached  to  the  other  end,  m.  The  degree  which  is  marked  by  the 
pointer,  when  the  horse  moves,  represents  in  Ibs.  the  force  exerted. 

Another  dynamometer  is  often  used,  similar  in  construction  to  the 


MOTION   AND   FORCE.  19 

last,  only  that  the  force  is  exerted  at  the  points  a  and  b,  fig.  7,  which 
are  made  to  approach  by  a  contrivance  similar  to  that  shown  in  fig.  5. 

It  is  evident  that,  in  this  last  arrangement,  the  force  is  applied  in  the 
most  favorable  position  for  producing  the  maximum  effect  in  collapsing 
the  spring ;  while  in  Reynier's  dynamometer,  the  force  is  applied  where 
only  the  minimum  effect  is  produced,  and  the  instrument  is  therefore 
generally  employed  for  determining  only  very  considerable  forces. 

38.  Equilibrium. — "When  all  the  forces  acting  on  a  body  are  mu- 
tually counterbalanced,  or  neutralized,  they,  and  the  body  on  which 
they  act,  are  said  be  in  equilibrium.     The  word  repose  and  equilibrium 
are  to  be  carefully  distinguished,  however,  as  signifying  different  con- 
ditions of  a  body.     Repose  implies   simply  a  state  of  rest,  without 
involving  any  idea  of  motion.    Equilibrium  signifies  the  state  of  a  body 
which,  submitted  to  action  of  any  number  of  forces,  is  still  in  the  same 
condition  as  if  these  forces  did  not  act.     By  the  definition  of  inertia 
(26)  a  body  may  be  in  motion  without  being  submitted  to  the  action 
of  any  force,  and  it  may  even  continue  its  motion  undisturbed,  although 
it  becomes  subject  to  forces  producing  equilibrium,  since  such  forces 
mutually  neutralize  each  other.    Equilibrium  does  not  therefore  include 
the  idea  of  immobility,  and  thus  the  words  repose  and  equilibrium  have 
significations  essentially  unlike. 

Equilibrium  may  exist  without  any  point  of  support  or  apparent 
resistance.  A  balloon  in  the  air,  or  a  fish  in  the  water,  are  examples, 
but  the  balloon  and  fish  are  balanced  by  counteracting  forces  hereafter 
explained.  What  are  familiarly  known  as  examples  of  stable  or  unsta- 
ble equilibrium  are  only  special  cases  of  the  action  of  the  force  of 
gravity,  to  be  explained  in  their  proper  place. 

39.  Statical  and  Dynamical  forces. — Statics  is  the  science  of 
equilibrium.     It  considers  the  relations  existing  between   the   three 
conditions  (36);  which  are  involved  in  the  case  of  every  force,  in  order 
that  equilibrium  may  result.  Archimedes  was  the  author  of  this  portion 
of  mechanical  science. 

Dynamics  considers  the  motions  which  forces  produce.  The  founda- 
tions of  this  part  of  mechanical  science  were  laid  by  Galileo  in  the 
early  part  of  the  seventeenth  century. 

Hydrostatics  and  Hydrodynamics  are  the  principles  of  statics  and 
dynamics  applied  to  the  phenomena  of  rest  and  motion  in  fluids. 

The  distinction  between  statics  and  dynamics  is  so  far  artificial  that 
the  same  force  may,  according  to  circumstances,  produce  either  pres- 
sure or  motion,  without  any  change  in  the  nature  of  the  force. 

40.  Direction  of  force. — It   is   self-evident  that  the  direction   in 
which  a  force  is  applied  must  determine  the  direction  in  which  the 


20  PHYSICS   OF   SOLIDS   AND    FLUIDS. 

body  receiving  the  force  will  move,  if  motion  results,  or  of  the  result- 
ing pressure,  if  the  body  is  not  free  to  move. 

Moreover,  the  action  of  a  force  upon  a  body  is  independent  of  Us  state 
of  rest  or  motion.  Daily  experience  and  observation  confirm  this  state- 
ment, which  is  also  susceptible  of  experimental  proof. 

It  follows :  1st.  That  if  two  or  more  forces  act  upon  a  body  at  the  same 
time,  each  of  these  forces  produces  the  same  effect  as  if  it  acted  alone, 
since  the  effect  which  each  produces  is  not  dependent  upon  any  motion 
which  the  others  are  capable  of  producing  in  the  same  body. 

2d.  Therefore,  a  body  under  the  influence  of  a  force,  constant  both 
in  direction  and  intensity,  moves  with  a  constantly  accelerated  velocity; 
for  as  in  each  second  the  variation  of  velocity,  v,  is  the  same,  in  t 
seconds  it  will  be  =  vt ;  i.  e.,  at  the  end  of  2  seconds  it  will  be  20,  of 
3  seconds  3w,  and  so  on.  In  other  words,  it  is  proportional  to  the  time. 
Reciprocally,  3d.  A  body  moving  in  a  right  line  with  a  uniform  accele- 
ration is  actuated  by  a  force  of  constant  intensity  acting  in  the  direction 
of  its  motion. 

41.  Measure  of  forces.     Mass. — In  mechanics  forces  are  usually 
measured  by  their  effects  rather  than  by  weight.    The  effects  of  a  force 
depend,  other  things  being  equal,  on  the  mass  of  the  body  acted  on. 

The  mass  of  a  body  is  the  quantity  of  matter  the  body  contains,  and 
is  proportional,  in  the  same  substance,  to  the  number  of  its  molecules. 
Masses  are  equal  when,  after  receiving  for  an  equal  time  the  impulse  of 
an  equal  and  constant  force,  they  acquire  equal  velocities. 

Since  we  know  forces  only  by  their  effects,  that  is  by  the  amount  of 
motion  or  pressure  they  produce,  let  us  look  for  a  just  measure  of  any 
given  force  in  the  amount  of  motion  which  it  causes.  The  following 
four  propositions  will  render  this  subject  clear. 

42.  Propositions  in  regard  to  forces. — PROPOSITION  I.   Two  con- 
stant forces  are  to  each  other  as  the  masses  to  which  in  equal  times  they 
impart  equal  velocities. 

Consider,  for  example,  n  equal  forces/,/,/,  parallel  to  each  other,  acting  upon 
n  equal  masses  m,  m,  m.  These  masses  receive  equal  Velocities,  and  conse- 
quently preserve  the  same  relative  positions,  and  we  readily  conceive  of  them, 
therefore,  as  bound  together  to  form  one  mass  equal  to  n  X  wi.  This  compound 
mass  (n  X  m)>  in  order  that  it  may  possess  the  same  velocity,  v,  which  any 
single  mass,  m,  receives  from/,  must  be  acted  on  by  the  force  n  X/ 

PROPOSITION  II.  Two  constant  forces  are  to  each  other  as  the  velocities 
which  they  impress,  during  the  same  time,  upon  two  equal  masses. 

Suppose  two  forces  F  and  F'  to  be  commensurable,  and  let  I  be  their  common 
measure,  so  that  F  •=.  nl  and  F'  •=  n'l.  Represent  also  by  u  the  velocity 
which  the  force  I  imparts  at  the  end  of  a  given  time  to  the  common  mass.  The 


MOTION   AND   FORCE.  2) 

force  nl  will  impart  to  this  mass  the  velocity  V  =  n«,  since  each  force  equal 
to  I  acts  as  if  it  were  alone ;  in  like  manner  the  force  n'l  will  impart  the  velo- 
city   V  —  n'u   to    the  same    mass.     Thence  follows    this   proportion, 
nl  :  n'l  =  nu :  n'u,  or  F:  F'  =  V:  V  which  was  to  be  proved. 
If  the  forces  compared  are  not  commensurable,  we  must  take  I  infinitely  small. 

PROPOSITION  III.  Two  constant  forces  are  to  each  other  as  the  products 
of  the  masses  by  the  velocities  which  they  impart  to  these  masses  in  the 
same  time. 

Let  F  F'  be  two  forces  acting  on  the  two  masses  MM',  and  imparting  to  them, 
at  the  end  of  the  same  time,  the  velocities  Fand  V ;  also  consider /another  force 
able  to  impart  to  the  mass  M,  in  the  same  time,  the  velocity  V ;  comparing  the 
forces  F  and/,  which  in  the  given  time  impart  to  equal  masses  MM  unequal  velo- 
cities Fand  V,  it  follows  from  Proposition  II.  that  F  :/=  F:  V. 

Comparing  the  forces /and  F',  which  impart  to  unequal  masses  J/and  M'  equal 
velocities  F'  and  V,  it  follows  from  Proposition  I.  that :— / :  F'  =  M  :  M'. 

Multiplying  the  two  propositions  term  by  term  we  have  F :  F'  =  MV:  M'  V, 
which  was  to  be  proved. 

From  these  principles  it  follows,  that  the  measure  of  any  force  is 
obtained  by  selecting  some  unit  of  force  to  serve  as  a  term  of  compari- 
son for  all  other  forces ;  such  a  force  acting  on  a  unit  of  mass,  during 
one  second  (the  unit  of  time),  should  impart  to  it  a  velocity  or  accele- 
ration of  one  foot,  one  yard,  one  metre,  or  any  other  arbitrary  measure, 
as  one  foot  per  second,  which  latter  measure  we  adopt. 

By  proposition  second  we  can  then  find  the  relation  that  any  force  F,  acting 
on  a  mass  of  matter  during  one  second,  will  bear  to  the  unit  of  force.  For  if 
F'  is  the  unit  of  force  in  the  proportion  F :  F'  =  MV :  Mf  F',  then,  by  the  defi- 
nition, both  M'  and  V  are  equal  to  unity,  and  we  have  F  =  MV.  That  is, 
according  to  the  definition,  F  contains  the  unit  of  force  as  many  times  as  there 
are  units  in  the  product  of  the  number  M  into  the  number  F.  Assume,  for 
example,  that  the  mass  moved  is  equal  to  six  units  of  mass,  and  the  acceleration 
v  in  a  unit  of  time  is  equal  to  ten  feet,  then  the  intensity  of  the  force  is  equal 
to  sixty,  i.  e.,  sixty  times  the  unit  of  force.  Hence  we  deduce  the  following : — 

PROPOSITION  IV.  The  measure  of  a  force  is  the  product  of  the  mass 
moved  by  the  acceleration,  or  velocity,  imparted  in  a  unit  of  time.* 

43.  Momentum. — The  momentum  of  a  moving  body  is  its  amount 
of  motion,  or  its  tendency  to  continue  in  motion.  The  momentum  of 
a  body  is  equal  to  its  mass  multiplied  by  its  velocity.  When  a  force 
acts  upon  a  body,  free  to  move,  it  produces  its  effect  as  soon  as  motion 
is  diffused  among  all  the  molecules,  and  the  force  is  then  transferred 
into  the  substance  of  the  moving  body.  In  consequence  of  the  inertia 

*•  In  all  the  propositions  relating  to  velocity  as  a  measure  of  force,  there  is 
supposed  to  be  no  resistance  to  motion  ;  the  force  acting  only  to  overcome  the 
inertia  of  the  body. 
5 


22  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

of  matter  (26),  if  the  moving  body  should  meet  no  resistance,  it  would 
continue  to  move  with  the  same  velocity,  and  in  the  same  direction, 
for  ever. 

The  expression  Mv  represents  the  intensity  of  the  force  which  has 
set  the  body  in  motion,  and  MV  represents  the  amount  of  force  that  is 
at  any  time  accumulated  and  retained  by  the  inertia  of  the  moving 
body.  In  either  case  the  moving  body  is  supposed  to  encounter  no 
resistance  from  any  other  object. 

It  is  a  fundamental  principle  in  mechanics  that  the  same  force  acting  upon 
different  bodies  in  similar  circumstances  imparts  velocities  in  the  inverse  ratio 
of  their  quantities  of  matter.  If  the  same  force,  in  the  absence  of  resistance, 
successively  projected  balls  whose  masses  were  as  the  numbers  1,  2,  3,  <fec.,  it 
would  impart  to  them  the  velocities  1,  £,  £,  Ac.,  so  that  a  mass  ten  times 
greater  would  acquire  a  velocity  of  only  1  .  The  product  of  each  of  these 
masses  into  its  velocity  is  the  same,  for  1  X  1  —  1,  2  X  J  =  1,  &c. 

When  a  moving  body  encounters  resistance,  depending  not  only  upon  inertia, 
but  also  upon  other  properties  of  matter,  the  effects  produced  depend  upon  the 
rapidity  with  which  the  force,  expressed  by  momentum,  is  brought  to  act  upon 
the  opposing  body.  This  class  of  effects  is,  therefore,  proportioned  to  momen- 
tum, multiplied  by  velocity.  This  product  J/F2  is  called  vis  viva,  the  applica- 
tion of  which  to  practical  mechanics  will  be  explained  hereafter  (111).  By  the 
principle  that  action  and  reaction  are  equal  (27),  we  know  that  when  a  musket 
is  discharged  the  force  of  the  explosion  reacts  upon  the  musket  with  the  same 
intensity  as  it  projects  the  ball.  -  According  to  the  principles  of  momentum,  the 
weight  of  the  gun,  multiplied  by  the  velocity  of  the  recoil,  must  be  equal  to 
the  weight  of  the  ball,  multiplied  by  the  velocity  of  its  projection,  yet  the  recoil 
of  the  gun  is  received  by  the  sportsmen  with  perfect  impunity,  while  the  moving 
ball  deals  death  or  destruction  to 'opposing  objects. 

III.    COMPOSITION  OF  FORCES. 

44.  System  of  forces.  Components  and  resultant. — Whatever 
may  be  the  number  and  direction  of  forces  acting  upon  one  point,  they 
can  impart  motion  or  pressure  in  only  one  direction.     We  therefore 
assume,  that  there  is  a  single  force  which  can  produce  the  same  action 
as  the  system  of  forces,  and  may  replace  them.     This  is  called  the 
resultant,  and  the  forces  to  whose  effect  it  is  equivalent,  are  termed  the 
components.      The   components   and   resultant   may   be   interchanged 
without  changing  the  condition  of  the  body  acted  on,  or  the  mechanical 
effect  of  the  forces  themselves. 

A  force  is  therefore  mechanically  equivalent  to  the  sum  of  its  com- 
ponents. On  the  other  hand,  any  number  of  forces  are  mechanically 
equivalent  to  their  resultant.  As  we  know  forces  only  by  their  effects 
in  producing  motion  or  pressure,  any  forces  which  produce  equal 
motions  or  pressures  are  equal.  We  shall  proceed  to  illustrate  this 
proposition  in  a  few  particular  cases. 

45.  The  parallelogram  of  forces. — It  has  already  been  stated  that 


MOTION    AND    FORCE.  23 

forces  may  be  represented  by  lines,  both  in  direction  and  intensity ; 
also,  that  two  forces  acting  on  the  same  or  equal  masses  of  matter, 
are  to  each  other  as  their  velocities,  or  F/  :  F"  =  V  :  V".  The  same 
principles  will  therefore  apply  to  the  combinations  of  forces  that  apply 
to  the  combinations  of  velocities  or  of  motions. 

When  several  forces  act  on  a  body,  they  may  be  arranged  in  three 
ways,  according  to  their  direction.  The  forces  may  act, 

1.  All  in  one  direction  ; 

2.  In  exactly  opposite  directions ;  or 

3.  At  some  angle. 

In  the  first  case,  the  resultant  is  the  sum  of  all  the  forces,  and  the 
direction  is  unaltered.  In  the  second,  the  resultant  is  the  difference 
of  the  forces,  and  takes  the  direction  of  the  greater.  If  opposite  forces 
are  equal,  the  resultant  is  nothing,  and  no  motion  is  produced.  In  the 
third  case,  a  resultant  is  found  to  two  forces,  whether  equal  or  unequal, 
by  the  parallelogram  of  forces,  according  to  the  following  law.  By 
any  number  of  forces  acting  together  for  a  given  time,  a  body  is  brought 
to  the  same  place  as  if  each  of  the  forces,  or  one  equal  and  parallel  to  it, 
had  acted  on  the  body  separately  and  successively  for  an  equal  time. 

Suppose  two  forces,  at  right  angles  to  each  other,  act  simultaneously 
on  the  point  a,  fig.  8,  one  in  the  direction  ax,  8 

and  the  other  in  the  direction  a  y.     Let  one  . 
force  be  such  that,  in  a  given  time,  as  a  second, 

it  will  move  the  point  from  a  to  b,  while  the      I ._*"/ 

other  will,  in  the  same  time,  move  it  from  a  to 

c,  then  by  the  joint  action  of  both  forces  it  will 

be  impelled  to  r  in  the  same  time.     The  first 

force,  by  its  separate  action,  would  impel  the      <t  6 

body  to  b  in  one  second,  and  if  it  were  then  to  cease,  the  second  force, 

or  one  equal  and  parallel  to  it,  would  impel  the  body  to  r  in  the  same 

time ;  or  the  body  might  be  carried  from  a  to  c,  and  from  c  to  r ;  in 

either  case  the  result  is  the  same. 

If  a  6  =  .I",  ac=  Y,  and  ar~Ry  then  R  =  y ' X*  +  F2.  If  we  call 
the  angle  r  a  b  =  a  CDS.  «  =  -f,  and  sin.  a  =  —  . 

Again,  suppose  the  forces  act  at  an  oblique  angle ;  let  the  point  P, 
fig.  9,  be  acted  on  by  two  forces  in  the  directions  P  A  and  P  B.  On 
P  A,  measure  P  a,  containing  as  many  units  of  length  as  the  force  A 
contains  units  of  force ;  and  on  P  B  take  P  b  in  the  same  manner. 
Complete  the  parallelogram  P  a  c  b  ;  the  diagonal  P  c  will  repre- 
sent the  direction  of  a  single  force  C,  equivalent  to  the  combined  effect 


/ 


24 


PHYSICS    OF  SOLIDS   AND   FLUIDS. 


of  A  and  B,  and  P  c  will  contain  as  many  units  in  length  as  C  con 
tains  units  of  force. 

In  the  same  manner  a  result-  9 

ant  may  be  found  for  three  or 
any  number  of  motive  forces,  by 
compounding  them,  two  by  two, 
successively. 

In  the  triangle  P  a  c,  fig.  9,  the 
sides  a  P  and  a  c  =  P  b,  are  known, 
and  also  the  angle  P  a  c,  which  is 
the  supplement  of  the  angle  a  P  b, 
formed  by  the  directions  of  the 
forces.  We  may  therefore  calculate 
the  side  P  c,  that  is,  the  intensity 
of  the  resultant,  and  the  angle 
a  P  c,  which  determines  its  direc- 
tion. 

Let  the  point  a,  fig.  10,  be  subjected  to  the  forces  whose  magnitudes 
and  directions  are  represented  by  the  lines  a  b,  a  C,  and  a  d.  We  first 
take  any  two  which  lie  in  10 

the  same  plane,  as  a  b  and 
oC,  and  find  their  result- 
ant a  X  ;  and  compounding 
this  with  the  third  force  a  d, 
we  find  ay,  which  will  re- 
present the  magnitude  and 
direction  of  the  general  re- 
sultant of  all  three  forces. 

The  resultant  of  any  num- 
ber of  forces  can  therefore 

be  determined  by  geometrical   construction,   or  calculated  from  well 
known  geometrical  principles. 

This  system  of  compounding  forces  is  called  the  parallelogram  of 
forces,  and  applies  equally  to  the  combination  of  velocities  or  motions. 

In  order  that  the  body  may  move  in  the  straight  line  a  r  (fig.  8),  the 
two  forces  must  act  in  the  same  manner.  They  may  be  instantaneous  im- 
pulses, which  will  cause  uniform  motion ;  or  both  may  act  continuously 
and  uniformly,  so  as  to  produce  a  uniformly  accelerated  motion ;  or, 
both  forces  may  act  with  a  constantly  varying  intensity,  increasing  or 
diminishing  at  the  same  rate,  and  the  body  will  still  move  in  a  straight 
line.  But  if  one  force  is  instantaneous  and  the  other  constant,  or  one 
constant  and  the  other  variable,  or  both  varying  by  different  laws,  then 
the  body  will  move  in  a  curve ;  but  in  every  case  it  will  reach  the  point 


4       si 

f/L 


MOTION    AND    FORCE.  25 

r  in  the  same  time  that  it  would  have  passed  from  a  to  6,  or  from  a  to  c, 
by  the  separate  action  of  either  force. 

If  the  three  forces  a  b.  a  C,  and  a  d,  all  pass  through  the  same  point, 
we  may  construct  a  parallelopipedon,  as  shown  in  fig.  10,  and  a  y,  the 
diagonal  of  the  parallelopipedon,  will  represent  the  direction  and  inten- 
sity of  the  resultant  force.  This  method  of  compounding  forces  is  called 
the  parallelopipedon  of  forces. 

Examples  of  the  composition  of  motion  and  force  are  of 
constant  and  familiar  occurrence. 

A  man  in  swimming,  impels  himself  in  a  direction  perpendicular  to  his  feet 
and  hands,  and  if  the  forces  are  equal  on  each  side,  he  will  move  in  a  resultant 
line,  passing  through  the  centre  of  his  body.  Another  instance  is  the  flight  of 
birds.  While  flying,  their  wings  perform  symmetrical  movements,  and  strike 
against  the  air  with  equal  force. 

In  the  case  of  flying  birds,  the  resistance  of  the  air  is  perpendicular 
to  the  surface  of  the  wings,  and  11 

may  be  represented,  fig.  11,  by 
C  A  and  D  A,  at  right  angles  to 
their  surface.  Neither  of  these 
pressures  tends  to  impel  the  bird 
straight  forward,  but  it  moves  in 
their  resultant;  for  if  the  wings 
are  equally  extended,  and  act  with 
equal  force,  the  lines  C  A  and  D  A 
make  equal  angles  with  A  B,  pass- 
ing through  the  centre  of  the  bird, 
and  hence  their  diagonal,  or  A  G, 
the  diagonal  of  equal  parts  of 
them,  will  coincide  with  A  B,  and  the  bird  will  fly  directly  forward. 

46.  Parallel  forces.  Resultant  of  unequal  parallel  forces. — 
Two  forces,  acting  side  by  side,  produce  the  same  effect  as  if  they  were 
in  the  same  straight  line.  Two  horses  drawing  a  cart  is  an  example. 
Hence  the  resultant  of  two  parallel  forces  acting  in  the  same  direction 
is  equal  to  their  sum,  and  is  parallel  to  them,  and  when  they  are  equal, 
is  applied  midway  between  them. 

If  the  parallel  forces  are  unequal,  the  point  of  application  of  the 
resultant  may  be  found  by  the  following  experiment.  Let  A  B,  fig.  12, 
a  bar  of  uniform  thickness  and  density,  be  balanced  on  its  centre  C. 
We  may  suppose  the  bar  to  be  divided  into  two,  A  D  and  D  B,  of 
unequal  lengths,  which  might  also  be  balanced  on  their  centres  E 
and  F.  Now  we  have  two  parallel  and  unequal  forces — the  weight 
of  A  D  and  the  weight  of  D  B — whose  resultant  is  not  midway 


26 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


13 


V\ 


between  their  points  of  application,  E  and  F,  but  passes  through  C, 
which  is  nearer  E  than  F  in  the  exact  ratio  that  the  force  atE  exceeds 
that  at  F  ;  for  tte  weights  12 

of  the  two  bars  are  as  their       ^ 

lengths,  and  C  E  measures        j— -  c       -^ 

half  the  length  DB/and 
C  F  half  the  length  of  A  D  ; 
so  that  C  E  is  to  C  F  in- 
versely as  the  weight  at  E  is 

to  the  weight  at  P.  The  truth  of  this  conclusion  may  be  tested  by  sus- 
pending at  E  and  F  two  additional  weights  which  have  the  same  ratio 
to  each  other  as  A  D  to  D  B,  and  the  equilibrium  will  be  undisturbed. 

Hence  the  resultant  of  two  parallel  but  unequal  forces  is  equal  to 
their  sum,  and  its  distances  from  them  are  inversely  as  their  intensities. 
Thus,  in  fig.  13,  if  any  two  parallel 
forces  act  at  A  and  A/,  and  their  inten- 
sities are  expressed  by  A  B  and  A/  B', 
then  their  resultant  will  be  repre- 
sented by  P  R,  provided  it  acts  at  P, 
a  point  so  situated  that  P  Ax :  P  A  = 
A  B :  A/  B'.  The  same  will  be  true 
whatever  be  the  common  direction  of  ^..,  ""?•••<  / , 

the  forces  ;  if  the  positions  of  A  B  and  *•  c 

A'  B'  are  changed  to  A  C  and  A/  C', 
then  P  R  must  move  to  P  R',  and  equilibrium  equally  obtains. 

47.  Resultant  of  two  parallel  forces  acting  in  opposite  direc- 
tions.— The  resultant  of  two  parallel  forces,  which 

act  in  opposite  directions,  is  found  by  the  same  con- 
struction as  before,  but  it  is  equal  to  the  difference 
of  the  intensities  of  its  components,  and  takes  the 
direction  of  the  greater.  Its  point  of  application, 
fig.  14,  is  in  the  prolongation  of  the  line  A  B,  at  the 
point  C,  situated  so  that  C  B  and  C  A  are  in  the  in- 
verse ratio  of  the  forces  Q  and  P.  The  point  C  will 
be  further  removed  as  the  difference  between  the 
forces  P  and  Q  are  diminished,  so  that  if  the  forces 
were  equal,  the  resultant  would  be  nothing,  and  situated  at  an  infinite 
distance. 

The  general  resultant  of  any  number  of  parallel  forces  may  be  found 
by  compounding  them,  successively,  two  by  two,  in  the  methods  already 
prescribed. 

48.  Couples. — Whenever  a  body  is  solicited  by  two  forces  which 


MOTION    AND    FORCE.  27 

are  equal,  parallel,  and  acting  in  opposite  directions,  it  is  impossible  to 
replace  them,  or  produce  equilibrium  by  a  single  force.  Such  a  sys- 
tem of  forces  is  called  a  couple,  and  its  tendency  is  to  produce  revolu 
tion  around  an  axis.  In  this  case,  the  value  of  the  resultant  is  evidently 
equal  to  zero,  and  the  point  of  application  is  also  at  an  infinite  distance 
from  the  points  of  application  of  the  two  equal  components. 

49.  Two  forces  not  parallel  and  applied  to  different  points 
may  have  a  resultant,  if  they  lie  in  the  same  plane.     It  is  found  by 
extending  the  lines  of  direction  until  they  intersect.     But  if  the  forces 
are  not  parallel,  and  lie  in  different  planes,  then  the  directions,  though 
infinitely  prolonged,  will  never  intersect,  and  they  cannot  have  any 
single  resultant,  or  be  in  equilibrium  by  any  single  force. 

50.  The  resolution  of  forces  is  the  converse  of  their  composition. 
Since  two  or  more  forces  can  be  replaced  by  a  single  force,  so,  com- 
monly, we  may  substitute  two  or  more  forces  for  one  ;  and  since  an 
infinite  number  of  systems  may  have  the  same  resultant,  conversely, 
one  force  may  be  replaced  in  innumerable  ways  by  a  system  of  several 
forces.     But  if  one  of  two  required  components  is  given  in  magnitude 
and  direction,  there  can  be  but  one  solution,  and  the  problem  is 
definite. 

When  a  force  acts  upon  a  body  at  any  other  than  a  right  angle,  a 
part  of  its  effect  is  lost.  By  resolving  such  an  oblique  force  into  two, 
one  parallel,  and  the  other  perpendicular  15 

to  the  body,  the  latter  component  will  re-  ^ 
present  the  actual  force  produced.  Let  a  b, 
fig.  15,  represent  a  force  acting  under  the 
angle  a  b  c  against  the  surface  M  N.  Re- 
solve a  b  into  a  c  perpendicular  to  M  N, 
and  a  d  parallel  with  it ;  then  a  c  will  be 
the  absolute  effect  of  the  force,  and  ab — 
a  c  is  the  loss. 

Example  of  the  resolution  of  force. — The  sailing  of  a  boat  in  a 
direction  different  from  the  wind  is  a  most  familiar  illustration  of  these 
principles.  For  example :  the  wind  blows  in  the  direction  v  a,  fig.  16, 
oblique  to  the  sail,  and  to  the  course  of  the  boat,  and  its  force  is 
resolved  into  two  components,  one  acting  in  the  direction  ca,  impelling 
the  boat  on  its  course  in  the  line  of  least  resistance,  the  other  in  the 
direction  b  a,  acting  to  carry  the  boat  laterally  on  in  the  line  of  greatest 
resistance.  As  the  model  of  the  boat  allows  it  to  advance  freely  through 
the  water  in  the  direction  c  a,  while  -it  offers  great  resistance  to  lateral 
motion,  the  force  of  the  wind  resolved  in  the  direction  b  a  produces 
little  effect  upon  the  motion  of  the  boat,  she  being  held  to  her  course 


28  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

by  the  rudder.     A  skillful  sailor  can,  by  thus  availing  himself  of  the 
principles  of  resolution  of  force,  sail  his  vessel  on  a  course  within  five 

16 


or  six  points*  of  being  directly  opposed  to  the  wind  which  impels  it. 

IV.    CURVILINEAR  MOTION CENTRAL  FORCES. 

51.  Of  curvilinear  motion. — It  has  been  shown  that  a  body  acted 
upon  by  two  forces  will  move  in  a  direction  which  is  the  resultant  of 
the  two  forces.     If  one  of  two  forces  acting  upon  a  body  is  a  continu- 
ous force,  acting  in  a  direction  tending  to  turn  the  body  out  of  the 
course  it  receives  from  the  other,  the  resultant  will  not  be  a  straight 
line,  but  a  curve,  having  its  concavity  turned  towards  the  direction  of 
the  continuous  force.     If  at  any  instant  the  continuous  force  ceases  to 
act,  the  body  will  continue  to  move  in  the  direction  in  which  it  was 
moving  when  the  constant  force  ceased  to  act.    This  direction  will  be  a 
tangent  to  the  curve  at  that  point. 

52.  Centrifugal  and  centripetal  forces. — Let  us  consider  a  mate- 
rial point  moving  with  a  uniform  velocity  in  the  circumference  of  a 
circle.     The  resultant  of  the  forces  acting  on  the  particle  will,  there- 
fore, by  the  necessity  of  the  case,  pass  through  the  circumference  of 
the  circle.     In  this  case  the  force  which  prevents  the  moving  particle 
from  darting  off  in  a  tangent  to  the  circle  is  called  the  centripetal,  or 
centre-seeking,  force.     This  force  at  every  instant  arrests  the  tendency 
of  the  particle  to  fly  away  from  the  centre.     The  tendency  of  the  par- 
ticle to  fly  away  from  the  centre  is  called  the  centrifugal,  or  centre- 
flying,  force.     These  two  forces  are,  together,  termed  central  forces. 
They  are  necessarily  antagonistic  to  each  other  at  every  instant  of  cur- 
vilinear motion. 


*  A  circle  is  divided  into  four  quadrants,  and  each  quadrant  into  eight  points, 
according  to  the  phraseology  of  seamen. 


MOTION    AND    FORCE. 


29 


To  understand  the  antagonism  of  central  forces,  take  m  c,  fig.  17,  an  infi- 
nitely small  arc  of  the  circumference,  and  making  17 
with  the  direction  c'  m  a,  of  the  preceding  element 
c'  m,  an  infinitely  small  angle  am  c.  Join  the  extremi- 
ties of  the  element  m  c  with  the  centre  of  the  circle  by 
the  radii  m  C,  c  C,  and  draw  b  c  parallel  to  m  a.  Since 
m  c  is  considered  infinitely  small,  a  c  and  m  b  are 
parallel  to  each  other,  and  macb  is  a  parallelogram. 
Therefore  it  follows  by  the  parallelogram  of  forces, 
that  while  the  body  was  moving  over  the  arc  m  c  it 
would  in  the  same  time  have  passed  over  the  space 
m  a,  in  virtue  of  the  velocity  acquired  in  passing 
over  c'  m,  if  no  other  force  intervened ;  while  by  reason 
of  the  central  force  acting  from  m  to  c,  it  would  have 
passed  over  the  space  m  b,  had  it  not  been  for  the 
original  impulse  c'  m.  This  is  the  centripetal  force, 
and,  compounded  with  the  original  impulse,  c'  m,  the 
particle  follows  the  resultant  m  c. 

Draw  now  a  d  parallel  to  m  c,  forming  the  second  parallelogram  mead.  The 
velocity  of  the  particle  following  the  diagonal  m  a  may  be  decomposed  into  the 
two  components ;  one  m  c  in  the  path  of  the  circular  motion,  and  the  second 
m  d  following  the  radius.  This  quantity  (m  d)  represents  the  centrifugal  force, 
and  as  m  d  =  a  c  =  m  6,  it  follows  that  at  each  instant  of  the  circular  motion 
the  centripetal  and  centrifugal  forces  exactly  counterbalance  each  other,  and 
that  the  sole  resulting  motion  is  in  the  arc  m  c.  If  at  any  instant  the  centri- 
petal force  ceases  to  act,  m  a,  the  resultant  of  the  forces  m.  c,  m  d,  will  throw  the 
particle  in  the  path  of  the  line  c'  m  a  tangent  to  TO.  The  term  centrifugal  force 
must  not  be  understood  to  mean  a  force  which  would  cause  the  body  to  fly 
directly  from  the  centre,  since  as  we  have  seen  it  must  in  that  case  move  also 
in  the  tangent. 

Examples  of  the  action  of  centrifugal  force. — A  stone  flies  from 
a  sling  with  a  velocity  equal  to  the  force  acquired  by  its  revolution  at 
the  moment  when,  by  releasing  one  of  the  strings  from  the  finger,  it 
flies  off  in  a  line  tangent  to  the  point  of  release.  The  water  flies  from 
a  grindstone,  or  mud  from  a  carriage  wheel,  whenever  the  centrifugal 
force  due  to  the  velocity  of  revolution  is  sufficient  to  overcome  the  force 
of  adhesion.  The  rapidity  of  revolution  may  be  sufficient  in  a  grind- 
stone to  overcome  the  cohesion  of  the  particles  of  the  stone,  when  it 
bursts  with  a  loud  explosion,  carrying  death  and  destruction  in  its  path. 
A  pail  filled  with  water  may  be  whirled  with  such  velocity  that  the 
centrifugal  force  overcomes  the  force  of  gravity,  and  the  liquid  is  not 
spilled. 

53.  Experimental  demonstration  of  the  effects  of  centrifugal 
force. — The  effects  of  centrifugal  force  may  be  illustrated  by  the  appa- 
ratus represented  in  fig.  18.  A  wire  is  stretched  upon  a  frame  a  6,  con- 
nected with  an  upright  shaft,  which  is  made  to  revolve  rapidly  by  means 
of  a  cord,  as  shown  in  the  figure.  Two  perforated  balls,  united  by  a  string, 


30 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


Blide  freely  upon  the  horizontal  wire.  If  the  two  sliding  balls  are  of  equal 
weight,  and  are  placed  at  equal  distances  from  the  axis  of  rotation,  still 

18 


united  by  the  string,  they  will  retain  the  same  position  with  any  velo- 
city of  rotation  which  may  be  given  to  the  apparatus ;  but  if  one  of  the 
balls  is  more  distant  from  the  axis  than  the  other,  it  will  draw  the 
other  along  with  it,  and  both  balls  will  strike  the  support  on  the  same 
side,  provided  the  distance  between  the  balls  is  less  than  half  the  line 
a  b.  If  the  two  balls,  united  as  before,  and  placed  at  equal  distances 
from  the  axis,  have  unequal  masses,  the  heavier  ball  will  draw  the 
other  towards  its  own  side  of  the  apparatus.  Two  unequal  balls, 
united  in  the  same  manner,  will  remain  at  rest,  if  their  distances  from 
the  axis,  on  opposite  sides,  are  in  the  inverse  ratio  of  their  masses. 
Admitting  that  the  centrifugal  force  is  proportional  to  the  mass  of  the 
body,  these  experiments  prove  that  the  centrifugal  force  is  proportional 
to  the  radius  of  the  circle  described,  when  the  times  of  revolution  are 
the  same. 

To  demonstrate  the  effects  of  centrifugal  force  in  liquids,  the  appa- 
ratus shown  in  the  upper  part  of  fig.  19  is  attached  by  screws  to  the 
coupling  at  the  top  of  the  re- 
volving shaft  shown  in  fig.  18. 
Two  flasks  with  long  necks  are 
placed  obliquely,  communica- 
ting with  a  reservoir  filled  with 
liquid  placed  at  the  middle  of 
the  bar  which  supports  them. 
As  the  apparatus  is  rapidly  re- 
volved, the  liquid  rises  into  the  flasks,  and  again  descends  when  the 
motion  is  arrested.  If  the  vase,  fig.  20,  containing  water,  is  attached  to 
the  machine,  and  made  to  revolve,  the  surface  of  the  water  becomes 
concave,  the  water  rising  by  the  sides  of  the  glass,  the  surface  becom- 
ing more  deeply  concave  as  the  motion  becomes  more  rapid.  The  piece 
of  apparatus  shown  at  the  bottom  of  fig.  19  carries  two  inclined  tubes, 
one  enclosing  water  and  a  metallic  ball,  the  other  water  and  a  ball  of 


MOTION   AND   FORCE.  31 

wood  floating  on  its  surface.  As  the  rotation  becomes  rapid,  the  water 
rises  to  the  top  of  the  tubes,  the  ball  of  wood  then  descends,  and  takes 
a  position  on  the  inferior  surface  of  the  liquid,  while  the  20 

metallic  ball  advances  through  the  liquid,  and  rises  to 
the  most  elevated  extremity  of  the  tube  which  contains  it, 
the  liquid  itself  rising  to  the  exterior  end  of  the  tube. 

The  different  effect  upon  the  two  balls  results  from  the 
fact  that  the  metal  has  a  greater  mass  than  an  equal 
volume  of  the  liquid,  while  the  contrary  is  true  of  the 
wood ;  the  centrifugal  force  being  in  proportion  to  the 
mass,  the  tendency  is  to  carry  the  denser  substance  to  the 
greater  distance  from  the  axis  of  rotation. 

If  a  tube  contains  different  liquids  incapable  of  acting  chemically 
upon  each  other,  they  will  place  themselves,  during  rapid  rotation,  in 
such  an  order  that  the  denser  fluid  will  be  more  distant  from  the  axis, 
the  outward  tendency  being  directly  proportional  to  the  mass  of  matter 
in  a  given  volume.  These  effects  do  not  take  place  till,  by  the  rapidity 
of  revolution,  the  centrifugal  force  becomes  greater  than  the  force  of 
gravity.  The  common  circular  or  fan  blowing  machine  is  an  example 
of  the  action  of  centrifugal  force  on  bodies  in  a  gaseous  condition. 
A  centrifugal  pump  has  been  devised  acting  in  this  manner.  The  fan- 
blower  is  also  used  as  a  ventilator,  drawing  its  supply  of  air  from  the 
space  to  be  ventilated,  to  supply  that  thrown  out  by  the  tangential 
opening. 

The  centrifugal  drying  machine  for  laundries  consists  of  a 
very  large  upright  cylinder,  having  a  smaller  cylinder  within  it.  The 
circular  chamber  between  the  two  cylinders  is  closed  by  covers,  by  open- 
ing which  the  linen  to  be  dried  can  be  introduced.  The  bottom  of  this 
chamber  is  pierced  with  holes  like  a  sieve,  through  which  the  water 
expressed  from  the  linen  can  flow  off.  A  rapid  rotation  being  given  to 
this  cylinder,  the  linen,  by  the  effect  of  centrifugal  force,  is  urged 
against  the  exterior  surface  of  the  cylinder,  and  is  there  squeezed  with 
a  force  which  increases  with  the  rapidity  of  rotation,  by  the  effect  of 
which  the  water  is  pressed  out  of  it,  and  escapes  through  the  holes  in 
the  bottom.  A  rotation  of  25  turns  per  second,  or  1500  per  minute,  is 
given  to  these  drying  cylinders,  by  which  the  linen,  however  moist  it 
may  be,  is  rendered  so  nearly  dry  that  a  few  minutes'  exposure  in  the 
air  renders  it  perfectly  so.  In  large  linen  manufactories  this  machine 
produces  a  great  saving  of  labor  in  the  laundry  department. 

In  the  motion  of  the  heavenly  bodies  we  find  the  most  wonderful  examples 
of  the  action  of  central  forces,  acting  as  they  do  to  prevent  the  moon  from  fall- 


32  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

ing  upon  the  earth,  and  the  planets  into  the  sun.     The  action  of  centrifugal 
force  will  be  further  considered  in  connection  with  terrestrial  gravity. 

54.  Analysis  of  the  motion  produced  by  central  forces. — 
Let  a  body  placed  at  a,  fig.  21,  receive  an  impulse  which  would  carry  it  to  d  in 
one  second,  or  any  small  portion  of  a  second,  and  21 

let  it  be  attracted  towards  c  by  a  constant  force 
which  would  move  it  to  b  in  the  same  time  that  the 
first  impulse  would  carry  it  to  d,  then  by  the  prin- 
ciples of  the  composition  of  forces  it  will  be  found 
at  the  end  of  the  given  time  at  e,  and  if  the  attrac- 
tive force  should  then  cease  it  would  continue  to 
move  in  the  direction  e  m.  If  the  attractive  force 
continues,  the  body  will  be  found  at  g  at  the  end 
of  the  second  period.  As  the  central  force  is  con- 
tinually acting,  the  body  will  diverge  more  and 
more  from  the  direction  of  the  first  force,  and  will 
describe  a  curve.  As  the  attractive  force  acts 
always  towards  the  central  point  c,  the  body 
will  revolve  around  that  point.  If  the  relation  of 
the  two  forces  is  such  that  c  e,  eg,  &c.,  are  each 
equal  to  c  a,  the  curve  of  revolution  will  be  a 
circle.  In  most  other  cases  the  curve  of  revolution 
will  be  an  ellipse. 

If  the  curve  described  is  a  circle,  and  we  assume 
the  arc  a  e  to  be  very  small,  it  will  not  sensibly  differ  from  a  straight  line,  and 
according  to  well  known  geometrical  principles  we  shall  have 

ab  :  ae  =  ae  :  ao. 


ab  = 


That  is,  the  centrifugal  and  centripetal  forces  of  a  body  describing  a  circle 
with  uniform  velocity  are  directly  proportional  to  the  square  of  the  velocity,  and 
inversely  as  the  diameter  of  the  circle. 

The  relation  of  these  forces  may  be  expressed  differently.  Considering  a  e 
as  the  space  described  iu  one  second,  it  will  be  the  velocity  of  the  body ;  but  in 
curvilinear,  just  as  in  rectilinear  movement,  the  velocity  is  equal  to  the  distance 
divided  by  the  time,  i.  e.,  equal  to  the  circumference  of  the  circle  divided  by  the 
time  of  revolution.  Let  R  represent  the  radius  of  the  circle,  T  the  time  of 
revolution,  v  the  velocity,  and  TT  the  ratio  of  the  circumference  to  the  diameter.* 

27TjK 

and  we  shall  have  a  e  =  v  =  .     Substituting  this  value  of  a  e  in  the  pre- 
vious equation,  and  considering  that  a  o  =  2R,  we  shall  have 
_ 

: 
Therefore  the   attractive   force   would   generate   in   one   second   a  velocity 


*  The  ratio  of  the  circumference  of  a  circle  to  its  diameter  is  3-14159,  and 
this  number  is  usually  represented  by  the  Greek  letter  TT  in  mathematical  for- 
mula. 


MOTION   AND   FORCE.  33 


expressed  by  twice  a  I,  the  distance  passed  over,  equal  to  —  —  .      The   angular 

velocity  per  second  is  expressed  by  the  actual  velocity,  divided  by  the  radius  ; 
calling  this  angular  velocity  V,  we  have 


=  vs. 

The  centrifugal  or  (which  is  the  same  thing)  the  centripetal  force  varies  directly 
as  the  radius  of  the  circle  of  revolution  multiplied  by  the  square  of  the  angular 
velocity.  Also  if  two  bodies  move  in  different  circles  and  in  different  times,  their 
centrifugal  and  centripetal  forces  will  be  directly  as  the  radii  of  their  circles,  and 
inversely  as  the  squares  of  the  times  of  revolution. 

It  is  also  evident  that  the  centrifugal  force  is  proportional  to  the  mass  of  the 
body. 

55.  Bohnenberger's  apparatus.  —  In  consequence  of  the  operation 
of  the  law  of  inertia,  moving  bodies  preserve  their  planes  of  motion. 
This  is  true  as  well  of  planes  of  rotation  as  of  planes  in  a  rectilinear 
direction.  By  means  of  Bohnenberger's  apparatus 

we  may  illustrate  the  tendency  of  rotating  bodies 

to  preserve  their  plane  of  rotation,  and  the  invaria- 

bility of  the  axis  of  the  earth  during  its  revolution. 

Bohnenberger's  apparatus  consists  of  three  rings, 

A  A  A,  fig.  22,  placed  one  within  the  other  ;  the 

two  inner  ones  are  movable,  and  connected  by 

pins  at  right  angles  to  each  other,  in  the  same 

way  as  the  gimbals  that  support  a  compass.     In 

the  smallest  ring  there  is  a  heavy  metallic  ball 

B  supported  on  an  axis,  which  also  carries  a  little  pulley  c.     The  ball 

is  set  in  rapid  rotation  by  winding  a  small  cord  around  c,  and  suddenly 

pulling  it  off.     The  axis  of  the  ball  will  continue  in  the  same  direc- 

tion, no  matter  how  the  position  of  the  rings  may  be  altered  ;  and  the 

ring  which  supports  it  will  resist  a  considerable  pressure  tending  to 

displace  it. 

56.  Parallelogram  of  rotations.  —  It  has  been  shown   (48)  that 
rotary  motion  is  produced  by  two  equal  parallel  forces  acting  in  oppo- 
site directions.     If  two  new  equal  parallel  forces  act  upon  the  same 
body,  tending  to  produce  rotation  about  another  axis  situated  in  the 
same  plane,  the  compound  resultant  will  tend  to  produce  rotation  about 
a  third  axis,  situated  in  the  same  plane,  between  the  directions  of  the 
other  two. 

Let  the  irregular  body  shown  in  fig.  23,  while  rotating  about  the  axis 

A  X  be  suddenly  acted  upon  by  forces  tending  to  produce  rotation  about 

the  axis  AY.     Suppose  the  parts  of  the  .body  lying  between  AX  and 

AY  to  be  impelled  in  opposite  directions  by  the  two  rotary  forces. 

6 


34 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


Take  any  point,  as  P,  and  drawing  from  P  perpendiculars  upon  the 
two  axis,  let  P  C  =  y  and  P  B  =  x,  also  let 
v  represent  the  angular  velocity  about  the 
axis  A  X,  and  v/  the  angular  velocity  about 
the  axis  A  Y,  then  will  vx  —  v'y  express 
the  resultant  force  exerted  upon  the  point 
P.  Now  since,  if  the  point  P  were  taken 
in  the  axis  AX,  we  should  have  vx  =  0,  and 
if  P  were  taken  in  A  Y  we  should  have  v'y 
—  0,  it  is  evident  that  P  may  be  so  taken 
that  vx  —  v'y  =  0,  or  vx  =  v'y.  Lay  off  on  A  X  a  distance  A  E,  such 
that  A  E  :  A  C  =••  v :  v',  construct  the  parallelogram  A  C  D  E,  and  draw 
the  diagonal  A  D ;  then  AE  :  A  C  =  D  C  :  D  E  =  v  :  v'  =  y  :  x.  But 
every  point  on  the  line  AD  Xx  will  have  the  same  relation  to  the  axis 
AX  and  AY.  Hence  every  point  in  this  line  will  remain  at  rest,  and 
A  X'  becomes  the  resultant  axis  of  rotation,  in  virtue  of  the  forces  pre- 
viously tending  to  produce  rotation  about  the  two  component  axes. 

To  determine  the  velocity  of  rotation  about  the  resultant  axis  A  X', 
take  any  point,  as  C,  on  the  axis  A  Y.  At  this  point  v'y  =  0,  and  the 
point  C  has  no  tendency  to  move  except  that  given  by  the  moment  vx 
about  the  axis  A  X.  Draw  the  perpendiculars  C  R  and  C  Q  upon  A  X 
and  A  X'  respectively.  Represent  C  R  by  r,  and  C  Q  by  r",  and  denote 
the  angular  velocity  about  A  X'  by  v".  Now  as  the  distance  passed 
over  by  the  point  C  during  any  instant  depends  only  on  the  moment 
vx,  it  will  be  the  same  whether  the  rotation  takes  place  about  A  X  or 


hence  vr  =  v"r 


/.  v"  =  —.   The  triangles  A  CD  and  A  CE 


are  equal,  being  each  one-half  the  parellelogram  AC  D  E,  hence  ADX 
CQ^AEXCR,    smdADXr"  =  vr,  hence  AD  =  ^.  Comparing 

this  equation  with  the  value  of  v"  found  above,  we  find  that  v"  —  AD. 

From  the  above  reasoning  it  appears  that, — 

Where,  a  body  is  acted  upon  by  two  systems  of  forces,  tending  to  pro- 
duce rotations  about  two  separate  axes,  lying  in  the  same  plane,  the 
resultant  motion  will  be  rotation  about  a  new  axis,  represented  in  direc- 
tion by  the  diagonal  of  a  parallelogram,  the  sides  of  which  will  be  repre- 
sented by  the  component  axes  of  rotation,  and  the  magnitudes  of  the  sides 
by  the  forces  tending  to  produce  rotation  about  those  axes.  The  velocity 
of  rotation  about  the  new  axis  represented  in  direction  by  the  diagonal 
of  the  parallelogram,  will  be  measured  by  the  length  of  the  diagonal. 

From  the  same  principles  it  follows  that,  If  a  body  is  acted  upon  by  three 
systems  of  forces,  tending  to  produce  rotation  about  three  different  axes,  all 


MOTION    AND    FORCE. 


35 


passing  through  the  same  point,  the  resultant  motion  will  be  rotation  about  a 
new  axis,  represented  in  direction  by  the  diagonal  of  a  parallelopipedon  formed 
on  the  original  axes  as  adjacent  edges,  with  the  magnitude  of  those  edges  corres- 
ponding to  the  respective  forces  acting  about  those  axes,  and  the  velocity  of  the 
new  rotation  will  be  represented  by  the  length  of  the  diagonal  of  the  parallelo- 
pipedon. 

In  describing  rotary  motions  it  is  customary  to  speak  of  the  motion 
as  right-handed  or  positive,  or  as  left-handed  or  negative. 

Let  A  X,  A  Y,  A  Z,  fig.  24,  be  three  rectangular  axes,  passing  through  the 
point  A,  which  is  called  the  origin  of  co-ordinates.  Distances  measured  from  A 
towards  either  X,  Y,  or  Z,  are  called  positive,  and  distances  measured  in  the 
opposite  directions  are  called  negative.  If  a  body  revolves  about  either  of  these 
axes,  or  about  any  axis  drawn  through  A,  in 
such  a  direction  as  to  appear,  to  an  eye  placed 
beyond  it,  and  looking  towards  A,  to  move  in 
the  same  direction  as  the  hands  of  a  watch, 
when  we  look  at  the  dial,  such  motion  is 
called  right-handed,  or  positive  rotation.  If 
rotation  takes  place  in  the  opposite  direction, 
it  is  called  left-handed,  or  negative.  If  a  body 
revolves  in  the  directions  shown  in  either  part 
of  fig.  24,  the  rotation  is  called  right-handed, 
or  positive.  If  the  three  axes,  A  X,  A  Y,  A  Z, 
tfere  brought  towards  each  other  till  they  co- 
incide,  these  rotations  would  all  coincide  in 
direction. 

57.  The  gyroscope,  or  rotascope,  is  an  instrument  exhibiting  some 
remarkable  results  of  the  combination  of  rotary  motions,  and  which 
also  shows,  as  in  Bohnenberger's  apparatus,  the  tendency  of  rotating 
bodies  to  preserve  their  plane  of  rotation.  A  common  form  of  the 
rotascope,  fig.  25,  con- 
sists of  a  metal  ring,  A  B, 
inside  of  which  is  placed 
a  metallic  disk,  C  D,  / 
loaded  at  its  edge,  and  / 
which  turns  independ-  \ 
eritly  of  the  ring,  upon 
the  axis.  Motion  is  com- 
municated by  means  of  a 
cord,  wound  around  the 
axis  of  the  disk  and  sud- 
denly drawn  off.  If,  when 
the  disk  is  rotating  rapid- 
ly, it  be  placed  on  the  steel  pin  F,  supported  on  the  column  G,  it  seems 
indifferent  to  gravity,  and  instead  of  dropping  it  begins  to  revolve  in  a 
horizontal  orbit,  H  I,  about  the  vertical  axis  F  G,  in  a  direction  corres- 
ponding with  the  movement  of  the  lower  part  of  the  disk.  This  hori« 


86 


PHYSICS    OP    SOLIDS    AND    FLUIDS. 


zontal  revolution  gradually  increases  in  velocity,  and  the  free  end  of 
the  disk,  in  some  circumstances,  vibrates  upward  and  downward,  in 
spiral  curves.  When  the  rotation  of  the  disk  is  considerably  diminished 
by  friction,  gravity  gradually  prevails  over  the  supporting  power,  and 
at  length  the  disk  falls,  in  a  descending  spiral  curve. 

To  explain  the  movement  of  the  gyroscope,  let  the  axis  Y  A  Y', 
fig.  24,  correspond  to  the  standard.  A 
being  the  point  where  one  end  of  the 
axis  of  the  revolving  disk  is  supported. 
Let  A  X  correspond  to  the  horizontal 
axis  around  which  the  disk  of  the 
gyroscope  revolves,  and  let  Z  A  Z'  be 
another  horizontal  axis,  at  right  angles 
with  A  X  and  A  Y.  Let  a  right- 
handed  rotation  be  given  to  the  disk  of 
the  gyroscope  about  the  axis  A  X,  as 
indicated  by  the  arrows.  While  the 
force  of  gravity  causes  the  free  end  of  the  axis  to  descend,  there  will 
also  be  commenced  a  right-handed  rotation  about  the  axis  A  Z.  Both 
these  rotations  may  be  supposed  to  have  constant  velocities  for  an  infi- 
nitely short  interval  of  time.  Let  v  denote  the  angular  velocity  about 
A  X,  and  v'  the  angular  velocity  about  A  Z.  Lay  off  on  A  X  a  distance 
A  B  =  v,  and  on  A  Z  a  distance  A  C  =  v',  complete  the  parallelogram 
A  B  D  C  ;  then  the  diagonal,  A  D,  will  represent  the  resultant  axis  of 
rotation,  and  the  length  of  this  diagonal  will  represent  the  velocity  of 
rotation  about  the  new  axis.  As  the  disk  can  only  rotate  about  the  new 
axis  by  moving  towards  D,  there  will  thus  be  commenced  a  new  move- 
ment of  rotation,  which  we  may  call  a  horizontal  revolution  about  the 
perpendicular  axis.  This  will  be  a  right-handed  rotation  about  A  Y. 

We  now  have  to  consider  rotation  about  three  axes,  all  passing 
through  the  axis  A.  To  construct  the  position  of  the  resultant  axis 
for  the  second  instant,  lay  off  on  A  Z,  considered  as  perpendicular  to 
A  D  and  to  A  Y,  a  distance  to  represent  the  angular  velocity  due  to 
gravity,  and  on  A  Y  the  angular  velocity  in  the  orbit,  acquired  in 
passing  from  the  position  A  X  to  A  D;  AD  represents  the  velocity 
with  which  the  disk  rotates.  Construct  a  parallelopipedon  on  these 
three  lines,  and  draw  its  diagonal  through  A.  This  diagonal  will  evi- 
dently give  a  direction  that  will  continue  the  horizontal  revolution 
already  commenced,  and  also  an  upward  tendency  in  opposition  to 
gravity.  The  same  process  of  construction  might  be  continued  for 
every  instant  the  rotation  continues.  It  is  evident  that  the  horizontal 
rotation  would  continually  increase  in  velocity,  and  the  tendency  to 


MOTION    AND    FORCE.  37 

lift  the  end  of  the  axis  of  the  disk  would  also  increase,  were  it  not  con- 
tinually counteracted  by  the  action  of  gravity.  As  the  velocity  of  the 
rotation  of  the  disk  is  continually  retarded  by  friction,  the  lifting  power 
exerted  against  gravity  diminishes  until  the  disk  gradually  descends 
with  a  spiral  revolution,  and  the  instrument  is  brought  to  rest. 

If  the  disk  of  the  gyroscope  were  made  to  rotate  in  the  opposite  direc- 
tion, or  left-handed,  the  motion  around  the  axis  Z  A  Z' ',  caused  by 
gravity,  would  also  be  left-handed  when  considered  from  the  point  Z', 
and  the  resultant  A  D'  would  lie  on  the  opposite  side  of  A  X.  This 
would  also  give  a  left-handed  rotation  about  the  perpendicular  A  Y, 
and  the  resultants  would  all  be  found  in  the  solid  angle  A  X,  A  Y, 
A  TS,  and  again  the  tendency  would  be  to  counteract  the  depressing 
force  of  gravity.  Thus  we  should  have  the  rotating  disk  supported, 
as  experience  shows  it  is,  in  whichever  direction  it  is  caused  to  rotate. 

If  the  weight  of  the  gyroscope  were  counterbalanced  (as  it  is  frequently  con- 
structed) by  an  equal  weight  on  the  opposite  side  of  the  vertical  axis,  it  can 
readily  be  seen  that  it  would  have  no  horizontal  rotation.  If  the  counter- 
balancing weight  were  so  great  as  to  raise  the  disk  upward,  the  horizontal 
revolution  would  be  performed  in  the  opposite  direction. 


Problems  on  Weights  and  Measures. 

1.  (a.)  How  many  English  yards  are  contained  in  135  French  kilometres  ? 
(6.)  Reduce  2-5934  centimetres  to  English  inches,     (c.)  What  part  of  an  English 
inch  is  1  millimetre?     (d.)  Reduce  3  centimetres  to  inches. 

2.  (a.)  Reduce  4  feet  7  inches  to  French  measure.     (6.)  Reduce  225  rods  to 
French    measure    of    length.      (c.)    Reduce    13   miles    to   French   kilometres. 
(d.)  Reduce  5  yards  to  French  metres. 

3.  (a.)  Reduce  3  pints  to  litres  and  cubic  centimetres.     (6.)  Reduce  5  litres 
to    English    measure,      (c.)    Reduce   7   gallons   to   litres    and   decimal   parts. 
(d. )  Reduce  7  cubic  centimetres  to  English  pints. 

4.  Reduce,  by  means  of  the  Table  II., — (a.)  25  inches  to  decimal  parts  of  a 
metre.     (6.)  139  centimetres  to  American  inches,     (c.)  75  feet  to  metres,     (d.)  5 
kilometres  to  American  yards. 

5.  Reduce,  by  means  of  the  table  at  the  end  of  the  book, — (a.)  7i  pints   to 
cubic  centimetres.     (6.)  10  gallons  to  cubic  centimetres,     (c.)  735  cubic  centi- 
metres to  gallons. 

Problems  on  Motion. 
*» 

6.  A  body  passes  uniformly  over  a  distance  of  200   yards  in  1  hour  and  6 
minutes  :  what  is  the  numerical  value  of  its  velocity,  according  to  the  usual 
conventions  concerning  the  units  of  space  and  time  ? 

7.  A  body  is  observed  to  describe  uniformly  a  feet  in  n  seconds ;  supposing 
the  unit  of  time  to  be  1  minute,  what  must  be  the  unit  of  distance  in  order  that 
the  numerical  value  of  the  body's  velocity  may  be  1  ? 

8.  A  man  walks  with  a  velocity  represented  by  2,  and  he  finds  that  he  walks 
7  miles  in  2  hours ;  if  1  foot  be  the  unit  of  length,  what  is  the  unit  of  time  ? 

9.  A  particle  is  moving  with  such  a  velocity,  and  in  such  a  direction,  that 

6* 


38  PHYSICS    OF    SOLIDS    AND    FLUIDS 

the  resolved  parts  of  its  velocity  in  the  directions  of  two  lines  perpendicular  to 
each  other,  are  respectively  3  and  4 ;  determine  the  direction  and  velocity  of 
the  particle's  motion. 

10.  A  is  a  more  powerful  and  a  heavier  man  than  B ;  the  greatest  weights 
which  they  can  lift  are  as  8  :  7,  and  their  own  weights  are  as  7:6.     Which  is 
likely  to  be  the  faster  runner  of  the  two? 

11.  Supposing  a  body  acted  upon  by  a  force  capable  of  causing  an  accelera 
tion  of  3  feet  per  second  :  what  will  be  its  velocity,  and  the  distance  passed 
over,  at  the  end  of  1  minute  ? 

12.  What  velocity  will  be  acquired  by  a  body  moving  100  feet,  under  the  in- 
fluence of  a  force  capable  of  causing  an  acceleration  of  2  feet  per  second  ? 

13.  If  a  body  starting  with  an  initial  velocity  of  125  per  second  is  found  to 
come  to  rest  after  the  end  of  5  seconds,  what  is  the  amount  of  retardation,  and 
what  distance  has  the  body  passed  over  ? 

14.  If  a  body  weighing   100  pounds  moves  with   a  velocity  of  a  mile  in  7 
seconds,  what  must  be  the  weight  of  a  body  moving  3  feet  per  second,  to  have 
the  same  momentum  as  the  former  ? 

15.  If  a  ship  weighing  2000  tons  strikes  a  pier  with  a  velocity  of  6  inches  per 
second,  what  velocity  must  be  given  to  a  64  pound  shot,  in  order  that  it  may 
strike  an  obstacle  with  the  same  momentum  ? 

16.  Uniform  force  is  defined  as  that  which  generates  equal  velocities  in  equal 
times ;  would  it  be  correct  to  define  it  as  that  which  generates  equal  velocities 
while  the  body  moves  through  equal  spaces  ? 


CHAPTER  III. 

GRAVITATION. 

§  1.  Direction  and  Centre  of  Gravity. 

58.  Definition. — The  fall  of  unsupported  bodies  to  the  earth,  and 
the  pressure  exerted  by  bodies  at  rest  on  the  earth's  surface,  is  due  to 
the  force  of  gravity.     The  amount  of  this  force  seen  in  the  downward 
pressure  of  any  body  is  called  its  weight.     Weight  is  due  to  the  earth's 
attraction  for  the  body  weighed.     This  is  only  a  particular  case  of  a 
general  force  in  nature,  by  reason  of  which  all  bodies  in  the  universe 
attract  each  other,  thereby  maintaining  the  order  and  stability  of  the 
heavenly  bodies. 

59.  Law  of  universal  gravitation. — The  law  of  gravitation   is 
stated  as  follows :  Every  particle  of  matter  attracts  every  other  particle 
in  the  DIRECT  ratio  of  its  mass,  and  in  the  INVERSE  ratio  of  the  square 
of  its  distance. 

Let  M  and  W  represent  two  masses,  D  and  D/  the  distances.     Take 
G  and  g  the  absolute  gravities  of  the  two  masses  at  a  given  distance, 


GRAVITATION  39 

and  g  :  G/,  the  ratio  of  the  force  of  gravity  at  distances  D  and  D/,  then 

G  :    g  =  M      :  M', 

g  ;  G'  =  D/2    :  D2,  compounding  these  proportions  we  have 

G:  G'=MD":M'D\    hence    G:,&::~-~, 


Or  the  force  of  gravity  of  different  bodies,  at  different  distances,  is 
directly  as  the  masses  and  inversely  as  the  squares  of  the  distances. 

This  law  was  discovered  in  1666,  by  Sir  Isaac  Newton.  Reflecting 
on  the  power  which  causes  the  fall  of  bodies  to  the  earth,  and  bearing 
in  mind  that  this  power  is  sensibly  the  same  on  the  highest  mountain 
as  in  the  deepest  valleys,  he  conceived  that  it  might  extend  far  beyond 
this  earth,  and  even  exert  its  influence  through  all  space.  He  assumed, 
in  conformity  to  the  relation  already  discovered  by  Kepler,  between 
the  times  of  revolution  of  the  planets  and  their  distances  from  the  sun, 
that  this  force  must  diminish  in  the  inverse  ratio  of  the  square  of  the 
distance.  His  first  results  were  unsatisfactory,  because  (as  afterwards 
appeared)  he  used  in  his  calculations  an  erroneous  value  of  the  earth's 
radius.  But  in  June,  1682,  he  received  Picard's  new  measurement  of 
the  arc  of  the  meridian  in  France,  from  which  it  appeared  that  the 
radius  of  the  globe  was  nearly  one  seventeenth  greater  than  had  been 
previously  supposed.  Armed  with  these  new  data,  Newton  resumed 
his  calculations,  and  in  1687  published  his  great  work,  the  "  Principia," 
in  which  he  develops  the  consequences  of  his  great  discovery  of  the 
laws  of  gravitation. 

60.  Direction  of  terrestrial  attraction.  Centre  of  gravity.  — 
As  the  direction  of  a  force  is  the  direction  of  the  motion  or  pressure 
caused  by  it,  (40),  it  follows  that  a  body  falling  under  the  influence  of 
gravity  moves  on  a  line,  which  would  pass,  if  extended,  through  a 
point  sensibly  near  the  centre  of  the  globe.  This  point  26 

in  the  globe  is  called  its  centre  of  gravity.  Therefore 
the  direction  of  the  force  of  gravitation  is  in  the  line 
uniting  the  centre  of  gravity  of  the  earth  with  that  of 
the  attractive  body.  The  plumb  line,  fig.  26,  gives  this 
direction.  Here  a  mass  of  lead  is  suspended  by  a  string, 
and  when  it  is  at  rest,  it  is  evident  without  a  mathe- 
matical demonstration,  that  the  direction  of  the  pressure, 
and  hence  that  of  the  force  of  gravitation,  coincides 
with  that  of  the  plumb  line.  This  direction  is  called 
the  vertical,  and  a  direction  perpendicular  to  it  is  called 
the  horizontal.  Such  is  the  surface  of  a  liquid  at  rest. 

It  is  plain,  on  the  slightest  reflection,  that  as  the 
plumb  line  coincides  at  every  point  of  the  earth's  surface  very  nearly 


40 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


to  the  radius  of  the  same  points,  that  several  plumb  lines  placed  near 
each  other,  are  sensibly  parallel  to  each  other  (but  are  not  mathemati- 
cally so),  because  the  distances  between  them  are  almost  insensible 
compared  to  the  length  of  a  radius  of  the  earth.  The  convergence  is 
only  one  minute  to  a  geographical  mile. 

The  rotation  of  the  earth  does  not  affect  the  direction  of  a  falling  body, 
because  it  had,  before  it  fell,  the  same  velocity  as  the  earth  itself.  Thus  a  bullet 
dropped  from  the  mast-head  of  a  ship,  sailing  never  so  rapidly,  falls  to  the  deck 
on  precisely  the  same  spot  as  if  the  ship  were  motionless — in  virtue  of  the  prin- 
ciple of  the  composition  of  motion,  (45).  Nevertheless,  if  bodies  fall  from  a 
very  great  height,  there  is  an  easterly  deviation,  as  Newton  announced,  because 
at  the  point  of  departure,  on  a  circumference  sensibly  larger  than  at  the  surface 
of  the  earth,  the  body  has  a  horizontal  velocity  sensibly  greater  than  the  latter. 
For  a  height  of  550  feet,  calculation  indicates  a  deviation  of  0-108  inch,  and 
experiment  gave  Reich  in  the  deep  mines  of  Freyberg  O'llO  inch. 

61.  Point  of  application  of  terrestrial  attraction. — As  every 
particle  of  a  body  is  equally  attracted  by  the  earth,  there  must  be  as 
many  points  of  application  for  this  force  as  there  are  particles  of  matter 
in  the  body.  Hence  from  the  principle  (46)  for  finding  the  resultant 
of  a  system  of  parallel  forces,  it  follows  that  if  a  tody  be  supported  by 
a  flexible  cord  from  a  fixed  point,  it  cannot  remain  at  rest  unless  the 
resultant  of  all  the  parallel  forces  which  gravity  exerts  on  it  passes 
through  the  point  of  support. 

It  is  thus  possible  to  determine  experimentally  the  position  of  the 
resultant  of  the  system  of  parallel  forces  which  gravity  exerts  upon 
a  body. 

For  example,  in   fig.  27, 

the  chair  is  held  by  a  string 

attached  to  one  arm,  and  the 

resultant  of  the   forces  ex- 
erted by   gravity  is  in   the 

line  A  B,  in  which  the  chair 

comes   to  rest.     But  if  the 

chair  is  supported  from  an- 
other point,  as  in  fig.  28,  it 

will  come  to  rest  in  a  new 

position,  and   the   resultant 

will  now  be  found  also  in  a 

new  position,  namely  in  the 

line  C  D,  and  so   for  every 

new  point  of  suspension  we 

«an    by   experiment    demonstrate  a    different    position    for 
sultant. 


27 


23 


GRAVITATION.  41 

62.  Centre  of  gravity.— As  there  is  in  every  solid  body  a  point 
about  which,  whan  it   is   suspended,  its   molecules   are  equally  dis- 
tributed in  every  direction,  all  the  attractions  exerted  upon  them  may 
be  replaced  by  a  single  resultant  force  applied  at  this  point.    But 
whatever  position  the  body  may  assume,  the  resultant  of  its  parallel 
forces  of  gravity  will  always  pass  through  the  same  point.     This  com- 
mon point,  of  intersection  of  the  resultants  of  gravity  in  any  body,  is 
called  the  centre  of  gravity.    As  we  may  find  the  resultants  experi 
mentally,   so   also  is   the  centre  of  gravity  of  any  solid 

easily  found.  If  any  irregular  solid  is  suspended,  as  in 
fig.  29,  its  centre  of  gravity  will  lie  in  the  line  c  d,  pro- 
longed through  its  axis.  It  will  alst  lie  in  the  line  a  b, 
by  which  the  body  is  a  second  time  suspended,  and  being 
found  in  both  lines,  it  must  necessarily  be  at  their  inter- 
section. A  correct  conception  of  the  important  relations 
of  the  centre  of  gravity  lies  at  the  foundation  of  the 
whole  science  of  mechanics,  and  especially  of  equi- 
librium. 

63.  Corollaries. — (1.)  The  centre  of  gravity  must  be  regarded  as 
the  point  of  application  of  the  resultant  of  the  forces  which  gravity 
exerts  upon  the  molecules  of  any  body.     This  is  proved  by  the  fact 
that  the  point  of  application  is  any  point  on  the  line  of  the  resultant, 
and  that  the  centre  of  gravity  is  a  point  common  to  all  the  resultants. 

(2.)  When  the  centre  of  gravity  is  supported,  the  body  remains  at 
rest.  Conceive  the  irregular  mass,  fig.  29,  to  be  sustained  on  an  axis 
passing  through  a  b  or  cd,  the  body  will  remain  at  rest  in  whatever 
position  of  revolution  it  may  be,  on  either  of  these  axes,  since  the  whole 
intensity  of  the  forces  of  gravity  is  expended  in  pressure  against  the 
points  of  support. 

(3.)  The  sum  of  all  the  attractions  exerted  by  any  mass  of  matter 
may  be  conceived  as  proceeding  from  its  centre  of  gravity.  Newton 
has  demonstrated  that  a  particle  of  matter  placed  without  a  hollow 
sphere  is  attracted  in  precisely  the  same  manner  as  if  the  whole  mass 
of  the  sphere  were  collected  at  its  centre,  and  constituted  a  single  par- 
ticle there.  The  same  must  be  true  of  solid  spheres,  since  they  may  be 
regarded  as  made  up  of  a  great  number  of  hollow  spheres,  having  the 
same  centre. 

The  principle  that  action  and  reaction  are  equal  and  opposite  (27), 
applies  perfectly  to  the  mutual  attractions  of  the  masses  of  matter. 
Hence  follows  the  somewhat  startling  inference  that  the  earth  must 
rise  to  meet  a  falling  body.  This  is  unquestionably  true,  but  since  the 
mass  of  the  earth  is  almost  infinitely  greater  than  that  of  any  body 


42  PHYSICS    OF    SOLIDS   AND    FLUIDS. 

falling  on  its  surface,  its  motion  must  likewise  be  almost  infinitely 
small,  since  the  velocity  v',  acquired  by  the  earth  at  the  end  of  one 
second  is  as  much  less  than  the  velocity  v,  acquired  by  the  falling 
body,  as  the  mass  of  the  body  (m)  is  less  than  the  mass  of  the  earth 
(M],  or  v'  :  v  =  m  :  M. 

64.  Centre  of  gravity  of  regular  figures. — In  case  of  solids  which 
have  a  regular  figure,  and  uniform  density,  it  is  not  necessary  to  resort 
to  experiment.  In  such  bodies,  the  centre  of  gravity  coincides  with 
the  centre  of  figure,  and  to  find  it  is  a  question  purely  geometrical. 
The  truth  of  this  assertion  may  be  shown,  if  we  suppose  a  plane  or 
line  to  be  divided  into  two  equal  and  similar  parts,  so  that  its  mole- 
cules are  arranged  two  by  two,  with  respect  to  the  dividing  line.  Take 
any  two  molecules  similarly  situated,  on  opposite  sides  of  the  division, 
their  attractions  will  be  equal  and  opposite ;  and  so  also  of  every  other 
pair ;  therefore,  the  resultant  of  the  system  must  be  at  the  point  of 
division,  and  the  centre  of  gravity  is  there  also. 

The  centre  of  gravity  of  a  circle,  or  sphere,  is  at  the  centre  of  each  ; 
of  a  parallelogram  or  parallelepiped,  at  the  intersection  of  the  diagonals  ; 
and  of  a  cylinder  at  the  middle  point  of  its  axis.  To  find  the  centre 
of  gravity  of  a  triangle,  fig.  30,  draw  a  line  A  D,  from  the  vertex  to 
the  middle  point  of  the  base;  it  will  30 

divide  equally  all  the  lines,  as  m  n,  drawn 
parallel  to  the  base.  If  the  triangle  is 
placed  so  that  the  line  A  D  may  be 
exactly  over  the  edge  of  the  prism  P  Q, 

each  one  of  the  rows  of  molecules  com-          / r — ^^s. 

posing  the  figure,  as   m  n,  will   be   in         /      ....--''\ 
equilibrium  on  the  edge  of  the  prism,  ' 

since  it  is  supported  at  its  centre.  The 
same  will  be  true  when  they  are  united, 
and  the  triangle  will  not  tend  more  to  one  side  than  another;  hence  its 
centre  of  gravity  must  be  in  the  line  A  D,  and  for  a  like  reason,  also 
in  the  line  B E  (situated  similarly  to  AD),  and  therefore  at  their  inter- 
section G.  It  may  be  shown  geometrically  that  the  point,  thus  found 
divides  the  line  joining  the  summit  and  the  middle  of  the  base,  into 
two  parts,  of  which  the  one  nearest  the  vertex  is  double  that  nearest 
the  base. 

SUPPORT  OF  A  TRIANGULAR  MASS  AT  ITS  ANGLES. — If  it  were  required  to  sup- 
port a  triangular  block  of  marble  at  its  angles,  we  may  find  what  part  of  the 
weight  will  be  sustained  by  each  support,  by  applying  the  foregoing  principles. 
The  weight  of  the  block,  fig.  31,  which  we  will  suppose  to  be  45  Ibs.,  is  a  force 
applied  to  its  centre  of  gravity,  g.  We  have  stated  that  the  distance  b  g  is  twice 


GRAVITATION. 


43 


the  distance  g  d,  and  hence  we  may  resolve  the  vertical  force  of  45  Ibs.,  acting 

at  g,  into  two  others;   one  of  15  Ibs.  at  6,  and  the  31 

other  of  30  Ibs.  at  d ;  but  the  last  force,  since  it  acts 

at  the  middle  point  of  a  c,  may  also  be  resolved  into 

two  others  of  15  Ibs.  each,  acting  the  one  at  a,  and 

the  other  at  c.     Hence  the  weight  of  the  triangle  is  c 

equivalent  to  three  equal  forces  acting  vertically  at 

its  angles  ;    and  the  three  points  of  support  sustain  15 

equal  pressures,  whatever   may  be   the  form  of  the 

triangle. 

65.  Centre  of  gravity  lying  without  the  body.— The  centre 
of  gravity  is  not,  necessarily,  in  the  body  itself,  32 

but  may  be  in  some  adjoining  space.  This  is 
evidently  true  of  the  solid  ring,  fig.  32,  and 
generally  of  any  hollow  vessel,  of  whatever 
form. 

Of  a  compound  body,  the  centre  of  gravity  is 
easily  found  by  composition  of  forces,  when  the 
weights  and  centres  of  gravity  of  the  parts  are 
known. 

60.  Equilibrium  of  solids  supported  by  an  axis. — A  solid  is  in 
equilibrium  when  its  centre  of  gravity  is  supported.  This  is  according 
to  §  63.  But  this  condition  may  be  fulfilled  in  different  ways,  according 
to  the  method  of  support.  If  a  disk  of  uniform  density,  fig.  33,  is  sup- 
ported by  an  axis,  passing  through  the  centre  a, 
which  is  also  its  centre  of  gravity,  it  will  be  in 
that  sort  of  equilibrium  which  is  called  indifferent, 
because  it  has  no  tendency  to  revolve,  either  to  the 
right  or  left,  but  remains  at  rest  in  all  positions. 
If  the  axis  passes  through  b,  the  disk  will  be  in 
stable  equilibrium ;  for  if  it  is  turned  about  its 
axis,  the  centre  of  gravity  will  move  in  the  arc  m  n, 
and  being  no  longer  vertically  below  the  axis,  it  will  not  be  directly 
supported  by  it,  but  tends  always  to  return  to  its  former  position.  If 
the  axis  is  at  c,  the  equilibrium  is  unstable  ;  for,  if  the  centre  of  gravity 
is  in  the  least  removed  from  a  position  vertically  above  the  axis,  it 
cannot  return,  but  it  will  describe  a  semicircle  in  its  descent,  until  it 
comes  to  rest  exactly  below  the  point  of  support. 

In  general  terms,  therefore,  a  body  attached  to  an  axis  may  be  in 
stable,  unstable,  or  indifferent  equilibrium,  according  as  its  centre  of 
gravity  is  below,  above,  or  upon  the  axis. 

67.  Equilibrium  of  solids  placed  upon  a  horizontal  surface. — 
In  bodies  placed  upon  a  horizontal  surface,  the  centre  of  gravity,  as  in 


33 


44 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


those  which  are  suspended,  tends  to  descend,  and  if  the  bodies  are  free 
to  move,  they  will  rest  in  one  of  the  positions  of  equilibrium  just 
named.  If  rays  are  drawn  from  the  centre  of  gravity  to  every  part  of 
the  surface,  some  of  these  rays  will  be  oblique,  and  some  perpendicular, 
or  normal  to  the  surface,  whatever  may  be  the  external  form  of  the 
body ;  and  among  the  normal  rays,  there  is  generally  a  longest  and  a 
shortest  ray.  If  the  body  rests  upon  the  plane,  at  the  extremity  of  one 
of  the  normal  rays,  its  centre  of  gravity  is  evidently  in  the  vertical  line, 
drawn  through  the  point  of  contact,  and  the  body  is  in  equilibrium. 
But  if  it  rests  at  the  extremity  of  an  oblique  ray,  the  centre  of  gravity 
is  not  supported,  since  it  is  not  in  the  vertical  of  the  point  of  contact, 
and  the  body  falls. 

If  the  normal  ray  at  the  point  of  contact  is  neither  longe&t  nor 
shortest,  but  simply  equal  to  the  adjacent  rays,  the  equilibrium  is  indif- 
ferent. Such  is  the  case  with  a  sphere,  placed  on  a  level  plane ;  it 
rests  in  every  position,  for  its  centre  of  gravity  can-  34 

not  fall  lower  than  it  is.  But  this  position  cannot 
be  assumed  by  a  body  not  strictly  spherical.  For 
example,  if  an  egg  rests  at  the  extremity  of  a  longest 
descending  ray,  a,  as  in  fig.  34,  it  will  be  in  unstable 
equilibrium,  since  motion  to  either  side  tends  to 
lower  the  centre  of  gravity,  and  enable  it  to  fall ;  but 
if  it  rests  at  the  extremity  of  a  shortest  ray,  a',  it 
will  be  in  stable  equilibrium,  since  any  motion  side- 
ways must  raise  the  centre  of  gravity,  and  it  will,  therefore,  fall  back 
to  its  original  position. 

68.  Centre  of  gravity  in  bodies  of  unequal  density  in  dif- 
ferent parts.— If  the  density  of  a  body  is  unequal  in  different  parts, 
its  centre  of  gravity  will  be  external  to  its  centre  of  magnitude,  and 
the  body  can  come  to  rest  in  only 

two  positions,   when    the  centre  of 

gravity  is  at  the  highest,  and  at  the 

lowest  place  in  the  vertical  of  the 

point  of  contact.     If  a  cylinder  of 

this  description  were  placed  upon  an 

inclined  plane,  as  in  fig.  35,  it  would 

be  in  equilibrium  when  its  centre  of 

gravity  was  at  either  e  or  a  ;  if  at  e, 

and  the  cylinder  were  moved  a  little  to  the  right,  the  centre  of  gravity 

would  fall  through  the  arc  e  a,  but  at  the  same  time  the  cylinder  itself 

would  perform  the  apparent  contradiction  of  ascending  the  plane. 

69.  Equilibrium  of  bodies  supported  in  more  than  one  point. — 


35 


GRAVITATION.  45 

When  a  body  is  supported  by  two  points,  the  vertical,  from  its  centre 
of  gravity,  ought  to  fall  on  the  centre  of  the  line  which  connects  them. 
If  a  body  has  four  points  of  support,  as  a  common  table,  the  vertical 
should  fall  upon  the  intersection  of  their  diagonals. 

In  carriages,  if  the  vertical  falls  in  a  different  manner,  the  load  is  improperly 
distributed,  and  the  carriage  will  be  liable  to  upset,  in  passing  over  an  uneven 
road. 

A  body  resting  on  a  base  more  or  less  extended,  will  be  in  equilibrium 
only  when  the  vertical  from  the  centre  of  gravity  falls  within  the  area 
of  the  base  ;  and  the  body  will  stand  firmer  in  proportion  as  the  centre 
of  gravity  lies  lower,  and  the  base  is  broader.  A  pyramid  is,  therefore, 
the  most  stable  of  all  structures. 

The  singular  feats  exhibited  by  children's  toys,  and  by  rope-dancers,  depend 
on  the  facility  with  which  the  centre  of  gravity  is  shifted. 

I  2.   Laws  of  Falling  Bodies. 

70.  Gravity  is  a  source  of  motion. — In  discussing  the  laws  of 
motion,  we  have  already  cited  gravitation  as  a  source  of  uniformly 
accelerated  motion.   We  have  now  to  consider  the  laws  of  falling  bodies, 
and  in  doing  so  we  shall  have  occasion  to  recapitulate  some  of  the 
ground  already  passed  over. 

71.  The  laws  of  falling  bodies  are  five,  as  follows : 

THE  FIRST  LAW  is — The  velocity  of  a  fatting  body  is  independent  of  its 
mass. 

Galileo  (born  1564),  who  first  demonstrated  the  laws  of  falling 
bodies,  at  Pisa,  argued  that  if  the  molecules  of  a  body  were  separated 
from  each  other,  each  molecule  would  fall  with  the  same  velocity,  since 
each  is  solicited  by  the  same  force ;  and  if  we  conceive  these  molecules 
reunited  into  a  mass,  each  particle  still  acts  alone,  and  hence  it  is  of  no 
importance  whether  the  particles  are  many  or  few.  The  velocity  of  the 
mass  will  be  that  of  one  of  its  particles — and,  consequently,  is  inde- 
pendent of  the  mass. 

THE  SECOND  LAW  is — The  velocity  of  a  falling  body  is  independent  of 
the  nature  of  the  body.  Experiment  alone  can  confirm  this  law,  which 
at  its  first  statement  appears  to  be  contradicted  by  common  obser- 
vation. 

For  example  :  a  gold  coin  falls  swiftly,  and  in  a  straight  line,  but  a  piece 
of  paper  descends  in  a  devious  course,  and  with  a  slow,  hesitating  motion. 
The  popular  explanation  is,  that  the  coin  is  heavy  and  the  paper  light ;  but 
this  cannot  be  the  true  reason,  since,  when  the  gold  is  beaten  out  into  thin 
leaves,  its  weight  remains  the  same,  but  the  time  of  its  fall  is  very  much. 
prolonged. 

7 


46  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

The  differences  in  the  time  and  manner  of  falling  are  caused  so  «ly 
by  the   resistance   of  the   air  ;   whick  resistance  varies,  36 

according  to  the  shape  and  volume  of  the  body,  and 
not  according  to  its  mass,  or  the  number  of  particles 
contained  in  it.  This  conclusion  is  established  by  the 
guinea  and  feather  experiment,  first  devised  by  New- 
ton, who  used  a  glass  tube  10  feet  long,  arranged  as 
in  fig.  36,  with  a  stopcock  for  removing  the  air  by  an  air- 
pump.  Bodies  of  unlike  density,  as  a  coin  and  piece  of 
paper,  within  the  tube  will,  when  it  is  suddenly  inverted, 
be  seen  to  fall  with  equal  rapidity,  and  strike  the  bottom 
together  ;  but  after  admitting  the  air,  the  one  will  descend 
swiftly,  and  the  other  will  be  retarded,  just  as  it  happens 
when  they  fall  under  ordinary  circumstances.  A  piece 
of  stiff  paper,  cut  to  the  exact  size  of  a  coin  and  placed  on 
it,  will  fall  with  it,  if  care  is  taken  to  drop  the  two  quite 
horizontally,  and  without  disturbing  the  position  of  the 
paper  on  the  coin.  This  simple  experiment  illustrates  the 
law  as  well  as  the  vacuum  tube,  the  resistance  of  the  air 
being  all  met  by  the  coin.  Thus,  when  no  resistance 
modifies  the  effects  of  gravity,  it  attracts  all  bodies  with 
the  same  energy,  and  gives  them  the  same  velocity,  what- 
ever may  be  their  weight,  and  whatever  the  kind  of  mat- 
ter of  which  they  are  composed. 

THE  THIRD  LAW  is  —  The  velocity  acquired  by  a  body 
falling  freely  from  a  state  of  rest  is  proportional  to  the 
times,  and  follows  the  order  of  the  natural  numbers  1,  2,  3, 
&c.  This  is  the  case  of  a  uniformly  accelerated  mo- 
tion, (32). 

THE  FOURTH  LAW  is  —  The  whole  spaces  passed  over  by  a 
falling  body,  starling  from  a  state  of  rest,  are  proportional 
to  the  squares  of  the  times  employed  in  falling  —  while  the 
spaces  fallen  through  in  successive  times  increase  as  the 
odd  numbers  1,  3,  5,  7,  &c.  The  velocity  of  a  body  when 
it  begins  to  fall,  is  nothing  ;  but  from  that  moment  it  regu- 
larly increases.  Let  us  represent  the  velocity  acquired  at  the  end  of  th« 
1st  second  by  g  ;  then  the  average  velocity  during  the  same  time  will  be, 


the  arithmetical  mean  between  0,  the  starting  velocity,  and  v,  the  final 
velocity.     A  body  moving  at  this  rate,  will  traverse  the  same  space  in 


GRAVITATION.  47 

one  second  which  it  would  have  fallen  in  one  second  ;  let  this  space 
=  «•;  then  the  space  being  equal  to  the  product  of  the  velocity  and  the 
time,  $g  X  1  —  5>  or  9  —  %s  >  that  is,  the  final  velocity  acquired  by  a 
body  falling  one  second,  is  double  the  space  through  which  it  has  fallen. 
It  has  been  ascertained  that  in  latitude  45°  this  space  "is  about  16  J_ 
feet,  (16-08538  feet,  see  90)  and  g=  32J  feet. 

In  the  2d  second,  the  body  starts  witli  a  velocity  of  g  =  32£  feet,  and 
acquires,  at  the  close,  the  velocity  of  2g  =  64£  feet.  The  space  fallen 
during  the  same  time  is  48|  feet  ;  viz.  32£  feet  by  the  velocity  acquired 
during  the  first  second,  and  16J.7  feet  by  the  gradual  action  of  gravity 
in  this  second  only.  Or  as  before,  the  space  described  by  the  body 
during  the  2d  second,  is  equal  to  the  space  it  would  have  fallen  with 
the  mean  velocity  between  its  initial  and  final  velocities  ;  i.  e.  with  the 
velocity 


the  space,  therefore,  =  3  X  16^  =  481  feet. 

In  the  same  way  we  find  that  the  velocity  acquired  at  the  end  of  the 
3d  second,  will  be  3#=96|  feet;  and  in  the  same  time  the  body  will 
have  fallen,  with  the  mean  velocity, 

2.?  +  Zg         5gr 
2  2 

through  a  space  of  55  =  5  X  16  J2  =  80-^  feet. 

-•A  falling  body,  therefore,  descends,  in  the  2d  second  of  its  fall, 
through  three  times,  and  in  the  3d  second,  through  five  times  the  space 
fallen  in  the  first  second.  Or  in  the  words  of  the  4th  law,  the  spaces 
increase  as  the  odd  numbers. 

"Whole  space  described  by  a  falling  body.  —  We  have  seen  that 
the  time  of  falling,  and  the  final  velocity,  increase  in  the  same  ratio  ;  and 
that  the  average  velocity  of  any  fall,  is  exactly  half  the  final  velocity, 
and  the  whole  distance  fallen  is  the  same  as  if  the  body  had  moved  at 
a  uniform  rate,  with  a  mean  velocity  ;  hence,  any  increase  in  the  time 
of  falling  is  attended  by  a  corresponding  increase  of  the  average 
velocity  during  the  whole  fall.  But  the  whole  space  described  in  any 
fall  is  jointly  proportional  to  the  time,  and  the  average  velocity  ;  if, 
therefore,  the  time  is  doubled,  the  body  falls  not  only  twice  as  long,  but 
also  twice  as  fast,  and  it  must  descend  through  four  times  the  distance. 
Again,  if  a  body  falls  three  times  as  long  as  another,  it  also  falls  with 
three  times  the  average  velocity,  and  descends,  altogether,  through 
nine  times  the  distance.  The  times  being  represented  by  the  order  of 
the  natural  numbers,  1,  2,  3,  &c.,  the  spaces  are  represented  by  their 
squares,  1,  4,  9,  16,  &c. 


48  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

THE  FIFTH  LAW  is  —  A  body  falling  freely  from  a  state  of  rest  acquires, 
during  any  given  time,  a  velocity  which  would,  in  the  same  time,  carry  it 
over  twice  the  space  already  traversed. 

We  have  seen  that  a  body  falling  for  any  time,  acquires  a  final  velo- 
city which  is  double  the  average  velocity  of  the  fall  ;  if,  therefore,  the 
action  of  gravity  were  suspended  at  the  end  of  any  given  time,  and  the 
body  continued  to  move  with  its  acquired  velocity,  it  would,  in  tlie 
same  time,  traverse  twice  the  distance  it  had  already  fallen.  For 
instance,  the  space  fallen  through  in  three  seconds  is  144f  feet,  and 
the  final  velocity  is  96£  feet  ;  now  a  body  falling  uniformly,  for  three 
seconds,  with  this  velocity,  would  pass  through  a  space  of  3  X  96£  = 
289  J  =  2X144|  feet. 

TABLE  EXPRESSING  THE  LAWS  OF  FALLING  BODIES.  —  The  following  table 
expresses  the  2d,  3d,  and  4th  laws:  (See  32.) 

Times,  1,     2,     3,       4,      5. 

The  final  velocities,  2,     4,     6,       8,     10. 

The  space  for  each  time,/   1,     3,     5,       7,       9. 

The  whole  spaces,  1,    4,    9,     16,     25. 

Let  D  =  the  distance,  t  —  the  time,  F—  the  final  velocity,  and  g  — 
the  velocity  acquired  during  the  first  second,  then  from  the  foregoing 
laws  we  may  deduce  the  following  equations,  by  which  practical  ques- 
tions are  readily  solved. 

(1.)  V=  gt,  whence  (2.)  t  =  —  . 
9 


(3.)  D  =  $gt\  whence  (4)t  =  -         • 

By  substituting  in  (3)  the  value  of  t  (2) 

i        y* 


And  substituting  (4)  in  (1), 

V=ff\l2~  =  \foD. 


72.  Verification  of  the  laws  of  falling  bodies ;  Atwood's  Ap- 
paratus.—It  is  evident  that  the  third  and  fourth  laws  of  falling  bodies 
cannot  be  verified  by  direct  experiment ;  both  because  the  results  of 
such  a  trial  would  be  disturbed  by  the  resistance  of  the  air,  and 
because  the  velocity  of  the  fall  is  too  great  to  be  followed  by  the  eye. 
But  there  are  mechanical  contrivances  by  which  the  intensity  of  the 
force  of  gravity  may  be  diminished,  without  changing  its  nature.  We 
can  cause  a  falling  body  to  descend  so  slowly  that  the  resistance  of  the 


GRAVITATION. 


air  becomes  imperceptible,  and  all  the  circumstances  of  the  fall  may  then 

be  observed  with  entire  precision.     Galileo  37 

used  an  inclined  plane  to  verify  his  laws, 

but  a  far  more  exact  form  of  apparatus  is 

now  in  use  for  this  purpose,  called,  from  the 

name  of  its  inventor,  Atwood's  apparatus 

This  apparatus,  fig.  37,  is  composed  of  a  ver- 
tical column,  about  eight  feet  in  height,  sur- 
mounted by  a  large  wheel,  moving  with  the 
least  possible  friction,  and  upon  which  is  sus- 
pended a  fine  silk  cord,  carrying  equal  weights, 
B  B',  at  its  extremities.  A  scale  of  feet  and 
inches  is  marked  on  the  standard,  parallel  to  the 
path  of  one  of  the  weights,  to  measure  the  spaces 
through  which  it  falls,  and  the  corresponding 
times  are  shown  by  the  seconds  pendulum.  To 
insure  the  simultaneousness  of  the  fall  with  the 
beat  of  the  pendulum,  the  weight  is  set  in  mo- 
tion by  the  fall  of  the  tablet  H,  which  is  released 
by  the  action  of  an  electro-magnet,  G,  (seen  on 
a  large  scale  in  fig.  38),  acting  as  will  presently 
be  explained.  The  weights  B  and  B'  being 
equal,  the  force  of  gravity  has  no  effect  upon 
them,  and  they  remain  at  rest  in  any  position. 
But  let  one  of  them,  as  B,  be  increased  by  a 
small  additional  weight,  B",  and  the  equi- 
librium will  be  immediately  disturbed.  The 
weight  of  B"  being  the  only  disturbing  force, 
the  motion  produced  is  of  the  same  kind  as  the 
motion  of  a  body  falling  freely,  but  the  rate  of 
acceleration  and  the  space  fallen  through,  are 
each  as  much  less  as  the  mass  of  B"  is  less  than 
the  combined  masses  of  B"  -|-  2  B. 

The  form  and  relation  of  B  and  B"  are  more 
clearly  shown  in  the  enlarged  scale  of  fig.  38. 
For  example ;  let  B"  be  a  quarter  of  an  ounce, 
and  the  weights  B  and  B'  be  each  24  ounces, 
or  96  quarter  ounces.  The  whole  mass  to  be 
moved,  by  the  action  of  gravity  upon  B"  only, 
is  193  times  the  weight  of  B",  and  therefore  the 
velocity  imparted,  and  the  space  fallen  through, 
must  be  193  times  less  than  the  velocity  and 
space  of  B"  falling  freely. 

In  the  apparatus  here  figured,  the  beats  of 
the  seconds  pendulum  are  announced  by  the 
bell,  whose  hammer,  I,  is  struck  by  the  electro- 
magnet, G,  as  neatly  constructed  by  Ritchie. 
A  point,  E,  on  the  pendulum  rod,  just  touches  a  drop  of  mercury  as  it  passes 
the  vertical  line,  and  thus  completes  for  an  instant  the  circuit  of  a  voltaic 
battery,  whose  terminal  wires  are  shown  at  the  base  of  fig.  37. 

7* 


50 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


The  electro-magnet  then  acts,  and  its  armature,  G'  I',  moves  to  the  pole* 
of  Q,  thus  releasing,  first  the  tablet  II,  and  with  it 
the  weight  B,  and  next  announcing  the  successive 
seconds  upon  the  bell,  at  each  swing  of  the  pendu- 
lum. No  clock-movement  is  required  to  secure 
the  accurate  beats  of  the  seconds  pendulum  during 
the  short  period  of  a  single  experiment.  Now  B, 
with  B"  attached  to  it,  will  fall  from  the  tablet  H, 
at  the  instant  the  first  sound  of  the  bell  is  heard, 
following  the  first  swing  of  the  pendulum.  At  the 
instant  of  the  next  ring,  the  weight  will  be  seen  to 
have  fallen  exactly  1  inch ;  during  the  second  beat, 
through  three  inches  more ;  during  the  third  beat, 
through  5  inches ;  during  the  fourth  beat,  through  7 
inches,  <fcc.,  according  to  the  fourth  law. 

In  the  same  experiment  it  appears,  that  the  whole 
space  fallen  through  at  the  end  of  the  1st  second,  is 
1  inch ;  at  the  end  of  the  2d  second,  4  inches ;  at 
the  end  of  the  3d  second,  9  inches ;  at  the  end  of  the 
4th  second,  16  inches,  &c.,  according  to  the  first 
clause  of  the  4th  law. 

To  demonstrate  the  3d  and  5th  laws,  it  is  neces- 
sary to  arrest  the  accelerating  force  at  a  given  mo- 
ment. This  is  accomplished  by  giving  to  B"  the 
form  of  a  slender  bar,  as  shown  in  fig.  38,  long 
enough  to  be  caught  by  the  sliding  stage  C,  while  B  continues  its  course  with 
a  uniform  velocity,  from  the  time  it  ceases  to  be  acted  on  by  the  gravity 
of  B".  The  velocity  at  the  end  of  any  second  is  determined  by  the  space 
traversed  during  the  next  second.  If  the  stage  C  is  fixed  at  the  distance 
of  one  inch  from  the  top  of  the  scale,  B"  will  be  detached  at  the  end  of 
the  first  second,  and  B  will  descend  uniformly  through  two  inches  during 
each  succeeding  second.  If  the  ring  is  fixed  at  the  fourth  division,  the  bar  will 
strike  at  the  end  of  two  seconds,  and  B  will  pass  on  at  the  rate  of  four  inches 
per  second.  By  the  use  of  this  simple  and  ingenious  apparatus,  a  most  satis- 
factory experimental  demonstration  of  the  truth  of  Galileo's  laws  of  falling 
bodies  is  obtained. 

Morin's  Apparatus. — Another  apparatus  for  the  verification  of  these 
laws  has  been  contrived  by  Morin,  a  French  physicist,  in  which  the  velocity  of 
the  falling  body  is  not  retarded,  and  the  error  from  atmospheric  resistance  is 
made  inconsiderable  by  the  use  of  a  large  weight.  The  falling  body  carries  a 
crayon  which  marks  a  line  on  a  rapidly  revolving  vertical  cylinder,  covered  with 
paper,  and  divided  by  vertical  and  horizontal  lines,  representing  respectively 
time  and  distance.  The  line  drawn  by  the  crayon  carried  by  the  falling  body  is 
a  portion  of  a  parabola,  a  curve  whose  distance  from  each  division  on  its  verti- 
cal axis  is  as  the  ratio  of  the  squares  of  the  successive  divisions  on  that  line. 

73.  Application  of  the  laws  of  falling  bodies. — The  laws  of 
falling  bodies  apply  equally  to  every  motion  produced  by  a  uniform 
force  or  pressure. 

In  every  such  motion,  the  velocities  are  proportional  to  the  times  elapsed 
since  the  motion  began  j  the  final  velocity  is  twice  the  average  velocity ;  the 


GRAVITATION. 


51 


spaces  described  in  equal  successive  times,  increase  as  the  odd  numbers ;  and 
the  whole  spaces  increase  as  the  squares  of  the  times  in  which  they  are  described. 
But  in  each  instance  the  velocity  acquired,  and  the  space  described  in  a  given 
time,  will  be  different;  and  the  rate  of  acceleration  will  never  be  so  rapid  as  in 
the  case  of  a  body  falling  freely,  because  in  no  other  instance  will  the  force  be 
so  great  in  proportion  to  the  quantity  of  matter  moved. 

74.  Descent  of  bodies  on  inclined  planes. — When  a  body  is 
placed  upon  an  inclined  plane,  it  descends,  as  just  explained,  with  a 
uniformly  accelerated  motion,  but  its  velocity  is  less  than  that  of  a  body 
falling  freely.  The  weight  of  the  body,  39 

or  its  gravitation,  represented  by  the  line  a 
e  g,  fig.  39,  is  resolved  (50)  into  two 
components,  one  of  which,  ef(o*pg),  is 
perpendicular  to  the  plane,  and  produces 
pressure  only,  and  the  other,  ep  (wfg}, 
is  parallel  to  the  plane,  and  is  the  cause 
of  the  accelerated  motion.  The  triangles 
efy  and  a  b  c  being  similar,  their  cor- 
responding sides  are  proportional,  and 
we  have  * 

fg:eg  =  ac:ab; 

that  is,  the  rate  of  acceleration  on  an  inclined  plane,  is  to  that  of  a  body 
falling  freely  as  the  height  of  the  plane  is  to  its  length. 

The  final  velocity  depends  on  the  height  of  the  plane.     In  40 

fig.  40,  let  a  c,  the  height  of  the  plane,  be  J  of  its  length  a  6 ;  a 
then,  that  part  of  the  weight  of  the  body  which  produces 
motion,  is  J  of  the  whole  force,  and  the  velocity  acquired, 
and  the  space  traversed  in  one  second,  by  the  action  of  this 
force,  would  be  J  of  the  velocity  and  space  of  a  body  falling 
freely.  Let  the  line  a  f  represent  16-L  feet,  and  take  a  d, 
equal  to  J  of  af;  then,  a  body  starting  from  a  would  arrive 
at  d  in  one  second,  or,  falling  freely,  it  would  reach  /  in  the 
same  time. 

Draw  the  horizontal  line  e  d  j  the  ratio  of  a  e  to  a  d  is  the 
same  as  the  ratio  of  a  c  to  a  b ;  that  is,  a  e  is  equal  to  J  of  a  d;  and  a  d  having 
been  taken  equal  to  J  of  a  f,  a  e  is  i  of  af.  Since  the  spaces  increase  as  the 
squares  of  the  times,  the  body  that  would  fall  to  /  in  .one  second  would  fall  to 
e  in  J  of  a  second;  and  (3d  law)  the  velocity  acquired  at  e  would  be  J  of  the 
velocity  acquired  at  /.  But  we  have  already  seen,  that  the  velocity  acquired 
by  a  body  descending  to  d,  is  J  of  the  velocity  acquired  by  the  same  body 
falling  to  f,  in  the  same  time ;  hence  the  velocity  of  a  body  descending  the 
inclined  plane  to  d,  is  equal  to  that  of  a  body  falling  freely  to  e ;  and  generally — 

The  velocity  acquired  at  any  given  point  on  an  inclined  plane,  is 
proportional  to  the  vertical  distance  of  that  point  below  the  point  of 
departure. 


52  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

From  this  it  also  follows  that  the  average  velocities  are  the  same  in 
descending  all  planes  of  the  same  height ;  and,  therefore,  the  times  of 
descent  are  proportional  to  their  lengths. 

75.  Descent  of  bodies  on  curves. — It  was  shown  by  Galileo  that 
all  bodies  starting  from  a  horizontal  plane  with  equal  initial  velocities 
arrive  at  the  level  of  a  second  horizontal  plane  with  equal  velocities, 
whatever  kind  of  curve  they  may  have  passed  over.     This  is  a  general 
truth  of  which  the  statement  at  the  close  of  the  last  paragraph  is  only 
a  particular  case.     From  these  principles  it  follows  that  the  velocity 
acquired  in  descending  any  regular  curve  is  the  same  as  would  be 
acquired  in  falling  freely  by  gravity  through  the  same  vertical  height. 
But  the  time  of  descending  a  curve,  concave  upwards,  is  less  than  is 
required  to  descend  an  inclined  plane  between  the  same  points,  while 
for  descending  a  curve  convex  upwards  a  greater  time  is  required. 

76.  Brachystochrone ;   or  curve  of  swiftest  descent. — it  was 
demonstrated  by  J.  Bernoulli,    and  is  confirmed  by  experiment,  that 
a  body  descending  a  cycloid,  whose  base  is  horizontal,   reaches   its 
goal  in  less  time  than  by  any  other  path  between  the  same  points.    The 
cycloid  is  a  plain  curve,  described  by  41 

a   point   on   the   circumference   of    a  h 
wheel,  rolling  on  a  level  surface  with- 
out slipping.     The   curve  h  d  in  the 
triangle   h  kd,   fig.  41,  is   part   of    a 
cycloid. 

At  first  it  would  seem  that  the 
straight  line  h  d,  being  an  inclined  plane,  would  be  the  brachy- 
stochrone,  since  it  is  shorter  than  the  cycloid  joining  the  same  points, 
but  the  latter  descends  very  rapidly  at  first,  and  so  the  falling  body 
acquires  near  its  starting  point  a  much  higher  velocity  than  it  would 
on  the  inclined  plane.  This  increased  velocity  it  adds  to  each  of  its 
subsequent  movements,  and  though  its  velocity  on  arriving  at  d  is  no 
greater  than  if  it  had  passed  down  the  inclined  plane,  it  arrives  there 
in  a  shorter  time  than  it  could  by  any  other  path.  Another  curioug 
property  of  the  cycloid  is,  that  a  body  will  descend  from  h  to  d  in  this 
curve,  in  the  same  time  it  would  descend  to  d  fi^em  any  intermediate 
point  in  the  cycloid. 

77.  Action  and  reaction  of  a  falling  body. — On  arriving  at  the 
"bottom  of  a  plane  or  curve,  a  body  will  have  acquired  (5th  law)  a  velo- 
city, such  as  would  carry  it,  in  the  same  time,  over  a  distance  equal  to 
twice  the  length  of  the  descent,  or  cause  it  to  ascend  another  similar 
curve.     The  ascent  of  the  body  being  opposed  by  the  constant  force  of 
gravity,  will  be  retarded  at  a  rate  which  exactly  corresponds  with  its 


GRAVITATION.  53 

previous  acceleration.     On  the  double  curve  ABC,  fig.  42,  the  body 
will  have  equal  velocities  at  any  42 

two  points  at  the  same  level,  as  at 
E  and  D ;  and  the  velocity  being 
nothing  when  the  body  has  arrived 
at  C,  it  will  descend  again  amd 
mount  to  A,  the  point  from  which 
it  first  started.  This  alternate 
movement  being  caused  by  the  constant  force  of  gravity,  would  con- 
tinue for  ever,  and  furnish  an  instance  of  perpetual  motion,  were  it  not 
for  the  resistance  of  the  air  and  friction,  by  which  the  body  is  gradually 
brought  to  rest  at  B. 

The  pendulum  is  an  example  of  a  body  alternately  ascending  and  descending 
a  very  small  circular  curve. 

g  3.    Measure  of  the  Intensity  of  Gravity. 

I.     PENDULUM. 

78.  The  pendulum. — Any  body  suspended  by  a  flexible  cord,  or 
wire,  from  a  fixed  point  of  support,  is  a  pendulum.     A  plumb  line  is 
a  pendulum,  and  when  it  is  at  rest,  as  we  have  seen  (60),  it  shows  the 
exact  vertical,  and  indicates  the  direction  of  the  force  of  gravity.     But 
if  it  is  moved  from  the  perpendicular  into  any  other  position,  and  left 
to  fall,  the  pendulum  swings  in  a  vertical  plane,  and  rises  on  the  other 
side  of  the  vertical  to  a  height  equal  to  that  from  which  it  had  fallen. 
The  cause  of  these  alternate  movements  is  gravity,  and  the  motion  is 
called  an  oscillation. 

To  aid  in  the  study  of  the  movements  of  the  pendulum,  mathema- 
ticians distinguish  between  tlje  simple,  or  mathematical  pendulum,  and 
the  compound,  or  physical  pendulum. 

79.  Properties  of  the  simple  pendulum. — The  simple  pendulum 
consists,  by  mathematical   conception,  of  a  single  heavy  particle  of 
matter,  suspended  at  the  extremity  of  a  line,  without  weight,  inexten- 
sible,  and  perfectly  flexible.     Such  an  instrument  is  purely  ideal,  and 
is  conceived  of  only  as  a  convenient  means  of  investigating  the  laws  of 
the  real,  or  physical  pendulum. 

Let  C  M,  fig.  43,  be  a  simple  pendulum,  in  a  vertical  position,  and 
consequently  in  equilibrium.  If  it  is  moved  to  the  position  C  m,  the 
weight  m  P,  acting  at  the  point  m,  is  decomposed  into  two  components, 
m  B  acting  in  the  direction  C  m,  and  consequently  destroyed  by  the 
resistance  of  the  point  of  support,  and  m  D  perpendicular  to  C  m, 
which  solicits  the  return  of  m  to  the  position  of  equilibrium.  This  'ast 


54 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


component  is  equal  to  g  sin.  a ;  calling  g  the  accelerating  force  of  gravity, 
represented  by  m  P,  and  a  the  angle  m  C  M,  or  43 

D  Am,  which  is  the  same  thing. 

It  is  plain  that  the  component  m  D  must 
diminish  with  the  angle  a,  that  is  in  proportion 
as  the  pendulum  approaches  the  point  of  equi- 
librium C  M.  The  accelerated  velocity  of  its 
fall  is  therefore  not  a  case  of  uniform  accelera- 
tion, since  it  becomes  null  when  the  pendulum 
is  vertical. 

The  pendulum  does  not  however  rest  at  M, 
but,  in  virtue  of  its  acquired  velocity  (momen- 
tum), it  rises  through  an  equal  ascending  arc, 
M  n,  with  a  retarded  motion,  since  the  compo- 
nent of  gravity,  tangent  to  the  arc  described,  is 

now  turned  in  the  opposite  direction — so  that  this  component  diminishes 
the  velocity  at  each  point  of  M  n,  by  a  quantity  equal  to  the  increase 
of  velocity  acquired  at  the  corresponding  points  of  m  M,  anrd  equi- 
distant from  M.  Thus  the  acquired  velocity  is  entirely  destroyed  when 
the  pendulum  has  passed  over  the  arc  M  n,  equal  to  M  m.  At  n  it 
rests  for  an  inappreciable  instant,  after  which  it  returns  again  to  M, 
mounts  to  m,  and  would  thus  continue  moving  for  ever  like  the  ball 
rolling  in  a  double  curve  (77),  supposing  it  met  no  resistance  from 
friction  and  the  air. 

Each  swing,  from  n  to  m,  or  m  to  n,  is  called  an  oscillation,  and  one 
half  the  angle  n  C  m,  or  one  half  the  arc  n  m,  which  measures  it,  is 
called  the  amplitude  of  the  oscillation.  The  time  occupied  in  describ- 
ing the  arc  m  n  is  the  time  or  duration  of  an  oscillation.  The  angle 
of  elongation  n  C  M,  or  M  C  m,  measures  the  deviation  of  the  pendu- 
lum from  the  vertical. 

80.  Isochronism  of  the  pendulum. — From  the  last  section  it  is 
evident  that  the  movements  of  the  pendulum,  on  each  side  of  the  verti- 
cal, are  made  in  equal  times.  But  it  is  also  true  that  the  duration  of 
an  oscillation  is  always  the  same,  in  the  same  locality,  and  provided 
the  angle  of  elongation,  n  C  M,  fig.  43,  does  not  exceed  4°  or  5°. 
Within  this  limit  the  time  of  oscillation  is  sensibly  the  same,  and  the 
pendulum  requires  as  much  time  to  describe  an  arc  of  one-tenth  of  a 
degree  as  one  of  ten  degrees.  The  explanation  of  this  curious  and  most 
remarkable  fact  is  to  be  found  in  the  varying  length  of  the  component 
D  m,  fig.  43,  which  increases  with  the  angle  of  elongation.  Hence, 
the  greater  length  of  arc  is  exactly  compensated  by  the  greater  velocity 
with  which  the  pendulum  describes  it.  This  is  what  is  meant  by  the 


GRAVITATION.  55 

isochronism  of  the  pendulum — from  two  Greek  words,  meaning  equal 
times.  This  isochronism  is  not,  however,  absolute,  unless  the  ampli- 
tude of  the  oscillation  is  infinitely  small.  * 

81.  Formulae  for  the  pendulum.— The  property  of  isochronism, 
and  the  other  properties  of  the  simple  pendulum,  when  the  amplitude 
is  infinitely  small,  are  comprised  in  the  formula — 


T  representing  the  duration  of  an  oscillation,  I  the  length  of  the  pen- 
dulum, TT  the  relation  between  the  circumference  and  diameter  of  a 
circle  (equal  to  3*1416),  and  g  the  accelerating  force  of  gravity. 

If  the  amplitude  of  the  oscillations  is  not  infinitely  small,  the  formula 
becomes,  for  ordinary  limits, 


where  a  is  one-half  the  length  of  the  arc  n  m,  fig.  43.  It  requires  the 
aid  of  the  higher  mathematics  to  demonstrate  these  formulae  fully,  but 
we  may  deduce  from  them  the  following  important  propositions : 

82.  Propositions  respecting  the  simple  pendulum. — 1st.  Oscil- 
lations of  small  amplitude  are  made  in  times  sensibly  equal.  By  substi- 
tuting in  the  first  formula  I  =  39*14056  inches,  as  determined  by  experi- 
ment, for  the  seconds  pendulum  at  London,  and  let  T=  1*,  we  shall 
find  the  accelerating  force  of  gravity,  <7  =  32'175  feet.  Substituting 
these  values  of  g  and  I  in  the  second  formula,  and  also  a  =  3'1416  -*-  90 
=  0-0349,  we  shall  have  for  the  time  of  vibration  when  the  elongation 
is  four  degrees  on  each  side  of  the  vertical  T=  T000076,  which  differs 
from  the  time  of  vibration,  when  the  arc  of  vibration  is  infinitely  small, 
by  only  seventy-six  millionths  of  a  second. 

2d.  The  duration  of  an  oscillation  in  pendulums  of  different  lengths, 
is  proportional  to  the  square  root  of  the  length  of  the  pendulum,.  This 
law  may  be  demonstrated  experimentally  by  comparing  pendulums  of 
different  lengths.  If  the  lengths  are  in  the  ratio  of  1,  4,  9,  then  the 
times  of  oscillation  will  be  as  1,  2,  3,  respectively.  Let  three  such 
pendulums,  arranged  as  in  fig.  44,  commence  to  oscillate  at  the  same 
time ;  it  will  be  found  that  the  one-foot  pendulum  makes  two  oscilla- 
tions for  each  oscillation  of  the  four-foot  pendulum,  and  three  oscil- 
lations for  each  one  made  by  the  nine-foot  pendulum.  The  time  of 
oscillation,  and  the  length  of  the  pendulum  being  known,  we  may 
determine  by  this  law.  1st,  the  length  of  a  pendulum  which  would 
oscillate  in  any  proposed  time ;  and,  2dly,  the  time  of  oscillation  of  a 
pendulum  of  any  proposed  length.  For  the  times  of  oscillation  are  aa 


56 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


the  square  roots   of  the   lengths,  or,   what   is   the   same   thing,   the 
lengths  are  as  the  squares  of  the  times. 

Or  mathematically,  by  substituting  in  the   first  equation 


(81)  G  =  **  I which  is  a  constant  quantity  at  any  given 

\   9  

place,  the  equation  becomes  T=  Cy  I.  For  a  pendulum  of 
any  other  length,  as  V,  we  have  T  —  #]/  V  and  comparing 
the  two 

T:  T'  =1/77-1/77      and  also 

?  .  jt rpl  ,    rpt'l 

3d.  In  a  pendulum  of  invariable  length  the  duration 
is  inversely  proportional  to  the  square  root  of  the  inten- 
eity  of  gravity.  Hence, 

1  1 

rr> .  wt  _^____  .    _____^ / /~ 

—      /       '       //   —  v a'   '•  i/<7. 
y9          y  9 

where  g'  and  g  represent  the  intensity  of  gravitation  at  two 
places. 

83.  The  physical  or  compound  pendulum: — Cen- 
tre of  oscillation. — The  simple  pendulum,  as  already 
remarked,  is  only  an  intellectual  conception,  and  cannot 
be  realized  in  experiment.  Practically,  we  employ  for  the  physical 
pendulum  a  heavy  body,  suspended  by  an  inflexible  rod  from  a  fixed 
point.  The  axis  of  suspension  is  usually  a  knife  45 

edge  of  steel,  resting  on  polished  agate  planes,  or 
hard  steel.  In  the  physical  pendulum  the  rod  has 
weight  as  well  as  the  ball ;  and  nearly  all  the  ma- 
terial points  of  both  rod  and  ball  are  placed  at 
different  distances  from  the  point  of  suspension. 
Let  us  examine  the  oscillations  of  any  two  of  these 
material  points,  m  and  n,  fig.  45.  If  they  were 
suspended  by  separate  threads,  then,  according  to 
the  3d  law,  m  would  oscillate  more  rapidly  than 
n  ;  but  if  they  are  suspended  by  the  same  inflex- 
ible wire,  they  must  move  together,  and  make  . 
their  oscillations  in  the  same  time.  The  first  <-..._  _—•-•* 

accelerates  the  second,  and  the  second  retards  the 
first,  so  that  their  common  velocity  is  intermediate  between  the  velocity 
of  either  of  them,  oscillating  alone.  Such  a  compensation  takes  place 
in^every  oscillating  body,  and  between  the  particles  which  are  nearer 
and  those  more  remote  from  the  point  of  suspension,  there  is  always  a 
point  so  situated  that  it  is  neither  accelerated  nor  retarded,  but  oscil- 
lates exactly  as  if  it  were  suspended  alone,  at  the  end  of  a  thread, 


GRAVITATION.  57 

without  weight.  This  remarkable  point  is  called  the  centre  of  oscilla- 
tion ;  and  its  distance  from  the  point  of  suspension  is  the  length  of  the 
pendulum.  This  is  equal  to  the  length  of  a  simple  pendulum  which 
would  oscillate  in  the  same  time  as  the  physical  pendulum. 

The  position  of  the  centre  of  oscillation  depends  upon  the  form,  mag- 
nitude, and  density  of  the  several  parts  of  the  pendulum,  and  the  posi- 
tion of  its  axis.  If  the  rod  of  the  pendulum  is  thick  in  proportion  to 
the  ball,  its  centre  of  oscillation  will  be  higher  than  in  a  contrary 
arrangement.  It  is  always  below  the  centre  of  gravity,  although  what- 
ever raises  or  lowers  the  centre  of  gravity  will  change  the  centre  of 
oscillation  in  the  same  direction.  Whatever  may  be  the  positions  of  the 
point  of  suspension,  and  the  centre  of  oscillation,  they  are  always  inter- 
changeable; i.  e.,  if  the  pendulum  is  suspended  by  its  centre  of  oscilla- 
tion, these  two  points  exchange  their  functions,  and  the  oscillations  are 
made  in  the  same  time  as  before.  It  is  by  an  experiment  of  this  kind, 
that  the  centre  of  oscillation,  and  consequently  the  length  of  a  pendu- 
lum, is  determined.  This  remarkable  property  of  the  compound  pen- 
dulum was  first  demonstrated  by  Huyghens. 

84.  Application  of  the  pendulum  to  the  measurement  of 
time. — Galileo,  to  whom  we  owe  the  discovery  of  so  many  important 
physical  laws,  discovered  also  the  properties  of  the  pendulum.  When  a 
choir  boy  in  the  great  Cathedral  of  Pisa  (from  whose  bell  tower — the 
leaning  tower  of  Pisa — he  demonstrated  long  afterward  the  laws  of 
falling  bodies),  and  not  yet  eighteen  years  of  age,  his  attention  was 
arrested  by  the  great  regularity  of  the  movements  of  a  lamp  suspended 
by  a  chain  from  the  ceiling  of  the  cathedral.  This  observation  led  him 
to  the  discovery  in  question.  Although  Galileo  attempted  to  employ 
the  pendulum  to  measure  time,  it  was  the  great  Dutch  philosopher, 
Christian  V.  Huyghens,  to  whom  we  are  indebted  for  the  invention 
(in  1656)  of  the  clock  escapement,  by  means  of  which  the  pendulum  is 
made  to  perform  its  proper  function  as  a  time-keeper.*  This  apparatus 
is  seen  in  fig.  46. 

An  oblique-toothed  wheel,  R,  called  a  racket  wheel,  is  moved  by  a  weight  and 
cord.  This  motion  is  controlled  by  a  piece,  a  b,  called  the  anchor  escapement, 
placed  above  the  wheel  so  as  to  oscillate  on  its  axis  of  suspension,  o  o',  at  right 
angles  to  the  wheel.  The  oscillatory  motion  is  imparted  to  the  anchor  a  b  by 
the  pendulum  c  P,  which  is  made  to  communicate  with  the  axis  o  o'  by  the 
crotchet  of.  If  the  pendulum  is  vertical  the  apparatus  is  at  rest,  for  then  the 

*  "  The  Arabian  astronomers,  and  more  especially  En-Junis,  at  the  close  of 
the  tenth  century  and  during  the  brilliant  epoch  of  the  Abbassidian  Califs,  first 
employed  these  vibrations"  (of  the  pendulum)  "  for  the  determination  of  time," 
(Humboldt's  Cosmo*,  Vol.  5,  p.  19.) 

8 


58 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


point  of  one  of  its  teeth. 
46 


pallet  b  of  the  escapement  holds  the  wheel  by  the 
If,  however,  the  pendulum  is  then  moved  to 
the  left,  the  wheel  is  released  and  moves  for- 
ward by  force  of  the  weight,  until  the  other 
point  of  the  escapement  a  again  arrests  its 
motion;  but  the  return  swing  of  the  pendulum 
in  its  turn  disengages  a,  and  the  wheel  R  re- 
volves the  space  of  another  tooth,  when  it  is 
again  caught  on  b,  and  so  on.  The  motion  of 
the  wheel  R  is  thus  made  up  of  small  equal 
advances,  succeeding  each  other  regularly  with 
the  oscillations  of  the  pendulum.  The  points 
of  the  teeth  on  the  racket  wheel,  and  also  the 
points  of  the  escapement  anchor,  are  carefully  .,, 
formed  to  offer  the  least  possible  friction  and  J  *5 
resistance  to  motion. 

The  pendulum  and  escapement  of  a  clock 
are  so  arranged  as  to  prevent  the  clock  from 
running  down,  except  by  the  regular  and 
measured  velocity  indicated  by  the  movement 
of  the  pendulum  and  escapement.  On  the 
other  hand,  the  escapement  is  so  constructed 
that  the  rachet  wheel  imparts  to  it  a  slight 
pressure  at  every  swing  of  the  pendulum,  suffi- 
cient to  counteract  the  retarding  force  of  fric- 
tion to  which  the  pendulum  is  subject.  The 
train  of  wheel-work,  of  which  the  clock  is  p 
composed,  serves  to  record  the  vibrations  of 
the  pendulum,  and  indicate  at  once  to  the  ob- 
server the  progress  of  time. 


85.  Cycloidal  pendulum.— Owing  to  the  resistance  of  the  air,  and 
to  friction,  a  pendulum  unconnected  with  other  machinery  has  the 
amplitude  of  its  vibrations  gradually  diminished,  and  vibrations  vary- 
ing greatly  in  amplitude,  vary  very  sensibly  in  the  time  in  which  they 
are  performed.     To  make  vibrations  of  different  amplitude  absolutely 
isochronous,  Huyghens  conceived  the  idea  of  making  the  pendulum 
describe  a  cycloid,  which,  it  will  be  remembered,  is  the  curve  of  swiftest 
descent  (76).     The  vibrations  of  such  a  pendulum  would,  in  theory,  be 
absolutely  isochronous ;  but  the  mechanical  difficulties  in  the  way  of 
adapting  the  pendulum  to  motion  in  this  curve  forbid  its  adoption. 

A  long,  heavy  pendulum  vibrating  in  a  very  small  circular  arc,  is  found  in 
practice  the  most  perfect,  and  is  for  this  reason  generally  used  in  astronomical 
clocks.  The  sources  of  error  in  the  clock  arising  from  inequalities  of  tempera- 
ture will  be  considered  in  the  chapter  on  heat. 

86.  Physical  demonstration  of  the  rotation  of  the  earth  by 
means  of  the  pendulum. — Mr.  Leon  Foucault,  in  1851,  executed  the 
first  physical  demonstration  that  had  been  made  of  the  rotation  of  the 


GRAVITATION.  59 

earth  upon  its  axis.  This  remarkable  and  most  interesting  experiment 
consists  in  suspending  a  heavy  ball  to  a  long  and  flexible  wire,  and 
allowing  the  whole  to  vibrate  freely,  in  the  manner  of  a  pendulum. 
Under  these  circumstances  it  will  be  found,  in  these  latitudes,  that  the 
plane  of  vibration  gradually  changes  its  position,  turning  slowly  from 
east  to  west,  or  with  the  motion  of  the  hands  of  a  watch. 

The  connection  between  the  motion  of  the  pendulum  plane  and  the 
earth's  rotation,  may  be  easily  understood.  A  pendulum  set  in  motion 
will  continue  in  the  same  plane  of  vibration,  however  the  point  of  sus- 
pension may  be  rotated.  This  may  be  proved  by  holding  in  the  fingers 
a  pendulum,  made  of  a  simple  ball  and  string,  and  causing  it  to  vibrate. 
Upon  twirling  the  string  between  the  fingers,  the  ball  will  rotate  on  its 
axis,  without,  however,  affecting  at  all  the  direction  of  its  vibrations. 
The  reason  for  this  is  obvious  ;  the  swinging  pendulum,  when  about  to 
return  (after  an  outward  oscillation)  from  its  point  of  rest,  is  made  to 
move  from  that  point  by  gravity  alone,  and  can,  therefore,  fall  in  but 
one  direction. 

If  a  pendulum  were  oscillating  at  either  of  the  poles  of  the  earth,  the 
plane  of  revolution,  as  it  would  not  change  with  the  revolution  of  the 
earth,  would  mark  this  revolution,  by  seeming  to  revolve  in  a  contrary 
direction,  and  in  24  hours  it  would  make  apparently  the  whole  circuit 
of  360  degrees.  But,  at  the  equator,  the  plane  of  vibration  is  carried 
forward  by  the  revolution  of  the  earth,  and  so  undergoes  no  change 
with  reference  to  the  meridians.  Between  the  equator  and  the  poles, 
the  time  required  for  the  pendulum  to  make  360°,  varies  according  to 
the  latitude,  being  greater  the  further  from  the  poles. 

The  observed  rate  of  motion  of  the  plane  of  vibration  nearly  coincides 
with  that  indicated  by  calculation.  Thus,  at  New  Haven  (N.  lat.  41° 
18%'),  the  calculated  motion,  per  hour,  was  9'928°,  the  observed  motion 
was  9-97°.  (C.  S.  Lyman.) 

The  greatest  length  of  the  pendulum  wire  hitherto  employed  was  that 
of  220  feet,  in  the  Pantheon  at  Paris.  At  Bunker  Hill  Monument  it 
was  210  feet  long ;  at  New  Haven  71  feet.  The  weight  of  the  ball  em- 
ployed (usually  lead),  has  varied  from  2  to  90  pounds.  The  longer  the 
wire,  and  the  heavier  the  ball  of  the  pendulum,  the  greater  will  be  the 
probability  of  accurate  results,  for  when  the  mass  of  the  body  is  great, 
and  its  motion  slow,  the  resistance  of  the  air  will  have  but  compara- 
tively little  effect  on  the  direction  of  the  vibration. 

87.  The  pendulum  applied  to  the  study  of  gravity.— By  the 
pendulum  we  ascertain  more  accurately  than  by  any  other  method  the 
truth  of  the  first  law  of  falling  bodies;  viz.,  that  gravity  acts  equally 
upon  matter  of  every  description  (71).  Newton,  and  more  recently 


60  PHYSIOS    OF    SOLIDS    AND    FLUIDS. 

Bessel,  verified  this  law,  by  using  a  pendulum  having  a  hollow  ball, 
which  was  filled,  successively,  with  various  substances — metals,  ivory, 
meteoric  stones,  wool,  feathers,  liquids,  &c. — that  could  not  be  otherwise 
submitted  to  trial.  This  experiment  affords  the  most  precise  and  unmis- 
takable evidence  that  gravity  (g]  acts  on  all  bodies  in  the  same  manner. 
Since  ft  is  a  constant  quantity,  the  formula  for  the  pendulum  shows 
that  if  T  and  I  do  not  vary,  g  remains  also  constant. 

88.  Use  of  the  pendulum  for  measuring  the  force  of  gravity. — 
The  value  of  the  term  g  for  any  place  may  be  easily  obtained  mathe- 
matically (the  length  of  a  pendulum  which  oscillates  in  a  given  time 
(T)  being  known),  by  transposing  the  formula  for  the  pendulum  (81) ; 
thus  we  have  for  the  intensity  sought — 

*H 
<7  =  -~7j,     and  assuming  ~T equal  unity,  then  I  is 

the  length  of  a  seconds  pendulum,  and  we  have 
g  =  *H. 

Experimentally,  we  may  determine  the  intensity  of  gravity  at  any 
place,  by  counting  with  exactness  the  number  of  oscillations  made  at 
the  place  of  observation  in  a  given  time,  by  a  pendulum  whose  length 
is  known,  and  then  dividing  the  time  by  the  number  of  oscillations. 
Any  error  in  observing  the  time  of  a  single  oscillation  is  thus  greatly 
diminished,  by  subdivision,  and  by  a  sufficient  number  of  repetitions 
this  error  may  be  reduced  to  a  quantity  too  small  for  consideration. 

It  was  thus  that  Borda  and  Cassini,  in  1790,  measured  with  great 
accuracy,  the  intensity  of  gravity  at  the  Observatory  in  Paris,  using  a 
pendulum  composed  of  a  platinum  ball,  suspended  by  a  fine  platinum 
wire,  upon  knife  edges  of  steel,  resting  on  agate  planes.  The  whole 
was  about  four  metres  long,  and  its  oscillations  were  counted,  not 
directly,  but  by  means  of  an  ingenious  comparison  with  the  motions  of  a 
clock  pendulum,  placed  a  few  metres  behind,  marking  by  a  telescope 
the  occurrence  of  a  coincidence  in  the  vertical  position  of  the  two  pen- 
dulums, and  then  observing  the  number  of  seconds  before  a  coincidence 
occurred  again.  The  pendulums  were  inclosed  in  glass  cases,  to  avoid 
currents  of  air. 

89.  Value  of  g  in   these  experiments. — After   carefully  elimi- 
nating the  errors  of  experiment  due  to  the  influence  of  the  air  (the  con 
sideration  of  which  would  load  us  too  far  into  the  refinements  of  this 
subject  for  our  limited  space),  Borda  and  Cassini  found  for  the  intensity 
of  gravity  at  Paris  g  =  9'8088  metres,  equal  to  32'1798  feet.     This 
value  has  been  confirmed  by  Arago,  Biot,  and  others,  and  slightly  cor- 
rected by  Bessel,  by  considering  the  loss  of  •weight  in  air  due  to  the 
motion  of  the  pendulum,  giving  the  quantity  g  —  9'8096  metres. 


GRAVITATION. 


61 


Seconds  pendulum. — On  the  other  hand,  when  we  know  the 
accelerating  force  of  gravity,  g,  at  any  given  place,  it  is  easy  to  calcu- 
late the  length  of  the  simple  pendulum  vibrating  seconds,  assuming  the 
oscillations  to  be  infinitely  small.  Thus  in  the  formula  for  the  pendu- 
lum (81),  making  T=  1s,  and  using  for  g  the  value  determined  for 
the  place,  we  have  Z  =  at  Paris  0*993866  metre  =  39 -127  inches,  and 
corrections  being  made  for  the  interference  of  the  air,  this  quantity,  as 
determined  by  Bessel,  is  0*993781  metre  =  39-12367  inches. 

II.     MODIFICATIONS   OF    TERRESTRIAL    GRAVITY    AND    THEIR    CAUSES. 

90.  The  intensity  of  gravity  varies  with  the  latitude. — Very 
numerous  observations  made  with  the  pendulum,  on  different  parts  of 
the  earth's  surface,  have  shown  that  the  force  of  gravity  is  by  no  means 
the  same  at  all  places,  and  particularly  that  it  increases  in  gofcg  from 
the  equator  toward  either  pole.  This  result  is  observed  in  the  increas- 
ing length  of  the  pendulum  vibrating  seconds,  since  by  $  88,  g  is  pro- 
portional to  I,  the  pendulum  must  be  longer,  as  the  force  of  gravity  is 
greater,  to  preserve  the  same  time  in  oscillation.  The  value  of  g  for 
any  latitude  is  obtained  with  approximate  accuracy  by  the  formula 
<7  =  32-17076  (1  —  0-00259,  cos.  2/1),  in  which  A  is  the  latitude  of  the 
place,  and  32.17076  feet  the  value  of  g  at  latitude  45°.  By  substituting 
for  A,  successively  0°  and  90°,  we  obtain  at  the  equator  g  —  32-0874377 
feet,  and  at  the  poles  g  =  32*254083  feet. 

The  following  table  of  the  variation  in  the  length  of  the  seconds  pendulum,  with 
the  latitude,  is  condensed  from  a  large  list  in  Saigey.  (Physique  du  Globe, 
p.  132,  t.  2.) 


Places  observed. 

Latitudes. 

Length  of  seconds 
pendulum  in   Ameri- 
can inches.* 

Names  of  observers. 

Spitzbergen,    .... 
Greenland,       .     .     .     . 
St.  Petersburg,    .     .     . 
Paris 

79°  49'  58"  N. 
74°  32'  19"  " 
59°  56'  31"  " 
48°  50'  14"  " 

39-2161492 
39-204339 
39-1704818 
39-1299322 

Sabine. 
it 

Lutk6. 

Biot. 

New  York,       .... 
Jamaica,  W.  I  ,   . 

40°  42'  43"  « 
17°  56'  07"  " 

39-1023743 
39-0362352 

Sabine. 

« 

•St.  Thomas,  W.  I.,  .     . 
Maranham,      .... 

0°  24'  41"  " 
2°  31'  35"  S. 
22°  55'  22"  " 

39-0216688 
39-0126141 
39-0452899 

n 

Foster. 
Basil  Hall. 

Cape  of  Good  Hope, 
Cape  Horn,      .... 
N.  Shetland,    .... 

33°  55'  56"  " 
55°  51'  20"  " 
62°  56'  11"  " 

39-0795405 
39-1567028 
39-1807176 

Fallows. 
Foster. 
it 

*  In  reducing  Saigey's  table  of  lengths  of  the  seconds  pendulum  at  different 
localities,  to  American  inches,  the  French  metre  has  been  taken  at  39-36850535 
inches,  as  adopted  by  the  United  States  Coast  Survey. 
8* 


62 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


Numerous  observations  on  the  U.  S.  Coast  Survey,  and  elsewhere, 
show  that  the  value  of  g  is  by  no  means  rigorously  the  same  at  all 
points  on  the  same  parallel ;  a  discrepancy  to  be  explained  only  by 
supposing  an  inherent  difference  in  the  constitution  of  the  earth's  crust 
at  different  places. 

The  variation  of  gravity  with  change  of  latitude  is  due  to  two  causes. 
1st.  To  the  flattening  of  the  earth  at  its  poles.  2d.  To  the  centrifugal 
force  created  by  the  revolution  of  the  earth  upon  its  axis.  The  last 
cause  also,  beyond  doubt,  induced  the  flattening  of  the  poles  in  the 
earlier  history  of  our  planet. 

91.  Influence  of  the  earth's  figure  upon  gravity. — Until  1666 
the  pjttfc't  sphericity  of  the  earth  had  not  been  questioned,  although  in 
the  preWlfing  century  the  flattening  of  the  planet  Jupiter  at  the  poles 
had  been  observed.  Subsequently  (in  1672),  Richer,  sent  by  the 
Academy  of  Paris  to  Cayenne,  remarked  that  his  pendulum  no  longer 
beat  seconds  at  the  latter  place,  until  it  was  shortened  a  line  and  a  quar- 
ter from  its  length  at  Paris.  This  observation  at  once  indicated  a  less 
force  of  gravity  at  Cayenne  than  at  Paris,  and  suggested  doubts  respect- 
ing the  sphericity  of  the  earth.  Huyghens  attributed  this  diminution 
of  the  force  of  gravity  to  centrifugal  force,  and  conceived  that  the  earth 
must  be  bulged  out  at  the  equator. 

Huyghens  and  Newton,  assuming  that  the  earth  had  become  solid 
from  an  originally  fluid  mass,  whose  particles  attracted  each  other, 
subject  to  the  laws  of  hydrostatics  and  of  the  centrifugal  force,  arrived 
at  the  conclusion,  from  mathematical  calculation,  that  the  earth's  figure 
was  that  of  an  oblate  spheroid,  whose  polar  diameter  was  about  26 
miles  less  than  its  equatorial.  Laplace  47 

reached  almost  the  same  conclusion,  by 
calculating  the  effect  of  the  equatorial 
mass  on  the  motions  of  the  moon.  The 
effect  of  the  centrifugal  force  upon  a 
yielding  mass,  may  be  shown  by  the  ap- 
paratus, fig.  47.  Two  circles  of  wire,  or 
flexible  metallic  ribbons,  are  attached 
below  to  an  axis,  and  above  to  a  sliding 
ring,  and  being  rapidly  rotated  by  the 
whirling  table,  the  circles  flatten  in  the 
direction  of  the  axis,  and  bulge  at  the 
equator,  as  shown  by  the  dotted  lines. 

But  it  was  only  by  the  actual  measurement  of  an  arc  of  meridian 
that  the  exact  figure  of  the  earth  became  known.  This  important  geo- 
desic operation  was  undertaken,  by  La  Condarnine  and  others,  in  1736 


GRAVITATION. 


63 


48 


in  Peru,  by  order  of  the  French  government,  and  was  less  accurately 
performed  by  Picard  in  France,  in  1669.  This  operation  led  to  the 
conclusion  (since  demonstrated  by  numerous  similar  measurements), 
that  the  successive  arcs  on  the  same  meridian,  comprised  between  two 
verticals  forming  an  angle  of  1°,  become  larger  and  larger  as  we  ad- 
vance toward  the  poles.  Consequently,  the  equatorial  radius  is  greater 
than  the  polar,  and  the  plumb  line  will  point  to  the  centre  of  the  earth 
only  in  one  of  those  radii. 

The  astronomers  Mason  and  Dixon,  who,  in  1764-6,  established  the 
boundaries  between  Pennsylvania,  Delaware,  and  Maryland,  afterwards, 
in  1768,  re-measured  a  line  of  538,067  feet,  with  great  accuracy,  very  near 
the  meridian,  for  the  purpose  of  determining  the  value  of  an  arc.  Four- 
fifths  of  this  (434,011^)  was  one  unbroken  line,  without  triangulation, 
on  a  vast  level  plain.  They  used  rods  of  fir,  frequently  compared  Avith  a 
standard  brass  measure  at  a  fixed  temperature.  They  found  the  length 
of  a  degree  of  latitude  to  be  363,763  English  feet.  (Phil.  Trans.  1768.) 

The  general  results  may  be  illustrated  by  the  following  diagram. 

Let  {he  line  A  P,  fig.  48,  represent  a  quad- 
rant of  a  meridian,  of  which  0  P  is  the  polar, 
and  0  A  the  equatorial  radius.  Let  us  take 
stations  on  this  meridian,  one  degree  distant 
from  each  other,  commencing  from  the  equa- 
tor, and  from  each  station  prolong  the  direc- 
tion of  the  plumb  line  until  it  intersects  the 
plumb  line  similarly  produced  from  the  pre- 
vious station ;  a  b  c  are  three  such  points,  and 
it  is  plain  that  the  intersections  of  the  plumb 
lines  from  each  of  the  ninety  verticals  on  the 
quadrant,  would  together  evolve  the  curve 
a  b  cp,  and  the  same  if  the  stations  were  in- 
finite. Objects  on  different  parts  of  the  earth's 
surface  are  not  attracted  to  a  common  centre 
of  gravity.  The  centre  of  gravity  for  any 
point,  A,  B,  C,  P,  on  the  quadrant,  A  P,  must  lie  in  the  corresponding  points, 
a,  fc,  c,  p,  where  the  respective  normals  cut  the  evolute  a  p.  At  A,  for  example, 
the  attraction  of  gravity  acts  as  if  it  originated  at  a,  for  B  at  6,  for  C  at  c,  <fcc. 
But  the  -intensity  of  gravity  is  greater  at  B  than  at  A,  at  C  than  at  B,  and  so  on. 

The  revolution  of  the  evolute  a  p  on  its  axis  0  p  will  evidently  generate  a 
surface  (called  a  locus),  in  which  will  be  found  the  centres  of  gravity  for  all 
points  on  the  upper  hemisphere,  and  a  similar  surface  may  be  produced  for  all 
points  on  the  lower  hemisphere  by  the  revolution  of  the  curve  ap'. 

Evidently,  therefore,  a  body  placed  at  the  equator  will  be  very  differ- 
ently affected  by  the  force  of  gravity,  from  what  it  would  if  placed  at 
the  poles.  The  amount  of  flattening  at  the  poles  is  about  ^  J^  of  the 
equatorial  radius,  or,  accurately,  3^.4  5  'that  is,  the  polar  radius  is  so 
much  shorter  than  the  equatorial— exactly  21'319  kilometres,  equal 
13-246483  miles;  or  in  the  diameter  nearly  26 £  milos  (26'492966).  In 


6-1  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

an  exact  model  of  the  earth  15  inches  diameter,  it  would  be  repre- 
sented by  -y^  of  an  inch ;  a  quantity  t^,  small  to  be  detected  by  the  eye 
or  hand. 

92.  Exact  dimensions  of  the  earth. — According  to  the  latest  cal- 
culations the  exact  dimensions  of  the  earth,  as  given  by  Kohler,  when 
reduced  to  American  standard  measures,  are  as  follows : 

Volume  of  the  earth,     259,756,014,917  cubic  miles. 
Surface  of  the  earth,     196,881,077          square  miles. 
Length  of  a  quadrant,  6213-99609  miles. 

Mean  radius  (lat.  45°),  3955-94978 
Equatorial  radius,  3962-57302 
Polar  radius,  3949-32654 

Difference  between  the  last  two  dimensions  13*24648  miles. 
The  equatorial  swelling,  or  that  portion  of  the  earth  which  lies  outside  of 
a  perfect  sphere,  whose  circumference  is  described  by  the  polar  radius, 
is  y^7  part  of  the  whole  volume  of  the  earth.  Two  verticals  include  an 
angle  of  V  when  they  are  101'7  feet  distant  from  each  other,  and  they 
will  inclose  a  sector  of  V  when  they  are  distant  from  each  other  1*15 
miles. 

93.  Sensible   weight  varies  in  different  localities. — The  same 
body  is  sensibly  lighter  at  the  equator  than  at  the  poles  of  the  earth,  in  the 
ratio  of  194  to  195.     This  difference  cannot  be  detected  by  the  balance,  because 
the   thing  weighed  is    counterpoised  by  an   equal 

standard  weight,  under  the  same  circumstances ; 
and  if  both  are  removed  to  another  station,  their 
weight,  if  changed,  will  be  changed  equally,  and  a 
body  and  its  counterpoise  once  adjusted,  will  con- 
tinue to  balance  each  other  wherever  they  are  car- 
ried. It  is  not  in  this  sense  that  194  Ibs.  at  the 
equator  will  weigh  195  Ibs.  at  the  poles ;  but  if  we 
conceive  a  body,  y,  suspended  by  a  cord,  imagined  .,/ 
without  weight,  passing  over  a  pulley  at  the  equator, 
as  in  the  annexed  figure,  49,  and  connected  by 
other  pulleys,  all  without  friction,  with  x,  another 
equal  weight,  at  the  poles;  then,  although  the 
weights  would  counterpoise  each  other  in  a  balance,  they  would  not  in  this 
situation,  but  the  polar  weight  would  preponderate,  and  y  would  require  to  be 
increased  by  y-g^th  part,  to  restore  the  equilibrium. 

The   above  phenomena  are  readily  demonstrated  by  the  spring-balance,  or 
dynamometer  (37.) 

94.  Effect  of  the    earth's  rotation    on   gravity. — Newton   and 
others  have  determined,  by  calculation,  that  the  increase  of  weight, 
due  to  the  spheroidal  form  of>  the  earth,  is  -s  Jg,  when  a  body  is  trans- 
ported from  the  equator  to  the  poles ;  yet  the  difference  of  weight  is 
found  experimentally  to  amount  to  the  much  more  considerable  quan- 


GRAVITATION. 


65 


tity  of  TJ?  part  of  the  total  weight  of  the  body.  This  large  difference 
is  accounted  for  by  the  centrifugal  force,  which  is  nothing  at  the  poles, 
and  regularly  increases  towards  the  equator,  where  it  is  greatest,  and 
in  the  same  ratio  diminishes  the  weight  of  bodies  on  the  earth's  sur- 
face. The  earth  revolves  once  in  24  hours,  but  if  it  revolved  seventeen 
times  more  rapidly  than  it  now  does,  or  in  Ih.  24m.  25s.,  the  centrifugal 
force  would  balance  the  force  of  gravity,  and  bodies  at  the  equator  would 
have  no  sensible  weight.  If  the  velocity  of  revolution  was  farther 
increased  the  oceans  would  be  thrown  off  like  water  from  a  grindstone, 
and  all  loose  materials  would  fall  into  space. 

Demonstration. — By  the  laws  of  centrifugal  force  it  follows  that  the  ob- 
served weight  of  any  substance  on  the  earth's  surface  is  the  difference  between  the 
earth's  attraction  and  the  centrifugal  force  developed  by  the  revolution  of  the 


earth.     By  §  54  the  centrifugal  force  at  the  equator  =  G  = 


j  R  being  the 


equatorial  radius,  and  T  a  diurnal  revolution.     If  G  represent  the  attraction  of 
the  earth,  and  g  the  weight  of  a  body  at  the  equator,  then  (  1  )  g  =  G — . 

Let  m,  fig.  50,  be  a  material  particle  taken  on  any  parallel,  and  represent  A  m, 
the  radius  of  this  parallel,  by  r,  the  centrifugal  50 

force  at  this  point,  mf=  c  =.  — -.    But  as  this 


force  does  not  act  in  the  direction  of  gravity,  de- 
compose it  into  two  others,  one  of  which,  m  b, 
being  at  right  angles  to  gravity,  has  no  effect 
upon  it,  and  the  other  m  a  acting  directly  against 
gravity.  Let  m  0  E,  the  latitude  of  the  place, 
which  is  equal  to  a  mf,  be  designated  by  L,  then  in 
the  right-angled  triangle  a  mf,  m  a  is  equal  to 
mf  X  cosine  of  amf—  c  cos.  L.  In  the  triangle 
A  m  0,  A  m  =  r  =  R  cos.  L.  It  follows  that  the  vertical  component  m  a  ~- 

cos.2  Z-.     The  force  of  gravity  at  m  is  then, 


(2)  g  =  G  — 


COS.2  L. 


The  diminution  of  gravity  due  to  the  centrifugal  force  is  therefore  propor- 
tional to  the  square  of  the  cosine  of  the  latitude.  At  the  pole,  where  L  =  90°, 
g  =  G.  At  the  equator  L  =  0,  and  g  is  found  by  the  formula.  In  the  first 
formula  (1 )  the  value  of  the  second  term  of  the  equation  being  very  small  in 

/           4*2/?\ 
relation  to  the  first,  gives  very  nearly  g  ==  0  f  1 ^-  J,  by  placing  G  as  a 

common  factor,  and  replacing  it  in  the  denominator  of  the  second  term  by  g. 

Taking  for  the  mean  radius  of  the  earth  R  =  20,887,413  feet,  and  g  =  32-1798 
feet,  and  T  —  86,164  seconds  (the  time  of  a  revolution  of  the  earth  on  its  axis), 

we  find  for  the  value  of  very  nearly =       .     If,  therefore,  the  earth 

Tl  289        172 


66  PHYSICS  OF  SOLIDS  AND  FLUIDS. 

revolved  17  times  faster  than  it  does  at  present,  making  T  seventeen  times 
smaller,  the  second  term  in  the  parenthesis  would  hecome  unity,  and  the  value 
of  g  would  be  zero,  or  bodies  at  the  equator  would  have  no  weight.  The  expres- 
sion (1)  enables  us  to  calculate  the  attractive  force  at  the  equator,  assuming  as 
a  starting  point  the  value  g  •=.  32-09025  feet  as  the  value  of  gravity  as  indicated 
by  the  pendulum.  We  then  find  the  attractive  force  at  the  equator  G  =  32-20147 
feet,  and  the  centrifugal  force  at  the  equator  =  0-111216  feet. 

95.  Variation  of  gravity  above  the  earth  and  below  its  sur- 
face.— By  the  law  of  gravitation  it  follows  that  as  we  rise  above  the 
earth  the  force  of  gravity  must  diminish.  This  diminution  is  sufficient 
to  be  appreciable  at  any  considerable  distance  above  the  level  of  the 
sea ;  therefore,  to  compare  the  results  of  experiments  relating  to  the 
force  of  gravity  at  different  situations  on  the  earth's  surface,  it  is  neces- 
sary to  reduce  all  observations  to  a  common  standard — the  sea  level. 

Representing  by  g'  the  intensity  of  gravity  at  any  elevation  k,  and 
the  earth's  radius  by  R,  neglecting  the  variation  of  the  centrifugal 
force,  we  have 

g  :  g>  =  (R  +  A)2 :  J2» ;  hence  g  =- g'  (^-^~- 

The  mean  distance  of  the  moon  from  the  earth's  centre  is  about 
sixty  times  the  equatorial  radius  of  the  earth,  and  it  completes  its  orbit 
(assumed  to  be  circular)  in  27 '322  days.  As,  therefore,  the  intensity 
of  the  earth's  attraction  at  the  moon  equals  the  centrifugal  force  (as  is 
evident  from  physical  astronomy),  this  force  can  be  calculated  by  sub- 
stituting for  R  sixty  times  the  earth's  radius,  in  the  formula  for  centri- 
fugal force.  Substituting  for  T  the  time  of  a  lunar  revolution  expressed 

in  seconds,  we  find  for  tjie  earth's  attraction  on  the  moon  g  = — 

=  0.00679  feet,  which  is  about  3600  times  less  than  the  attraction  of 
the  earth  for  bodies  on  its  surface  at  the  equator  (assuming  for  bodies 
as  distant  as  the  moon  that  the  attraction  of  the  earth  is  concentrated 
at  its  centre).  This  agrees  with  the  law  of  gravitation,  the  square  of 
60  being  3600. 

Below  the  earth's  surface,  assuming  the  earth  to  be  a  sphere,  the 
force  of  gravity  is  proportional  to  the  distance  of  the  particle  from  its 
centre.  It  is  plain  that  the  force  of  attraction  at  any  point  beneath 
the  surface  is  diminished  by  whatever  part  of  the  earth  is  above  the 
particle,  and  the  resultant  force  is  the  difference  between  the  two  com 
ponents.  Could*  a  body  be  placed  in  empty  space  at  the  Centre  of  the 
earth,  it  would  be  sustained  there  without  any  material  support  by  the 
equal  and  opposite  attractions.  It  can  also  be  demonstrated  mathe- 
matically that,  if  the  earth  were  a  hollow  sphere  of  uniform  density, 
a  material  particle  would  remain  at  rest  at  any  point  within  it.  It 


GRAVITATION.  07 

follows  from  this  that: — The  attraction  of  the  earth,  for  a  particle  of 
matter  below  its  surf  ace,  is  directly  proportional  to  its  distance  from  the 
centre  of  the  earth. 

\  4.  Mass  and  Weight. 

96.  Mass. — The  mass  of  a  body  is  the  quantity  of  matter  which  it 
contains ;  and  since  the  absolute  weight  of  a  mass  of  matter  is  the  sum 
of  the  attraction  of  gravitation  upon  all  its  molecules,  it  follows  that,  in 
the  same  place,  the  masses  of  bodies  are  to  each  other  as  their  weights. 
Calling  the  mass  M  and  the  weight  W,  and  the  force  of  gravity  g,  for 
any  given  body,  then  W=  Mg.     We  have  already  seen  (41)  that  the 
masses  of  bodies  may  be  compared  by  the  forces  required  to  impart  to 
them  equal  velocities.     Since  gravity  acts  equally  on  matter  of  what- 
ever description,  this  comparison  may  also  be  made  by  comparing  their 
weights  when  otherwise  under  the  same  conditions. 

97.  Weight. — The  term  weight  as  used  above,  and  always  in  scien- 
tific language,  means  the  pressure  exerted  by  a  given  mass,  due  to  the 
force  of  gravity.    This  varies,  as  we  have  seen,  with  the  force  of  gravity, 
and  is  not  the  same  for  the  same  mass  at  all  parts  of  the  earth's  sur- 
face (93).     The  weight  of  any  given  kind  of  matter  varies  also  with  its 
mass.     A  mass  of  two,  three,  or  ten  times  a  given  unit  weighs  two, 
three,  or  ten  times  as  much  as  that  unit  at  the  same  place,  and  hence 
we  are  very  prone  to  confound  the  weight  of  a  substance  with  its  mass. 
On  the  surface  of  the  earth  this  confusion  of  terms  can  lead,  as  we  have 
seen  (93),  to  an  error  of  only  about  one  two-hundredth  part  of  the 
whole  (TJ5).    That  is,  a  mass  of  iron  weighing  1000  Ibs.  on  the  equator 
would  weigh  1005  Ibs.  at  the  pole.     Such  a  mass  of  iron  would  weigh 
only  500  Ibs.  at  a  distance  of  2000  miles  below  the  surface  of  the  earth, 
or  1650  mfles  above  the  earth,  and  only  160  Ibs.  on  the  moon,  while  it 
would  weigh  about  2600  Ibs.  on  the  planet  Jupiter,  and  28,000  Ibs.  if 
placed  on  the  sun. 

98.  Density. — The  density  of  a  body  is  the  mass  comprised  under  a 
unit  of  volume,  or  M—  VX  D,  where  the  mass,  M,  of  a  body  is  equal 
to  its  volume,  F,  multiplied  by  its  density,  D ; 

M 
transferring,  we  have      ^-=^J- 

This  may  be  otherwise  stated,  thus— 1st,  the  mass  is  proportional  to 
the  volume ;  2d,  for  an  equal  volume  the  mass  is  proportional  to  the 
density  ;  and,  3d,  the  density  of  the  same  mass  is  inversely  proportional 
to  the  volume  it  occupies. 

99.  Specific  weight  is  the  weight  contained  in  a  unit  of  volume;  this 
is  also  often  called  specific  gravity.    Representing  specific  weight  by  w, 


68  PHYSICS  OF  SOLIDS  AND  FLUIDS. 

and  absolute  weight  by  W,  we  have  W=  V  X  w,  hence,  1st,  the  weight 
is  proportional  to  the  volume ;  2d,  for  an  equal  volume  the  absolute 
weight  is  proportional  to  the  specific  weight ;  and,  3d,  for  equal  abso 
lute  weights  the  specific  weight  is  inversely  as  the  volume. 

By  the  first  formula  we  have  w  =  Dg,  whence  w  is  the  weight  of  the 
unit  of  volume,  and  D  its  mass.  Replacing  w  by  this  value  in  the  last 
formula,  it  becomes  W=  FX  D  X  ff» 

Specific  weight  differs  therefore  from  density  exactly  as  weight 
differs  from  mass.  Both  weight  and  gravity  vary  with  the  latitude, 
and  the  unit  accepted  as  a  standard  varies  also,  but  when  the  same 
standards  are  employed,  the  numbers  expressing  the  weights  remain 
unchanged,  and  no  sensible  error  results.  The  terms  density  and 
specific  gravity  have  thus  been  used  interchangeably  for  each  other, 
although,  speaking  strictly,  involving  different  quantities.  The  balance 
is  the  common  instrument  used  to  determine  weights.  It  will  be 
described  under  the  lever,  of  which  it  is  one  form. 

100.  French  system  of  weights. — As  in  measures  (16),  so  in 
weights  it  is  indispensable  to  assume  some  arbitrary  standard  unit. 
The  French  have  assumed  as  their  unit  of  weight,  the  pressure  exerted 
by  one  cubic  centimetre  of  pure  water  at  its  maximum  density  (39°.2 
Fahrenheit),  in  a  vacuum,  and  at  the  latitude  of  Paris.  This  unit  is 
called  a  gramme,  and  it  weighs  (nearly)  15*433  grains  English.  The 
gramme  is  multiplied  and  divided  decimally,  and  these  multiples  and 
subdivisions  are  named  on  the  same  plan  with  the  parts  of  a  metre : 
Thus  we  have, 


1  Kilogramme    =1000  grammes, 
1  Hectogramme  —    100          " 
1  Decagramme   =10          " 
1  Gramme  =        I          " 


1  Gramme          =  1-000  gramme, 
1  Decigramme    =  0-100          " 
1  Centigramme  =  0-010          " 
1  Milligramme  =  0-001          " 


The  kilogramme  is  the  commercial  unit  of  weight,  and  is  rather  less 
than  2£  Ibs.  avoirdupois,  being  15,432*42  English  grains. 

The  French  unit  is  of  course  a  gramme  only  at  Paris,  and  at  higher 
or  lower  latitudes  weighs  (according  to  the  principles  before  explained) 
more  or  less  than  a  gramme.  But  this  leads  to  no  practical  inconve- 
nience, so  long  as  a  set  of  exact  measurements  made  in  one  latitude  are 
not  brought  into  rigorous  comparison  with  those  made  by  the  same 
standard  in  another  latitude.  The  general  acceptance  of  the  French 
system  among  scientific  men,  and  its  special  fitness  for  scientific 
research,  owing  to  the  very  simple  relation  which  exists  between  it  and 
the  system  of  measures  already  described,  would  seem  to  render  the 
universal  adoption  of  a  decimal  system  of  weights  and  measures  for 
the  Uuited  States  one  of  the  great  desiderata  still  to  be  accomplished 
for  our  common  country. 


GRAVITATION.  69 

101.  English  and  American  system  of  weights. — In  England, 
as  in  the  United  States,  two  distinct  units  of  weight  are  in  common  use, 
leading  to  constant  confusion,  both  of  terms  and  quantities.     These 
units,  the  Troy  pound  and  the  Avoirdupois  pound,  are  entirely  arbitrary. 
They  are  represented  by  certain  masses  of  brass,  declared  by  law  to  be 
the  legal  standards  of  the  above  names.     These  pounds  are  related  to 
each   other   in  the   ratio  of  144  to  175,   and,   excepting  the  grains, 
none  of  their  subdivisions  are  alike.     The  troy  pound  contains  5760 
grains  divided  among  12  ounces,  and  the  avoirdupois  pound  contains 
7000  grains  divided  among  16  ounces.     The  legal  standard  of  weight 
in  the  United  States  is  the  troy  pound,  copied  by  Capt.  Kater  in  1827 
from  the  English  Imperial  Troy  pound,  for  the  U.  S.  Mint  at  Philadel- 
phia, where  it  now  is.     The  avoirdupois  pound  is,  however,  the  unit 
of  weight  in  actual  use  in  most  commercial  transactions.     Rater's  copy 
of  the  troy  pound  is  a  standard  at  62°  of  Fahrenheit's  thermometer  and 
30  inches  of  the  barometer.     A  cubic  inch  of  distilled  water  weighs  in 
the  air  at  62°  Fahrenheit  and  30  inches  barometric  pressure  252*456 
grains. 

The  English  standard  of  weight  is  connected  with  that  of  measure  by 
the  parliamentary  enactment,  that277'274  cubic  inches  shall  constitute 
the  Imperial  gallon  of  70,000  grains,  or  ten  pounds  of  pure  water  at 
62°  F.  and  30  inches  barometric  pressure. 

The  American  standard  gallon  contains  at  39°'83  F.  (the  maximum 
density  of  water  adopted  by  Hassler)  58,372  grains  of  pure  water  at  30 
inches  barometric  pressure.  Tables  for  the  comparison  and  reduction 
of  the  French,  English,  and  American  units  will  be  found  at  the  end 
of  this  volume. 

102.  Estimation  of  the  density  of  the  earth  by  experiment. — 
In  the  vicinity  of  a  mountain  a  plumb-line  is  not  truly  perpendicular, 
but  is  drawn  to  one  side  by  the  lateral  attraction  of  the  mountain.    The 
amount  of  this  deviation  is  measured  by  observations  on  the  zenith  dis- 
tances of  a  star,  at  two  stations  on  opposite  sides  of  the  mountain,  and 
on  the  same  meridian.     This  deviation  was  first  noticed  near  Mount 
Chimborazo  in  1738,  by  the  French  Academicians  engaged  in  measuring 
a  meridian  arc  in  Peru,  where  the  deviation  was  7/x'5.     In  1774,  Mas- 
kelyne  found  a  deviation  of  5/A83,  caused  by  the  lateral  attraction  of 
Schehallien,  an  isolated  mountain  in  Scotland.     Hutton  spent  three 
years  in  ascertaining  the  mean  attraction  of  one  thousand  stations  on 
this  mountain ;    a  labor  rewarded  by  the  Royal   Society  of  London. 
Estimating  the  mean  density  of  the  rocks  of  Schehallien  at  2'5  to  3  2, 
as  determined  by  Playfair,  the  mean  density  of  the  earth  was  deter- 
mined to  be  over  five  times  the  density  of  water.     The  accurate  ii 

9 


70  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

tigation  of  this  problem  was  one  of  the  highest  importance  in  astronomy, 
since  it  furnished  the  means  of  determining  the  mean  density  of  the 
earth,  by  comparing  its  attraction  with  the  attraction  of  a  part  of  its 
mass,  whose  density  could  be  ascertained  by  direct  experiment. 

This  problem  is  solved  with  much  greater  precision,  by  the  famous 
experiment  of  Cavendish,  in  which  the  earth's  attraction  is  compared 
with  that  of  a  mass  of  lead. 

Cavendish's  determinations  of  the  density  of  the  earth  were  made,  in  1798, 
by  means  of  an  apparatus  suggested  by  the  Rev.  John  Michell. 

"  Michell's  apparatus  was  a  delicate  torsion  balance,  consisting  of  a  light 
wooden  arm,  suspended  in  a  horizontal  position,  by  a  slender  wire  60  inches 
long,  and  having  a  leaden  ball,  about  2  inches  in  diameter,  hung  at  either  ex- 
tremity. Two  heavy  spherical  masses  of  metal  were  then  brought  near  to  the 
balls,  so  that  their  attractions  conspired  in  drawing  the  arm  aside.  The  devia- 
tion of  the  arm  was  observed;  and  the  force  necessary  to  produce  a  given  devi- 
ation of  the  arm,  being  calculated  from  its  time  of  vibration,  it  was  found  what 
portion  of  the  weight  of  either  ball  was  equal  to  the  attraction  of  the  mass  of 
metal  placed  near  it.  From  the  known  weight  of  the  mass  of  metal,  the  dis- 
tance of  the  centres  of  the  mass,  and  of  the  ball,  and  the  ascertained  attraction, 
it  is  easy  to  determine  the  attraction  of  an  equal  spherical  mass  of  water,  upon 
a  particle  as  heavy  as  the  ball  placed  on  its  surface.  Now  the  attraction  of  this 
sphere  will  have  to  that  of  the  earth  the  same  ratio  as  their  densities;  and  as 
the  attraction  of  the  earth  is  equal  to  the  weight  of  the  ball,  it  follows,  that  as 
the  calculated  attraction  is  to  the  weight  of  the  ball,  so  is  the  density  of  watei 
to  the  earth's  density,  which  is  thus  determined."  (  Wilson's  Life  of  Cavendish.) 

A  comparison  of  about  two  thousand  experiments  with  an  improved 
form  of  this  delicate  apparatus,  conducted  by  Mr.  Francis  Bailey,  in 
1842,  determined  the  mean  density  of  the  earth  to  be  5-6604  times  that 
of  water.  It  is  worthy  of  remark  that  Newton,  whose  guesses  were 
often  worth  more  than  the  researches  of  less  sagacious  men,  had  con- 
jectured the  earth's  density  to  be  between  5  and  6  times  the  density 
of  water. 

The  calculation  is  conducted  thus.  Let  L  be  half  the  length  of  the  horizontal 
arm  of  wood.  0  the  attraction  of  the  masses  of  lead,  and  t  the  time  of  an 
oscillation — neglecting  the  effect  of  torsion — Then,  according  to  the  theory  of 
the  pendulum  (81), 


Take  I  for  the  length  of  a  simple  pendulum  oscillating  in  the  same  time  (t)  by 
gravity,  and  we  have 

*  =  *,;.!_;      or  L  :   0  =  I :  g,  and  I :  L  .=  g  :  G. 

*  g 

Calling  the  attraction  of  the  unit  of  mass  upon  the  unit  of  mass  at  the  unit  of 
distance  a ;  the  mass  of  each  sphere  of  lead  m ;  d  the  distance  from  the  centre 
of  this  sphere  to  that  of  the  attracted  sphere  when  in  the  position  of  equilibrium  ; 


GRAVITATION.  71 

and,  lastly,  M  the  mass  and  R  the  mean  radius  of  the  earth,  and  we  have, 
according  to  the  laws  of  attraction, 

am  aM 

=  ~d*~f  g  ~  IF ' 

By  substituting  these  values  of  G  and  g  in  the  last  proportion,  it  becomes 

I  :  L  =  d*M  :  R*m,     or 
M:m=  IR*  :  Ld\ 

which  fixes  the  ratio  between  the  mass  of  the  earth  ( M)  and  that  of  one  of  the 
masses  of  lead  (m),  as  given  by  the  balance.  The  volume  of  the  earth  being 
represented  by  F,  and  its  mean  density  by  D,  we  have  by  (98)  J/  =  FX-#, 
from  which,  M  and  F  being  known,  D  is  deduced. 

The  inference,  unavoidable,  from  these  facts  is,  that  the  interior 
parts  of  the  earth  must  be  much  more  dense  than  the  superficial  crust. 
Granite  and  other  rocks  on  the  earth's  surface  have  an  average  density 
of  about  2'5.  This  remarkable  fact  may  be  explained,  partly  by 
remembering  that  the  interior  parts  of  the  earth  sustain  the  enormous 
pressure  of  the  surface  portions,  and  partly  by  the  hypothesis  of  primi- 
tive fluidity,  which  authorizes  the  belief  that  the  more  dense  portions 
of  the  planet  would  seek  the  lowest  place,  and  the  lighter  parts  the 
surface. 

§  5.    Motion  of  Projectiles. 

103.  Projectiles  are  bodies  thrown  into  the  air  by  some  momentary 
force.  They  are  therefore  subject  to  two  forces,  one  the  projectile 
force,  which  is  momentary,  the  other  the  constant  force  of  gravity. 

When  a  body  is  projected  vertically  upward,  it  rises  with  a  uniformly 
retarded  motion,  the  action  of  gravity  diminishing  the  velocity  of  ascent, 
at  every  instant,  until  the  projectile  force  is  expended,  when  the  body 
commences  to  descend,  and  passing  every  point  in  its  downward  path 
at  the  same  rate  as  in  its  upward  flight,  it  acquires  at  the  end  of  its 
fall  a  velocity  equal  to  that  with  which  it  was  projected. 

In  the  same  manner  when  a  body  is  projected  vertically  downwards 
its  path  is  the  same  as  that  of  a  body  falling  freely,  but  the  spa<* 
traversed,  and  also  the  velocity,  are  resultants  of  the  sum  of  the 
forces.    These  are  simple  cases  under  the  laws  of  uniformly  accelerat 
or  retarded  motion  already  considered  (32). 

If  the  direction  of  the  projectile  is  not  perpendicular,  then  the  path 
of  the  projectile  must  be  a  curve  (51). 

Thus,  if  a  cannon-ball  is  shot  in  the  direction  a  b  (fig.  51),  with  a  velocity 
which  would  carry  it  through  the  space  a  I  in  one  second,  then,  by  the  laws  of 
inertia,  it  would  continue  in  this  line,  passing  through  equal  spaces  in  equal 
times.  If  it  was  acted  upon  by  gravity  alone,  it  would  move  in  the  vertical 
a  c,  through  the  «paces  I'  II'  III',  in  corresponding  seconds.  But,  while  it  ia 


PHYSICS    OP    SOLIDS    AND    FLUIDS. 


projected  in  the  direction  a  b,  it  is  subject  also  to  the  action  of  gravity,  and, 
like  any  other  body,  must  fall  through  the 
vertical  space  of  16-C  feet  during  the  1st 
second ;  at  the  end  of  that  time,  therefore,  it 
will  be  found  at  e,  instead  of  at  I.  In  the 
same  manner,  at  the  end  of  the  2d  and  3d 
Beconds,  it  will  be  at  /  and  g,  instead  of  II 
and  III;  and  at  the  end  of  four  seconds  the 
body  will  arrive  at  Ji,  the  result  by  the  paral- 
lelogram of  forces  being  exactly  the  same  as 
if  it  had  been  first  carried  by  the  projectile 
force  in  the  line  a  b  during  four  seconds,  and .__ 
then  allowed  to  fall  during  four  seconds  by 
the  action  of  gravity  over  b  h  =  a  c.  Since 
the  action  of  the  projectile  force  is  only  mo- 
mentary, while  the  effect  of  gravity  is  con- 
stantly increasing,  the  body  will  not  describe 
the  diagonals  of  the  parallelograms,  a  e,  af, 
Jkc.,  but  a  curve,  which  in  mathematics  is 
called  a  parabola,  indicated  by  the  dotted 
^Ine  connecting  a  efg  and  h. 

By  a  similar  construction,  we  find  the  path 
of  a  body  projected  horizontally,  or  obliquely  downwards,  in  which  cases  the 
projectile  will  describe  one-half  of  a  parabola.  In  every  case  the  path  of  the 
projectile  is  a  complete  or  partial  parabola,  whose  axis  is  in  the  direction  of 
gravity;  and  its  vertical  distance  below  the  line  of  projection  at  any  given 
moment,  is  always  equal  to  the  space  it  would  have  fallen  freely  during  the  time 
since  it  was  projected. 

By  the  principle  of  parallelogram  of  velocities,  it  is  evident  that  in  the  time 
the  body  would  describe  the  curve  a  efg  h,  it  would,  without  the  action  of 
gravity,  describe  the  line  a  b  =  vt,  v  being  the  velocity  of  projection,  and  t  the 
time  of  flight.  Let  a  be  the  angle  of  elevation  b  a  h,  v'  the  vertical  velocity, 
and  v"  the  horizontal  velocity,  then  v'  =  v  sin.  a,  and  v"  —  v  cos.  a.  The  ver- 
tical velocity  would  evidently  be  spent  in  one-half  the  time  of  flight,  and  an 
equal  descending  velocity  would  be  acquired  at  the  time  of  striking  the  point  h, 

2v  sin.  a 

hence,  v'  =  v  sin.  a  =  %gt,  and  t  = =  the  time  of  flight.     The  hori- 

ff 
zontal  range  will  equal  the  horizontal  velocity  v"  multiplied  by  the  time  of 

2v  sin.  a        2w2  sin.  a  cos.  a        v2  sin.  2a 
flight  =  v  cos.  a  X  = = • 

.     g  9 

This  value  of  the   horizontal  range 

ah  is  evidently  the  greatest  for  any 
value  of  v,  when  sin.  2a  =  1,  or  a  = 
45° ;  and,  for  elevations  equally  above 
and  below  45°,  the  horizontal  range 
will  be  equally  diminished;  that  is, 
the  horizontal  range  will  be  the  same 
for  an  elevation  of  40°  as  for  50°,  and 
the  same  for  an  elevation  of  30°  as  for 
60°.  Fig.  52  shows  the  form  of  the  curves  described  by  projectiles  at 


GRAVITATION. 


73 


53 


angular  elevations  of  0°,  15°,  45°,  60°,  and  90°  (A  B,  A  C,  A  D,  A  E, 
AF).  The  dotted  lines  show  the  angles  of  projection,  and  the  smooth 
lines,  with  corresponding  letters,  show  the  paths  described  by  the 
projectiles.  The  effect  upon  the  flight  of  projectiles  produced  by 
resistance  of  the  air,  will  be  considered  hereafter. 

104.  The  ballistic  pendulum  is  an  instrument  employed  to  mea- 
sure the  velocity  of  projectiles.  A 
heavy  mass  of  wood  and  iron,  shown 
at  b,  fig.  53,  is  suspended  at  C,  on  a 
shaft  three  or  four  yards  in  length 
over  a  graduated  arc  BED.  The 
ball,  fired  in  the  direction  N  N, 
strikes  the  ballistic  pendulum  at  A, 
and,  penetrating  the  heavy  mass, 
imparts  to  it  a  velocity  which  is 
determined  by  comparison  of  the 
arc  E  D  described  by  the  pendu- 
lum, and  the  time  in  which  the 
whole  mass  is  found  to  vibrate.  S 
is  supposed  to  be  the  centre  of 
gravity,  M  the  centre  of  oscillation, 
C  G  the  arm  of  impact,  and  M  H  the 
perpendicular  height  through  which  the  pendulum  rises.  From  these 
data  the  velocity  of  the  ball  at  the  moment  of  impact  can  be  calculated. 


Problems. — Falling  Bodies. 

17.  If  a  stone  is  dropped  into  a  well,  and  it  is  seen  to  strike  the  water  at  the 
end  of  3  seconds,  what  is  the  depth  of  the  well  ? 

18.  A  body  is  projected  upward  with  a  velocity  which  will  carry  it  to  the 
"height  of  64  feet  4  inches ;  after  how  long  a  time  will  it  be  descending  with 
half  the  original  velocity  ? 

19.  Find  the  velocity  with  which  a  body  must  be  projected  upwards  from  the 
foot  of  a  tower,  so  as  to  meet  half  way  another  body  let  fall  at  the  same  time 
from  the  top  of  the  tower. 

20.  A  balloon  is  ascending  vertically  with  a  given  velocity,  and  a  body  is  let 
fall  from  it,  which  reaches  the  ground  in  t  seconds  :  find  the  height  of  the  balloon 
at  the  moment  of  the  body  leaving  it. 

21.  A  body  is  observed  to  fall  the  last  a  feet  of  its  descent  from  rest  in  t 
seconds  :  find  the  height  from  which  it  fell. 

22.  A  body  has  fallen  through  the  distance  of  half  a  mile ;   what  was  the 
distance  described  in  the  last  second? 

23.  A  body  is  projected  upwards  with  a  velocity  of  64£  feet  in  a  second ;  how 
far  will  it  ascend  before  it  begins  to  return  ? 

9* 


74  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

24.  A  stone  dropped  from  a  bridge  strikes  the  water  in  2£  seconds ;  what  is 
the  height  of  the  bridge?     Also  if  the  stone  be  projected  downwards  with  a 
velocity  of  3  feet  per  second,  in  what  time  will  it  strike  the  water  ? 

25.  A  stone  thrown  horizontally  from  the  summit  of  a  high  cliff  is  seen  to 
strike  the  ground  at  the  end  of  5  seconds ;  what  is  the  height  of  the  cliff  above 
the  point  where  the  stone  falls  ? 

4Z6.  A  body  is  projected  vertically  upwards,  and  the  time  between  its  leaving  a 
given  point  and  returning  to  it  again  is  given;  find  the  velocity  of  projection 
and  the  whole  time  of  motion. 

27.  From  what  elevation  must  a  body  weighing  500  pounds  fall,  to  strik 
with  the  same  momentum  as  a  body  weighing  900  pounds  falling  from  an  elev» 
tion  of  64J  feet  ?  , 

Descent  of  Bodies  on  Inclined  Planes.* 

28.  What  time  will  be  required  for  a  body  to  descend  an  inclined  plane  whos« 
length  is  200  feet,  and  whose  elevation  is  64J  feet. 

29.  What  velocity  will  be  acquired  by  a  body  descending  a  plane  inclined  at 
an  angle  of  30°,  the  perpendicular  height  being  145 £  feet? 

30.  If  a   railway  train,  with   a  speed  of  30   miles   per  hour,  arrives    at   a 
descending  grade  of  60  feet  to  the  mile,  and  has  no  force  applied  to  check  its 
speed,  what  will  be  its  velocity  after  running  3  miles  on  the  grade  ? 

31.  If  a  train,  moving  at  the  rate  of  25  miles  an  hour,  arrives  at  a  grade  of 
60  feet  per  mile,  2  miles  in  length,  and  no  more  steam  is  applied  than  before 
arriving  at  the  grade,  what  will  be  the  velocity  of  the  train  after  ascending  the 
grade  ? 

Central  Forces. 

32.  Find  th«  force  with  which  a  body  weighing  8  Ibs.  would  stretch  a  string, 
3  feet  long,  retaining  it  in  a  circle,  when  the  body  makes  3  revolutions  per 
second. 

33.  What  must  be  the  weight  of  a  body  revolving  7  times  per  second  in  a 
circle  10  feet  in  diameter,  in  order  that  the  centrifugal  force  of  the  revolving 
body  may  be  equivalent  to  a  weight  of  1000  Ibs.  ? 

34.  How  many  times  must  the  revolution  of  the  earth  be  increased  to  have 
the  weight  of  bodies  at  the  equator  diminished  one-half,  calling  the  radius  of 
the  earth  4000  miles  ? 

35.  What  must  be  the  number  of  revolutions  per  second  of  a  body  weighing 
17  Ibs.,  revolving  in  a  circle  whose  radius  is  5  feet,  that  its  centrifugal  force  may 
be  the  same  as  that  of  a  body  weighing  25  Ibs.,  revolving  9  times  per  second  in 
a  circle  whose  radius  is  3  feet  ? 

Pendulum  and  Gravity. 

36.  What  is  the  time  of  vibration  at  Paris  of  a  simple  pendulum  whose  length 
is  3  metres  ? 

37.  What  is  the  force  of  gravity  in  a  deep  mine  where   the  length  of  the 
seconds  pendulum  is  found  to  be  38  inches  ? 

38.  What  is  the  time  of  vibration  of  a  simple  pendulum  30  inches  in  length, 
where  the  accelerating  force  of  gravity  is  32  feet  per  second  ? 

39.  What  is  the  time  of  vibration  of  a  simple  pendulum  at  Paris,  the  length 
of  the  pendulum  being  one  metre,  and  the  amplitude  of  vibration  being  a  =  9°  ? 

*  In  these  problems  the  retarding  force  of  friction  is  not  to  be  considered. 


THEORY    OF    MACHINERY.  75 

40.  What  is  the  accelerating  force  of  gravity  at  New  York?  at  Boston?  at 
New  Orleans  ?  at  Cape  Horn  ?  at  Stockholm  ? 

41.  If  the  force  of  gravity  at  the  earth's  surface  be  regarded  as  unity,  what 
will  be  the  force  of  gravity  at  a  distance  below  the  surface  equal  to  one-tenth 
part  of  the  earth's  radius  ? 

Plight  of  Projectiles.* 

42.  What  distance  will  a  ball  be  thrown  on  a  horizontal  plane,  if  it  is  fired 
from  a  cannon  with  a  velocity  700  feet  per  second  at  an  angular  elevation  of  33°  ? 

43.  What  is  the  greatest  distance  to  which  a  ball  can  be  thrown  on  a  hori- 
zontal plane,  if  it  leaves  the  mouth  of  the  cannon  with  a  velocity  of  1000  feet 
x>er  second  ? 

44.  If  a  ball  leaves  the  cannon  at  an  elevation  of  30°,  with  a  velocity  of  800 
feet  per  second,  in  what  time  will  it  strike  the  horizontal  plane  ? 

45.  At  what  angle  of  elevation  must  a  ball  be  fired  that,  with  an  initial  velo- 
city of  600  feet  per  second,  it  may  strike  a  horizontal  plane  at  a  distance  of  two 
miles  ? 

46.  If  a  ball  discharged  from  the  mouth  of  a  cannon,  at  an  elevation  of  35°, 
strikes  the  horizontal  plane  at  a  distance  of  three  miles,  what  was  its  original 
velocity  ? 


CHAPTER  IV. 

THEORY    OF    MACHINERY. 
§  1.  Machines. 

105.  Principle  of  virtual  velocities. — It  was  shown  in  g  46,  that 
when    a   body,    having   a   fixed  54 

point  of  support,  is  acted  on  by      a  \fr 

two  parallel  forces  in  the  same     /"""•• "  \ 

direction,  the  forces  will  be  in  ^ ...-  -:;ix:C.  •? 

'.  ..-•"""'  *"*"^-  ' 

equilibrium,  if  they  are  to  each     2""  / 

other  inversely  as  their  distances  '"* Ih 

from  the  supporting  point.  Thus  in  fig.  54,  if  an  inflexible  rod,  sup- 
ported at  C,  is  acted  on  by  two  forces,  W  and  P,  such  that 

W  :  P  =  C  P  :  C  W, 

then  they  will  be  in  equilibrium.  But  as  in  every  proportion  the  pro- 
duct of  the  first  and  last  terms  is  equal  to  the  product  of  the  second 
and  third ;  so  instead  of  saying  that  the  forces  are  inversely  as  their 
distances,  the  same  thing  is  expressed  by  W  X  C  W  P  ,  C  P.  The 

*  In  these  problems  no  account  is  supposed  to  be  taken  of  the  resistance  of 
the  air. 


76  PHYSICS    OF    SOLIDS   AND    FLUIDS. 

principle  may  be  otherwise  illustrated  thus : — Let  the  bar  W  P  be  made 
to  oscillate  gently  about  the  point  of  support  C.  It  is  plain  that  the 
spaces  described  by  the  ends  of  the  bar  will  be  proportional  to  their 
distances  from  the  axis ;  for  the  angles  at  the  axis  being  equal,  the 
arcs  af  and  bh  are  directly  proportional  to  their  radii  C  W  and  C  P. 
Hence 

W  :  P  =  b  h  :  af; 

That  is,  two  forces  are  in  equilibrium  when  they  are  to  each  other 
inversely  as  the  spaces  which  they  describe.  The  arcs  being  described 
in  the  same  time,  represent  the  velocities,  and  the  principle  is  usually 
thus  stated :  forces  in  equilibrium  must  be  to  each  other  inversely  as  their 
velocities.  The  products,  therefore,  of  the  forces  multiplied  by  their 
respective  velocities,  are  equal : 

WX«/=PX^. 

These  products  are  called  the  moments  of  the  forces,  and  when  these 
momenta  are  equal  the  forces  are  in  equilibrium.  If  the  movement  is 
doubled,  halved,  or  raised  in  any  proportion,  the  efficacy  of  the  force  is 
similarly  varied.  Any  arrangement  by  which  two  forces  are  brought 
into  this  relation  to  each  other,  constitutes  a  machine. 

106.  Machine,   Power,  Weight. — In  extension  of  the  statement 
last  made,  a  machine  is  any  arrangement  of  parts  in  an  apparatus,  by 
which  force  may  be  transmitted  from  one  point  to  another,  usually  with 
some  modification  of  its  intensity  or  direction,  and  with  reference  to  the 
performance  of  mechanical  work. 

The  moving  force  in  a  machine  is  called  the  power;  the  place  where 
it  is  applied  is  the  point  of  application  ;  and  the  line  in  which  this  point 
tends  to  move  is  the  direction  of  the  power.  The  resistance  to  be  over- 
come is  called  the  weight,  and  the  part  of  the  machine  immediately 
applied  to  the  resistance  is  the  working  point. 

The  moving  powers  and  the  resistances  in  mechanics  are  both 
extremely  various;  but  of  whatever  kind  they  may  be,  they  can 
always  be  expressed  by  equivalent  weights,  i.  e.,  such  as  being  applied 
to  the  machine  would  produce  the  same  effects. 

107.  Equilibrium  of  machines. — When  the  power  and  weight  are 
equal,  the  machine  is  in  equilibrium,  and  it  may  be  at  rest,  or,  as  is 
usually  the  case,  in  a  state  of  uniform  motion.     If  a  machine  in  this 
case  is  put  into  uniform  motion,  it  must,  by  force  of  inertia,  continue 
to  move  indefinitely  ;  for  the  power  and  weight  being  equal,  neither  of 
these  forces  can  stop  or  modify  the  motion,  without  some  extraneous 
force,  which  is  contrary  to  the  supposition. 

Thus,  if  an  engine  draws  a  railway  tran  with  uniform  velocity,  the  power 


THEORY    OF    MACHINERY  77 

of  the  engine  is  in  equilibrium  with  the  resistance  of  the  train.  At  starting 
the  power  is  greater  than  the  resistance,  and  the  motion  of  the  train  is  conse 
quently  accelerated,  until  the  resistance  becomes  equal  to  the  power,  when 
equilibrium  is  again  established.  If  any  part  of  the  power  is  now  withdrawn, 
the  power  becomes  less  than  the  resistance,  and  the  motion  is  consequently 
retarded  until  the  train  is  brought  to  rest. 

The  mechanical  energy,  or  moving  force  of  the  power,  is  found  by 
multiplying  its  equivalent  weight  by  the  space  through  which  it  moves, 
or  its  velocity;  and  the  value  of  the  resistance  is  estimated  in  the  same 
manner.  As  we  have  just  seen,  the  relation  between  these  moments 
determines  the  state  of  the  machine. 

108.  Utility  of  machines. — It  is  sometimes  said,  in  illustration  of 
the  usefulness  of  machines,  that  a  great  weight  may  be  supported  or 
raised  by  an  insignificant  power;    but  such  statements,  if  literally 
understood,  are  obviously  untrue.     No  machine,  however  ingenious  its 
construction,  can  create  any  force,  and  therefore  the  working  point  can 
exert  no  more  forc$..  than  is  transmitted  to  it  from  the  source  of  power. 
Every  machine  has  certain  fixed  points,  which  are  arranged  to  support 
any  required  part  of  the  weight,  while  the  remainder  of  the  weight, 
and  that  part  only,  is  directly  sustained  by  the  power.    This  remainder 
cannot  be  greater  than  the  power. 

109.  Relation  of  power  to  weight. — But  if  the  weight  is  not  only 
supported,  but  raised  through  a  given  space,  then  the  power  must  move 
through  a  space  as  much  greater  than  the  weight  moves  through,  as  the 
weight  itself  is  greater  than  the  power ;  in  other  words,  the  power  and 
weight  must  be  inversely  as  their  velocities.     This  inverse  proportion 
is  expressed  when  it  is  said,  that  power  is  always  gained  at  the  expense 
of  time. 

To  raise  1000  Ibs.  to  a  height  of  one  foot  by  a  single  effort,  would  require  a 
force  equivalent  to  1000  Ibs. ;  but  the  same  thing  may  be  accomplished  by  a 
power  of  1  Ib.  acting  for  1000  times  successively,  through  a  space  of  one  foot. 
If  a  man  by  exerting  his  entire  strength  could  lift  200  Ibs.  to  a  certain  height, 
in  one  minute,  no  machine  whatever  can  enable  him  to  lift  2000  Ibs.  to  the  same 
height  in  the  same  time.  He  may  divide  the  weight  into  ten  parts,  and  lift  each 
part  separately ;  or  by  the  intervention  of  a  machine  he  may  raise  the  whole 
mass  together,  requiring,  however,  ten  minutes  for  the  task. 

On  the  other  hand,  it  is  often  the  object  of  a  machine  to  move  a  small 
resistance  by  a  great  power. 

In  a  watch,  the  moving  force  of  the  mainspring  is  very  much  greater  than 
the  resistance  of  the  hands,  revolving  about  the  dial.  In  a  locomotive  engine, 
each  full  stroke  of  the  piston  moves  the  train  through  a  space  equal  to  the 
circumference  of  the  driving  wheel;  if  the  length  of  stroke  is  cne  foot,  and  tho 
circumference  of  the  wheel  12  feet,  then  the  velocity  of  the  piston  will  be  to  the 
velocity  of  the  train,  as  2  to  12 ;  consequently  the  power  acting  on  the  piston  ia 
than  the  resistance  of  the  train,  in  the  proportion  of  12  to  2. 


78  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

110.  Adaptation  of  the  power  to  the  weight  in  machinery.-  — 

The  use  of  machines  is  to  adapt  the  power  to  the  weight.  If  the  inten- 
sity, direction,  and  velocity  of  the  power,  were  the  same  as  the  intensity 
and  direction  of  the  resistance,  and  the  velocity  required  to  be  given  to 
it,  then  the  power  might  be  directly  applied  to  the  resistance,  without 
the  intervention  of  a  machine.  But  if  a  small  power  is  required  to 
move  a  great  resistance ;  or,  if  a  power  acting  in  one  direction,  is 
required  to  impart  motion  in  another ;  or,  to  impart  a  velocity  greater 
or  less  than  its  own,  then  it  is  necessary  to  employ  a  machine  which 
will  modify  the  effect  of  the  power  in  the  required  manner.  Besides 
these,  the  motion  of  the  power  may  differ  from  the  motion  required  in 
the  resistance  in  a  great  variety  of  ways. 

The  power  may  have  a  reciprocating  motion,  as  in  the  locomotive  engine,  and 
be  requiredrto  produce  a  continuous  motion  in  a  straight  line,  as  in  moving  a 
train  upon  a  railway.  Or,  the  power  may  have  a  rectilinear  motion,  as  a  stream, 
and  be  employed  to  produce  the  circular  motion  of  the  stones  in  a  grist-mill,  or 
the  reciprocating  motion  of  a  saw,  in  a  saw-mill.  «• 

In  every  class  of  machines,  the  relations  existing  between  the  power 
and  the  resistance,  depend  solely  on  the  construction  of  the  machine ; 
but  even  a  general  account  of  the  ingenious  contrivances  by  which  the 
moving  force  is  regulated,  modified,  and  adapted  to  the  varying  condi- 
tions and  requirements  of  the  resistance,  would  lead  us  far  beyond  the 
limits  and  design  of  this  work. 

111.  Vis  viva,  or  living  force,  is  the  power  of  a  moving  body  to 
overcome  resistance,  or  the  measure  of  work  which  can  be  performed 
before   the  body   is  brought  to  a   state  of  rest.     The  vis  viva   of  a 
body  is  represented  by  M V2,  or  the  mass  of  the  body  multiplied  by  the 
square  of  its  velocity. 

When  a  body  is  projected  vertically  upwards,  the  height  to  which  it 
will  ascend  is  proportional  to  the  square  of  its  velocity.  If  ^represent 
the  weight  of  the  body,  and  h  the  height  to  which  it  is  elevated  by  a 
given  impulse,  the  amount  of  work  performed  will  be  represented  by 

F2 
Wh,  but  W=  Mg  and  h  —  r— ,  substituting  these  values  of  JFand  h, 

we  have  the  work  performed  =  £  MV2.  Hence  the  work  which  can  be 
performed  by  the  accumulated  power  of  a  moving  body  is  equal  to  one- 
half  the  mass  multiplied  by  the  square  of  the  velocity. 

Take  the  case  of  a  pile-driver,  in  which  a  heavy  mass  of  iron  is  ele- 
vated to  a  height  of  30  or  40  feet,  and  is  then  suddenly  allowed  to  fall ; 
the  resistance  overcome  in  raising  the  driver  is  exactly  proportional  to 
the  elevation  to  which  it  is  raised,  and  the  accumulated  power  of  the 
stroke  increases  in  the  same  ratio ;  hence  it  is  evident  that  the  vis 


THEORY    OP    MACHINERY.  79 

viva,  or  power  of  overcoming  resistance,  must  be  truly  represented  by 


Again,  in  the  case  of  a  railway  train  moving  with  a  velocity  F,  the  great- 
est velocity  attainable  by  a  given  power  of  steam  ;  let  v  be  the  accelera- 
tion of  velocity  imparted  to  the  train  by  the  locomotive  during  the  first 
second  of  its  action,  and  M  the  mass  of  the  moving  train,  including  the 
locomotive.  If  the  movement  of  the  train  were  not  retarded  by  friction, 
or  some  other  opposing  force,  we  should  have  V  =  vt,  or  the  velocity,  F, 
would  go  on  constantly  increasing  ;  but  such  we  know  is  not  the  case, 
for  the  train  soon  attains  a  maximum  velocity,  when  the  entire  force 
of  the  locomotive  is  every  instant  expended  in  overcoming  friction,  and 
the  train  moves  on  with  a  momentum  expressed  by  MV,  but  its  vis  viva 
is  expressed  by  MV'1.  If  the  force  of  steam  were  suddenly  discon- 
tinued, the  power  of  the  moving  train  to  ascend  a  grade,  td*overcome 
any  obstacle,  or  to  deal  destruction  to  itself,  or  to  any  object  with 
which  it  comes  in  collision,  would  still  be  proportional  to  vis  vica  or 
MV2.  Now  suppose  the  velocity  of  the  train  to  be  doubled,  so  that 
V/  =  2V.  It  is  evident  that  in  any  given  interval  of  time  the  train 
will  pass  over  twice  as  many  points  of  resistance  as  before,  and  as  it 
passes  each  point  at  twice  the  previous  velocity,  it  will  encounter  at 
every  point  twice  as  much  resistance  to  motion  as  before.  Hence  to 
impart  to  the  train  a  double  velocity,  a  fourfold  force  is  required  ;  and 
the  power  of  the  train  to  overcome  resistance  will  be  proportional  to 
its  vis  viva,  MV/2.  This  will  be  the  true  measure  of  the  force  which 
has  imparted  the  velocity  V,  and  which  is  now  constantly  expended 
in  overcoming  the  resistance  encountered  by  the  moving  train.  The 
same  principles  determine  the  power  expended,  or  work  actually  per- 
formed (resistance  included),  by  any  kind  of  machinery. 

It  may  be  necessary  to  explain  more  fully  the  distinction  between 
momentum  and  vis  viva,  so  that  it  may  be  readily  understood  when  the 
one  or  the  other  is  to  be  taken  as  the  measure  of  force. 

Momentum,  MV,  expresses  the  relation  of  force  to  inertia,  or  the 
amount  of  motion  in  a  moving  body.  Vis  viva,  M  F2,  is  the  measure 
of  twice  the  amount  of  work  which  a  moving  body  can  perform  before 
it  is  brought  to  rest.  Vis  viva  is  the  measure  of  force  required  to 
maintain  a  constant  motion,  MV,  against  the  resistance  caused  by  the 
positive  properties  of  bodies,  as  attraction,  cohesion,  repulsion.  Momen- 
tum is  the  measure  of  the  force  required,  without  regard  to  time,  to  set 
a  body  in  motion  with  a  velocity  V,  when  no  other  body  interferes  with 
its  motion,  as  in  the  case  of  a  body  falling  freely  in  a  vacuum.  In  the 
case  of  the  railway  train,  the  mass  of  the  train  multiplied  by  its  velo- 
city is  the  measure  of  useful  work  performed  in  a  unit  of  time,  but  it 


80  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

is  not  the  measure  of  resistance  overcome,  or  actual  work  performed, 
or  of  the  force  which  has  been  expended  in  performing  that  work.  The 
latter  is  measured  by  one-half  the  vis  viva,  or  J  MV2. 

Illustrations  of  vis  viva. — Suppose  a  battering-ram  weighing  4000  Ibs. 
to  be  impelled  with  a  velocity  of  30  feet  per  second,  its  vis  viva,  J/F2=  4000  X 
30  X  30  =  3,600,000  ;  yet  a  cannon  ball  weighing  64  Ibs.,  flying  with  a  velocity 
of  1000  feet  per  second,  will  have  a  power  of  dealing  destruction  more  than 
seventeen  times  as  great,  for  its  vis  viva  equals  64,000,000.  Calculations  of  this 
sort  explain  the  origin  of  the  terribly  destructive  power  of  the  engines  of 
modern  warfare. 

A  railway  train  moving  50  miles  an  hour  will  possess  more  than  six  times 
the  vis  viva  that  it  would  have  when  going  twenty  miles  an  hour ;  and,  there- 
fore, it  will  possess  more  than  six  times  the  power  of  dealing  destruction,  either 
to  itself  or  to  an  obstacle,  at  the  former  than  at  the  latter  rate.  Thus  the  well 
known  relation  between  speed  and  amount  of  damage,  in  case  of  accident,  is 
readily  accounted  for,  as  also  the  enormous  comparative  cost  of  fuel,  and  wear 
and  tear  of  trains  of  high  speed. 

The  destructive  power  of  hurricanes,  which  move  from  60  to  100  miles  an 
hour,  is  readily  understood  when  we  know  that  the  power  of  dealing  destruction 
increases  in  proportion  to  the  square  of  the  velocity. 

112.  Impact  and  its  results. — When  a  body  in  motion  encounters 
another,  the  velocity  and  momentum  of  both  undergo  certain  changes, 
which  depend  on  the  elasticity  of  the  bodies,  and  other  physical  circum- 
stances. 

Impact  considered  with  reference  to  momentum. — a — When 
a  body  in  motion  strikes  another  at  rest,  it  can  continue  to  move 
only  by  pushing  this  body  before  it,  and  it  must  impart  so  much 
momentum  that,  after  impact,  both  may  move  with  a  common  velo- 
city. If  the  masses  of  the  two  bodies  are  equal,  it  is  evident  that, 
after  impact,  the  momentum  will  be  equally  divided  between  them,  and 
their  velocity  will  be  one-half  of  the  velocity  of  the  moving  body 
before  collision.  If  the  mass  at  rest  is  double  the  mass  in  motion,  the 
common  velocity  will  be  one-third  ;  and  generally,  when  a  moving  body 
communicates  motion  to  a  body  at  rest,  the  velocity  of  the  two  united 
will  be  to  that  of  the  moving  body  as  the  mass  of  the  latter  is  to  the 
sum  of  the  masses  of  both. 

If  a  musket  ball,  whose  weight  is  _L  lb.,  and  its  velocity  1300  feet  a  second, 
strikes  a  suspended  cannon  ball  weighing  48  Ibs.,  it  will  put  it  in  motion,  and 
their  common  velocity  will  be  to  that  of  the  bullet  as  l  is  to  48  +  1  ,  or  as  1 
is  to  961;  the  velocity  of  the  two  is  therefore  Iffl-f,  or  about  H  feet  a  second. 

b — Bodies  moving  in  the  same  direction  may  impinge,  if  their  velo- 
cities are  different.  If  an  inelastic  body  overtakes  another,  the  first 
will  accelerate  the  second,  and  the  second  will  retard  the  first,  until 
they  have  acquired  a  common  velocity,  when  they  will  move  on  together 


THEORY    OF    MACHINERY.  81 

Since  the  bodies  move  in  the  same  direction,  there  can  be  no  increase 
or  diminution  of  the  total  momentum  by  impact,  but  only  a  re-distri- 
bution. If  they  are  equal  in  mass,  their  velocity,  after  impact,  will  be 
half  the  sum  of  their  previous  velocities. 

If  before  impact,  A  had  a  velocity  of  6,  and  2?  a  velocity  of  4,  then  theii 
common  velocity  will  be  5. 

The  two  bodies  may  have  unequal  masses  as  well  as  velocities. 

If  the  mass  of  A  is  8,  and  its  velocity  17,  its  momentum  will  be  136.  If  B 
has  a  mass  of  6,  and  velocity  of  10,  its  momentum  will  be  60.  The  sum  196 
is  the  total  momentum  of  the  united  masses  after  impact;  and  this  sum 
divided  by  the  sum  of  the  masses  gives  14,  the  common  velocity. 

c  —  If  two  equal  bodies,  moving  with  equal  velocities  in  opposite 
directions,  impinge  on  each  other,  their  moments  being  equal,  will  be 
mutually  destroyed,  and  the  bodies  will  remain  at  rest.  The  force  of 
the  shock,  in  this  case,  is  equal  to  that  which  either  would  sustain,  if, 
while  at  rest,  it  were  struck  by  the  other  with  a  double  velocity.  If 
the  moments  of  the  bodies  are  unequal,  then,  after  impact,  they  will 
move  together  in  the  direction  of  the  greater,  and  their  joint  momentum 
will  be  equal  to  the  difference  of  their  previous  moments,  and  their 
velocity  will  be  found  by  dividing  that  difference  by  the  sum  of  the 
masses. 

d  —  These  laws  may  be  shown  experimentally  by  suspending  two  balls 
at  the  centre  of  a  graduated  arc,  and  producing  impact  according  to 
the  conditions  described. 

If  two  bodies  moving  in  different  lines  impinge  on  each  other,  then, 
after  contact,  they  will  move  together  in  the  diagonal  of  that  parallelo- 
gram whose  sides  represent  their  previous  moments  and  directions. 

From  these  principles  it  follows  that,  if  two  inelastic  bodies,  M  and  N,  moving 
in  the  same  direction,  with  velocities  V  and  V,  come  in  contact,  their  common 

MV+NW 
velocity  after   impact   will   be   expressed   by  the  formula   V"  =   —  —  -  TT""- 

When  the  bodies  move  in  opposite  directions,  the  velocity  of  the  body  having 
the  greater  momentum  is  to  be  taken  as  positive,  and  the  other  negative  ;  the 
resultant  velocity  will  be  in  the  direction  of  the  body  which  previously  had  the 
greater  momentum. 

Impact  considered  with  reference  to  vis  viva.  —  When  a  body 
in  motion  strikes  another  body  at  rest,  which  is  free  to  move,  the  two 

KfV 
bodies  have  a  common  velocity,   V"  ==  M       •.    The  vis  viva  after  im- 


pact  will  be  expressed  by  (M  +  N)    V"      =      -<'     Suppose  the 


second  body  N  to  be  a  certain  number  of  times,  (represented  by  a,) 
10 


82  PHYSICS   OF    SOLIDS   AND   FLUIDS. 

greater  than  the  first  body  M,  then  N  =  a  M.     The  vis  viva  of  the  com- 

M*v*          M*V*          MV* 
bmed  mass  after  impact  will  then  become  — =  — — = . 

M-^-N      M(l  +  a)       1-fa 

Hence : — 

When  a  moving  body  strikes  a  body  at  rest,  and  the  two  move  on  together, 
the  vis  viva  of  the  combined  mass  is  as  many  times  less  than  the  vis  viva 
of  the  first  body  before  impact  as  the  combined  mass  is  greater  than  the 
first. 

This  principle  shows  how  a  man  may  receive  the  most  violent  strokes  of  a 
sledge-hammer,  upon  an  anvil  laid  upon  his  chest,  without  the  slightest  injury, 
when,  if  only  a  light  board  were  interposed  between  his  person  and  the  descend- 
ing hammer,  the  stroke  would  be  instantly  .fatal  to  life.  The  interposition  of 
any  heavy  body  wards  off  the  force  of  a  blow  on  the  same  principles. 

Pressure  produced  by  impact. — Beaufoy  determined  that  a  body 
of  1  Ib.  weight,  with  a  velocity  of  1  foot  in  a  second,  strikes  with  a  pres- 
sure equal  to  0-5003  Ib.     To  find  the  pressure  produced  by  the  impact 
of  any  projectile,  we  have  the  general  formula, 
Pressure  =  0'5003  M V\ 

If  the  body  descends  vertically,  the  weight  of  the  body  itself  must  of 
course  be  added  to  the  direct  effects  of  impact. 

Destructive  effects  of  impact. — The  motion  communicated  to  very 
large  or  immovable  bodies,  by  an  impact  o*f  small  ones,  is  not  lost, 
but  becomes  insensible  from  its  enormous  diffusion.  Motion  can  be 
destroyed  only  by  motion  ;  friction  and  resistance  disperse,  but  do  not 
destroy  it.  An  impact  can  act  directly  upon  only  a  few  of  the  mole- 
cules of  the  body  to  which  it  imparts  motion. 

The  power  which  projects  a  bullet  acts  on  only  one-half  its  surface. 

The  motion  must,  therefore,  be  diffused  from  the  parts  struck  to  all 
the  other  parts  of  the  body,  before  it  can  begin  to  move ;  and  this  dif- 
fusion requires  time,  which  may  be  short  indeed,  but  is  not  infinitely 
so.  It  happens,  therefore,  that  a  movable  body,  if  struck  by  another 
moving  with  great  velocity,  may  be  penetrated  or  broken  at  the  point 
of  impact,  without  being  itself  put  in  motion.  The  part  of  the  body 
which  receives  the  blow  is  set  in  motion  with  such  velocity  that  its  par- 
ticles are  rent  asunder  before  motion  can  be  communicated  to  the  mass 
of  the  body.  Such  effects  appear  incredible  to  persons  unacquainted 
with  the  inertia  of  matter  and  its  consequences. 

A  rifle  ball  may  be  fired  through  a  pane  of  glass  suspended  by  a  thread, 
without  shattering  the  glass,  or  even  causing  it  to  vibrate.  A  door  half  open 
may  be  perforated  by  a  cannon  ball  without  being  shut  by  it.  A  soft  missile, 
like  tallow,  or  a  light  one,  like  a  feather,  will  act  with  the  force  of  lead,  if  suffi- 
cient velocity  is  given  to  it.  Firing  a  tallow  candle  through  a  board  is  a  well- 


THEORY    OF    MACHINERY. 


83 


known  feat  of  showmen.  In  ricochet  firing,  a  cannon  ball,  shot  at  an  elevation 
of  from  3°  to  6°,  rebounds  from  the  surface  of  water,  just  as  every  boy  has 
made  flat  stones  skip  from  point  to  point  on  its  surface. 


§  2.  Mechanical  Powers. 

113.  The  lever. — A  lever  is  any  inflexible  rod,  fig.  55,  resting  on  a 
point,  F,  called  the  fulcrum,  and  around  which  any  two  forces  tend  to 
turn  it.  Levers  may  be  either  straight,  or  bent ;  simple,  or  compound. 
It  is  usual  to  divide  levers  into  three  classes,  according  to  the  position 
of  the  fulcrum  in  relation  to  the  power  and  weight. 


55 


56 


•w 


l\ 


58 


Fig.  55  is  a  lever  of  the  first  class,  where  the  fulcrum  is  between  the 
power  and  the  weight.  In  the  second  class,  fig.  56,  the  weight  is  be- 
tween the  fulcrum  and  the  power.  In 
the  third  class,  fig.  57,  the  power  is 
applied  between  the  fulcrum  and  the 
weight. 

The  arms  of  a  lever  are  the  lines  on 
each  side  of  the  fulcrum,  at  right  angles 
to  the  direction  of  the  power  and  weight. 
In  the  three  figures  just  given,  the  levers  being  horizontal  and  the 
forces  vertical,  the  arms  of  the  lever 
are  evidently,  in  each  case,  the  por- 
tions  into  which  it   is   divided.     If, 
however,   the  lever  is  bent  or  is  in- 
clined to   the  direction  of  either,  or 
both,  of  the  forces,  then  the  arms  are 
the  perpendiculars  between  the  ful- 
crum  and   directions   of   the   forces. 
Thus  in  fig.  58  the  power  acting  in 

the  direction  B  P,  the  moment  of  the  power  is  not  expressed  by 
P  X  A  F,  but  by  P  X  B  F.  The  distance  from  the  fulcrum  is  called 
the  leverage. 


84  PHYSICS    OF    SOLIDS    AND    FLUIDS. 

114.  Conditions  of  equilibrium  in  the  lever.— These  conditions 
are :  1st,  The  lines  of  direction  of  the  two  forces  must  be  in  the  same 
plane  with  the  fulcrum  ;  2d,  The  two  forces  must  tend  to  turn  the  lever 
in  opposite  directions;  3d, .Whatever  may  be  the  class  of  the  lever  the 
weight  and  power  will  be  in  equilibrium  when  they  are  inversely  as 
their  distances  from  the  fulcrum.  Thus  in  either  of  the  three  figures 
above 

P:W  =  FW:FP     or     PXFP  =  WXFW. 

Consequently  the  moment  of  the  power,  or  its  tendency  to  turn  the 
lever  will  be  augmented,  either  by  increasing  the  power  itself  or  its 
distance  from  the  fulcrum. 

The  pressure  on  the  fulcrum,  when  the  power  and  weight  are  in 
equilibrium,  is  found  by  applying  the  principle  of  the  composition  of 
forces  (46).  In  a  lever  of  the  first  class,  the  resultant  of  the  power 
and  weight  is  a  single  force,  equal  to  their  sum,  and  passing  through 
the  fulcrum  ;  consequently,  the  pressure  will  be  equal  to  the  sum  of  the 
power  and  weight.  In  a  lever  of  the  second  or  third  class  the  resultant 
is  equal  to  the  difference  of  the  power  and  the  weight. 

Compound  levers. — When  a  small  force  is  required  to  sustain  a 
considerable  weight,  and  it  is  not  convenient  to  use  a  very  long  lever,  a 
combination  of  levers,  or  a  compound  lever  is  employed.  When  such 
a  system  is  in  equilibrium,  the  power,  multiplied  by  the  continued  pro- 
duct of  the  alternate  arms  of  the  levers,  commencing  from  the  powerv 
is  equal  to  the  weight  multiplied  by  the  continued  product  of  the  alter- 
nate arms,  commencing  from  the  weight.  For  example,  the  system 
represented  in  fig.  59,  consisting  of  three  levers  of  the  first  class,  will  be 

59 
A  "B v      r. 


fc 


IS" 


in  equilibrium  when 

P  X  A  F  X  B  Fx  X  C  F/x  =  W  X  D  F"  X  C  Fx  X  B  F. 

If  the  long  arms  are  6,  4,  and  5  feet,  and  each  of  the  short  arms  1  foot, 
then  1  Ib.  at  A  will  sustain  120  Ibs.  at  D ;  but  if  a  simple  lever  had 
been  used,  the  long  arm  being  increased  simply  by  adding  these  quanti- 
ties, we  should  have  gained  a  power  of  only  6  -f-  4  -j-  5  =  15  to  1. 

115.  Application  of  the  lever. — Machines  and  utensils  in  daily 
use  offer  us  familiar  examples  of  the  three  classes  of  levers. 


THEORY    OF    MACHINERY. 


85 


Of  the  first  class  we  name  the  crowbar  and  poker,  when  used  to  raise 
the  load  on  their  points.    Scis-  60  * 

sors,  snuffers,  and  pincers  are 
pairs  of  levers  of  this  class, 
th^e  point  C,  fig.  60,  which  con- 
nects them  being  the  fulcrum. 
The  power  is  applied  at  the 
handles,  and  the  resistance  is  the  object  between  the  blades. 

Another  example  of  the  bent  lever  is  seen  in  the  ordinary  truck,  fig.  61,  used 
for  moving  heavy  goods  a  short  distance.  In  this  machine,  the  axis  of  the 
Wheels,  F,  is  the  fulcrum,  against  which  the  foot  is  placed,  while  the  weight  at  R 
is  raised  off  the  ground  by  the  hand,  applied  at  P. 

61 


The  scale  beam,  or  balance,  is  one  of  the  most  useful  applications  of 
the  first  class  of  levers.  The  beam  is  a  lever  poised  at  its  centre  on  a 
knife-edge  of  steel,  a,  fig.  62.  From  its  ends  A  B  are  suspended  the 
scale  pans  C  E.  The  centre  of  gravity,  m,  is  placed  below  the  fulcrum, 
a,  to  secure  a  horizontal  position  of  the  beam  when  in  equilibrium.  If 
it  coincided  with  the  fulcrum  the  balance  would  rest  equally  well  in  all 
positions,  and  if  it  were  above  the  fulcrum  the  beam  would  be  upset  by 
a  slight  disturbance. 

The  steelyard  is  a  lever  of  the 
first  class,  with  unequal  arms.  The 
mass,  Q,  to  be  weighed,  is  attached 
to  the  short  arm,  A,  fig.  63,  and  it 
is  counterpoised  by  a  constant 
weight,  G,  shifted  upon  the  longer 
arm,  marked  with  notches  to  indi- 
cate pounds  and  ounces,  until  equi- 
librium is  obtained.  It  is  evident 
that  a  pound  weight  at  G  will 
balance  as  many  pounds  at  Q  as  the  distance  G  C  is  greater  than  A  C. 
10* 


86 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


Levers  of  the  second  class  occur  less  frequently.  A  pair  of  nut- 
crackers, with  the  fulcrum  at  the 
joint  C,  fig.  64,  is  a  double  lever 
of  this  class.  An  oar  is  another 
example ;  the  water  is  the  ful- 
crum, the  boat  is  the  weight,  and 
the  hand  the  pow«r.  A  door  moving  on  its  hinges,  and  a  wheelbarrow, 
are  other  examples  of  levers  of  the  second  class. 

In  levers  of  the  third  class,  the  power  being  nearer  the  fulcrum,  is 
always  greater  than  the  weight.  On  account 
of  this  mechanical  disadvantage,  it  is  used 
only  when  considerable  velocity  is  required, 
or  the  resistance  is  small.  Fig.  65  represents 
such  a  lever,  W  F,  moving  on  a  hinge  as  a  ful- 
crum ;  it  is  plain  that  the  power  P  moves 
through  a  small  arc,  and  the  weight  through  a 
large  one,  and  since  they  are  described  in  the 
same  time,  the  velocity  of  the  power  is  less 
than  that  of  the  weight. 

The  common  fire-tongs,  sugar-tongs,  and  sheep-shears,  are  douhle  levers  of 
this  class.  The  most  striking  illustrations  of  this  class  of  levers  are  seen  in  the 
animal  kingdom.  The  compact  form  and  beautiful  symmetry  of  animals  depend 
on  the  fact  that  their  limbs  are  66 

such  levers.  The  socket  of  the 
bone,  a,  fig.  66,  is  the  fulcrum; 
a  strong  muscle,  b  c,  attached 
near  the  socket  is  the  power, 
and  the  weight  of  the  limb  and 
whatever  resistance  10  may  op- 
pose to  motion,  is  the  weight. 
The  fore-arm  and  hand  are 
raised  through  a  space  of  one 
foot,  by  the  contraction  of  a 
muscle  applied  near  the  elbow, 
moving  through  less  than  J_  that  space.  The  muscle,  therefore,  exerts  12  times 
the  force  with  which  the  hand  moves.  The  muscular  system  is  the  exact  in- 
version of  the  system  of  rigging  a  ship.  The  yards  are  moved  through  small 
spaces  with  great  force,  by  hauling  in  a  great  length  of  rope  with  small  force  ; 
but  the  limbs  are  moved  through  great  spaces  with  comparatively  little  force, 
by  the  contraction  of  muscles  through  small  spaces  with  very  great  force. 

Examples  of  compound  levers  are  familiar  in  the  various  platform 
scales,  such  as  Fairbanks'  and  others.  However  various  in  form,  they 
all  depend  upon  the  principles  already  explained. 

The  principle  of  the  construction  of  the  weighi  \g  machine  is  illustrated  in 
fig.  67.  It  consists  of  a  wooden  platform,  placed  over  a  pit  made  in  a  loca- 


HEORY    OF    MACHINERY. 


87 


tion  convenient  for^  driving  heavy  loads  upon  it,  and  is  so  arranged  as  to  move 
freely  up  and  down  without  touching  the  walls  of  the  pit.  The  platform  rests 
upon  four  levers,  A  F,  B  F,  C  F,  and  D  F,  all  converging  toward  the  centre  F, 
and  each  moving  on  a  fulcrum  at  A,  B,  C,  D,  securely  fixed  in  each  corner  of 
the  pit.  The  platform  rests 
on  its  feet,  a'  c'  d',  which 
rest  on  steel  points,  abed. 
The  four  levers  are  sup- 
ported at  the  point  F,  un- 
der the  centre  of  the  plat- 
form, by  a  long  lever,  G  E, 
resting  on  a  steel  fulcrum 
at  E,  while  its  longer  arm 
at  G  is  connected  with  a 
rod,  which  is  carried  up 
and  attached  to  the  shorter 
arm  of  the  steelyard,  and 
is  counterpoised  by  the 
weight  P,  which,  by  its 
position  on  the  longer  arm, 
indicates  at  once  the  weight 
of  the  load  placed  upon 
the  platform. 

As  the  four  levers  A,  B,  C,  D,  are  perfectly  equal  and  similar,  and  all  act 
upon  the  same  fulcrum  F,  the  effect  of  the  weight  placed  upon  any  part  of  the 
platform  is  the  same  as  if  it  were  concentrated  at  either  of  the  points  a,  b,  c,  d. 

In  order  therefore  to  ascertain  the  conditions  of  equilibrium,  we  need  only 
consider  one  of  these  levers,  as  A  F.  Suppose  the  distance  from  A  to  F  to  be 
10  times  as  great  as  from  A  to  a,  a  force  of  1  Ib.  at  F  would  balance  10  Ibs.  at  a, 
or  on  any  part  of  the  platform.  So,  also,  if  the  distance  from  E  to  G  be  10 
times  greater  than  the  distance  from  the  fulcrum  E  to  F,  a  force  of  1  Ib.,  ap- 
plied so  as  to  raise  up  the  end  of  the  lever  G,  would  counterpoise  a  weight  of 
10  Ibs.  on  F,  therefore,  1  Ib.  tending  to  raise  G,  would  balance  100  Ibs.  on  the 
platform.  If  the  poise,  P,  is  placed  5  times  as  far  from  the  fulcrum  of  the  steel- 
yard as  the  attachment  of  the  rod  connected  with  G,  then  2  Ibs.  at  P  will  balance 
10  Ibs.  at  G,  or  100  Ibs.  at  F,  or  1000  Ibs.  on  the  platform.  If  the  weight  of  P 
and  the  graduation  of  the  steelyard  are  arranged  on  these  principles,  the  weight 
of  the  heaviest  loads  on  the  platform  may  be  determined  with  great  facility. 

Weigh-locks  on  canals,  and  many  other  applications  of  the  compound  lever, 
are  arranged  on  the  same  principles. 

Roberval's  counter  platform  balance. — The  exterior  appearance 
of  this  balance  is  shown  in  fig.  68,  and  its  interior  arrangement  in 
fig.  69.  The  equilibrium  of  this  system  of  levers  is,  like  that  of  fig.  67, 
independent  of  the  position  of  the  load  on  the  pans,  and  the  mechanism 
is  such  that  the  pans  move  on  a  vertical  stem  with  no  deflection  from  a 
horizontal  plane. 

Each  pan  is  supported  by  a  system  of  three  levers,  A  B,  C  D,  E  F,  fig.  69. 
The  lever  D  C,  which  supports  the  pan  P,  rises  and'  falls  equally  at  both  ends 
with  the  motions  of  the  beam  A  B,  C  being  attached  to  the  end  of  the  beam  B, 


88 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


and  D  being  attached  at  E  to  the  lever  E  F  ;  E  H  being  equal  to  G  B,  wh;ie  F 
is  securely  attached  to  the  base,  E  and  B  rise  and  fall  equally*  and  D  C  is  always 

68 


69 


horizontal  in  every  position  of  the  beam  A  B.  Since  the  lever  D  C  preserves  its 
horizontal  position,  the  stem  a  supporting  the  pan  P,  moves  vertically,  what- 
ever may  be  the  position  of  the  load  on  the  pan.  The  indices  n  m  are  in  the 
same  horizontal  line  when  the  pans  are  in  equilibrium.  This  system  is  named 
from  the  inventor,  Mr.  Roberval  of  Paris,  and  dates  from  about  A.  D.  1660. 

116.  The  wheel  and  axle. — The  common  lever  is  chiefly  employed 
to  raise  weights  through  small  70 

spaces,  by  a  succession  of  short 
intermitting  efforts.  After  the 
weight  has  been  raised  it  must 
be  supported  in  its  new  posi- 
tion, until  the  lever  can  be 
again  adjusted,  to  repeat  the 
action.  The  wheel  and  axle  is 
a  modification  of  the  lever, 
which  corrects  this  defect ;  and, 
since  it  converts  the  intermit- 
ting action  of  the  lever  into  a 
continuous  motion,  it  is  sometimes  called  the  perpetual  lever. 

This  machine  consists  of  a  cylinder  called  the  axle,  turning  on  a 


THEORY    OF    al^OHINEEY. 


89 


centre,  and  connected  with  a  wheel  of  much  greater  diameter.     The 

power  is  applied  to  the  circumference  of  the  wheel,  and  the  weight  is 

attached  to  a  rope,  wound  around   the  axle  in  a  contrary  direction. 

Instead  of  the  whole  wheel,  the  power  may  be  applied  to  a  handle 

named  a  winch,  or  to  one  or  more  spokes  in-  71 

serted  in  the  axle.    When  the  axle  is  horizontal 

the  machine  is  called  a  windlass,  fig.  70,  when 

it  is  vertical  it  forms  the  capstan,  fig.  71,  used 

on  shipboard,  chiefly  to  raise  the  anchor.     The 

head  of  the  capstan  is  pierced  with  holes,  in 

each  of  which  a  lever   can  be  placed,  so  that 

many  men  can  work  at  the  same  time,  exerting 

a  great  force,  as  is  often  necessary  in  raising  an 

anchor,  while  the  recoil  of  the  weight  is   arrested  by  a  catch  at  the 

bottom. 

The  law  of  equilibrium  is  the  same  as 
in  the  lever.  Draw  from  the  centre,  or 
fulcrum  c,  fig.  72,  the  straight  lines  c  b 
and  c  a,  or  c  a',  to  the  points  on  which 
the  weight  and  power  act ;  ac  b,  or  a'  c  b, 
is  evidently  a  lever  of  the  first  class,  in 
which  the  short  arm  c  b  is  the  radius  of 
the  axle,  and  c  a  or  c  a',  the  long  arm, 
is  the  radius  of  the  wheel.  Hence, 


Or, 


P :   W=  c  b  :  a  c. 


That  is  to  say,  the  wheel  and  axle  are  in  equilibrium,  when  the 
power  is  to  the  weight  as  the  radius  of  the  axle  is  to  the  radius  of  the 
wheel. 

In  one  revolution  of  the  machine,  the  power  moves  through  a  space 
equal  to  the  circumference  of  the  wheel,  and  the  weight  moves  through 
a  space  equal  to  the  circumference  of  the  axle ;  hence  the  power  and 
weight  are  inversely  as  their  velocities,  or  the  spaces  they  describe. 

117.  Trains  of  wheel-work. — The  efficiency  of  this  machine  is 
augmented  by  diminishing  the  thickness  of  the  axle,  or  by  increasing 
the  diameter  of  the  wheel.  But  if  a  very  great  power  is  required, 
either  the  axle  would  become  too  small  to  sustain  the  weight,  or  the 
wheel  must  be  made  inconveniently  large.  In  this  case  a  combination 
of  wheels  and  axles  may  be  employed.  Such  a  system  corresponds  to 
the  compound  lever,  and  has  the  same  law  of  equilibrium.  The  power 


90 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


73 


being  applied  to  the  first  wheel  transmits  its  effect  to  the  first  .*xle, 
this  acts  on  the  second  wheel,  which  transfers  the  effect  to  the  second 
axle,  &c.,  until  the  force,  transmitted  through  the  series  in  this  order, 
arrives  at  the  last  axle,  where  it  encounters  the  resistance.  In  equi- 
librium, the  power  multiplied  into  the  continued  product  of  the  radii 
of  all  the  wheels,  is  equal  to  the  weight  multiplied  into  the  continued 
product  of  all  the  axles. 

Trains  of  wheel-work  are  connected  by  an  endless  band,  or  by  cogs 
raised  on  the  surfaces  of  the  wheels  and  axles.  Cogs  on  the  wheel  are 
called  teeth,  and  those  on  the  axle  are  called  leaves ;  the  axle  itself  is 
named  a  shaft.  The  number  of  teeth  on  the  wheels,  arid  leaves  on  the 
pinions  is  proportional  to  their  circumferences,  and  also  to  their  radii. 
Hence,  the  number  of  teeth  and  leaves  is  substituted  for  the  radii  of  the 
wheels  and  axles,  and  the  law  of  equilibrium  is  stated  as  follows : 

The  power  multiplied  into  the  product  of  the  number  of  teeth  of  all  the 
wheels,  is  equal  to  the  weight  multiplied  into  the  product  of  the  number 
of  leaves  in  all  the  pinions. 

Analysis  of  a  train  of  wheel-work. — A  system  of  wheels  is  rep- 
resented in  fig.  73.  If  the  number 
of  leaves  in  b,  the  pinion  of  the  first 
wheel,  is  one-sixth  of  the  number  of 
teeth  on  the  second  wheel,  e,  the  wheel 
will  be  turned  once  by  every  six  turns 
of  the  pinion.  Let  the  second  pinion, 
c,  have  the  same  relation  to  the  third 
wheel,  f\  then  the  first  wheel  will  re- 
volve 36  times  while  the  third  revolves 
once ;  and  the  radius  of  a,  the  wheel 
to  which  the  power  is  applied,  being  3 
times  the  radius  of  d,  the  axle  which 
ssutains  the  weight,  the  velocity  of  the 
power  is  3  X  36  =  108  times  the  velo- 
city of  the  weight.  Or, 

P:  W=  1:108. 

Combinations  of  wheel-work  are  employed  eitber  to  concentrate  or  to  diffuse 
force;  eitber  to  set  heavy  loads  in  motion  by  means  of  a  small  power,  or  to  pro- 
duce a  high  velocity  by  exerting  a  considerable  power.  In  the  first  case,  the 
power  is  applied  to  the  first  wheel  of  the  series,  and  is  transmitted  in  the  order 
already  described.  In  the  second  instance,  this  arrangement  must  be  reversed ; 
the  power  must  exert  itself  on  the  shaft,  d,  in  order  to  produce  rapid  revo- 
lution of  the  last  wheel.  The  crane  for  hoisting  goods  is  an  example  of  the  first 
kind  j  the  watch  is  an  instance  of  the  second. 


THEORY    OP    MACHINERY. 


91 


118.  The  pulley.—  Fixed  pulley.—  The  usual  form  of  this  machine 
is  a  small  wheel,  turning  on  its  axis,  and  having  74 

a  groove  on  its  edge,  to  admit  a  flexible  rope  or  d~  ~~~j 

chain.     In  the  simple  fixed  pulley,  fig.  74,  there 

is  no  mechanical  advantage,  except  that  which 

may  arise  from    changing   the   direction  of  the 

power.     Whatever  force  is  exerted  at  P,  is  trans- 

mitted, without  increase  or  diminution   (except 

from  friction  and  the  rigidity  of  the  rope),  to  the 

resistance  at  the  other  end  of  the  cord.    From  the 

axis  C,  draw  C  a  and  C  b,  radii  of  the  wheel,  at 

right  angles  to  the  direction  of  the  forces  ;   a  C  b 

represents  a  lever  of  the  first  class,  with  equal 

arms;    hence,    in   equilibrium,    the    power    and 

weight  must  be  equal,  and  they  describe  equal  spaces. 

119.  Movable  pulley.  —  When  the  block  or  frame  is  not  fixed,  the 
pulley  is  said  to  be  movable.     The  weight  is  75 
suspended  from  the  axis  of  the  movable  pul- 

ley, and  the  cord  is  fastened  at  one  end,  and 
passing  over  a  fixed  pulley,  is  acted  on  by  the 
power  at  the  other.  In  this  arrangement, 
fig.  75,  it  is  plain  that  the  weight  is  supported 
equally  by  the  power  and  the  beam  at  D.  For 
the  pulley  acts  as  a  lever  of  the  second  class, 
whose  arms  are  to  each  other  as  1:2;  the 
fulcrum  is  at  b,  be  is  the  leverage  of  the 
weight,  and  b  a  the  leverage  of  the  power. 
The  diameter  6  a  is  twice  the  radius  b  c,  there- 
fore equilibrium  will  obtain  when  the  power 
is  equal  to  one-half  of  the  weight  :  i.  e., 

P:  W=bc:  ba^l  :  2, 
therefore, 


To  raise  the  weight  one  foot,  each  side  of  the  cord  must  be  shortened 
one  foot,  and  the  power,  consequently,  passes  over  two  feet.  The 
space  traversed  by  the  power  is  twice  the  space  described  by  the 
weight. 

120.  Compound  pulleys.  —  Sometimes  compound  pulleys  are  used, 
each  consisting  of  a  block  which  contains  two  or  more  single  pulleys, 
generally  placed  side  by  side,  in  separate  mortices  of  the  block.  Such 
an  arrangement  is  shown  in  fig.  76.  The  weight  is  attached  to  the 


92 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


movable  block,  and  the  fixed  one  only  serves  to  give  the  power  the 

required  direction.     It  is  easily  seen  that  the  power 

required  at  Pis  just  the  same  as  would  be  required  at 

any  point  between  A  and  B.     The  weight  is  divided 

equally  among  the  pulleys  of  the  movable  block,  and, 

of  course,  among  the  cords  passing  around  them  ;  and 

as  the  power  required  to  sustain  a  given  weight  is 

diminished  one-half  by  a  single  movable  pulley,  it 

follows  that  such   a   system  will  be   in   equilibrium 

when  the  power  is  equal  to  the  weight  divided  by  the 

number  of  cords,  or  by  twice  the  number  of  movable 

pulleys. 

P:  W=l:2n,     or,     P=  -^. 

2iii 

In  this  system,  as  in  the  single  movable  pulley,  the 
space  through  which  the  weight  is  raised,  is  as  much 
less  than  the  space  through  which  the  power  descends, 
as  the  weight  is  greater  than  the  power. 

P  :  W=  velocity  of  weight  :  velocity  of  power. 
If  the  power  is  moved  through  6  feet,  fig.  76,  each  division  of  the  cord 
in  which  the  movable  block  hangs  will  be  shortened  one  foot,  and  the 
weight  raised  one  foot. 

Another  system  of  pulleys  is  represented  in 
fig.  77.  In  this  arrangement  each  pulley  hangs 
by  a  separate  cord,  one  end  of  which  is  attached 
to  a  fixed  support,  and  the  other  to  the  adjacent' 
pulley.  The  effect  of  the  power  is  rapidly  aug- 
mented, being  doubled  by  each  movable  pulley 
added  to  the  system.  The  numbers  placed  near 
the  cords  show  what  part  of  the  weight  is  sus- 
tained by  each,  and  by  each  pulley.  Such  a 
system,  however,  is  of  little  practical  use,  on 
account  of  its  limited  range.  In  the  common 
block  system,  fig.  76  (in  practice  the  pulleys  or 
sheaves  of  each  block  are  placed  side  by  side, 
to  save  room,  here  they  are  separated  for  sake 
of  clearness),  the  motion  may  continue  until 
the  movable  block  touches  the  fixed  one ;  but 
in  this  only  till  D  and  E  come  together,  at 
which  time  A  will  have  been  raised  only  |  of  that  distance 

P:W-=l..V     „     P=K 

2"      ' 


THEORY   OP   MACHINERY. 


93 


121.  The  inclined  plane.— This  mechanical  power  is  commonly 
used,  whenever  heavy  loads,  especially  such  as  may  be  rolled,  are  to 
be  raised  a  moderate  height.  In  this  way  casks  are  moved  in  and  out 
of  cellars,  and  loaded  upon  carts.  The  common  dray  is  itself  an  inclined 
plane  (as  is  clearly  seen  by  inspecting  fig.  78).  Suppose  a  cask  weigh- 

78 


ing  500  Ibs.  is  to  be  raised  4  feet  by  means  of  a  plank  12  feet  long ;  it 
is  plain,  that  while  the  cask  ascends  only  four  feet,  the  power  must 
exert  itself  through  12  feet,  and  hence,  12  :  4  =  500  :  166|,  the  force 
necessary  to  roll  the  cask. 

In  mechanics,  the  inclined  plane  is  a  hard,  smooth  surface,  inclined 
obliquely  to  the  resistance.  The  lengt^  of  the  plane  is  R  S,  fig.  79, 
S  T  its  height,  and  R  T  its  base.  The  power  may  be  applied, 

a — In  a  direction  parallel  to  the  length  ; 

b — Or  parallel  to  the  base  ; 

c — Or  in  any  other  direction. 

In  each  case  the  conditions  of  equilibrium  may  be  derived  from  those 
of  the  lever. 

•  122.  Application  of  the  power  parallel  to  the  length  of  the 
inclined  plane. — When  a  body  is  placed  upon  an  inclined  plane,  fig 
79,  its  weight,  which  is  the 
resistance  to  be  overcome, 
acts  in  the  direction  of  the 
force  of  gravity,  namely  in 
the  perpendicular  b  a.  Let 
the  power,  P,  act,  by  means 
of  the  cord,  in  the  direction 
a  c,  parallel  to  the  inclined 
plane  R  S,  then  from  the 
point  a  draw  a  d  at  right 
angles  with  the  inclined 
plane,  and  complete  the 
parallelogram  acbd.  The  force  of  gravity  will  be  resolved  into  twc 
11 


94 


PHYSICS   OF   SOLIDS   AND   FLUIDS. 


other  forces  ;  one  represented  by  b  c  causing  pressure  on  the  inclined 
plane  ;  the  other,  represented  by  c  a,  tending  to  cause  motion  down  the 
inclined  plane.  This  latter  force  is  to  be  balanced  by  the  power  ap 
plied  to  move  the  body.  The  body  will  therefore  be  sustained  when 

P:  W=ac:  ab; 
and  since  the  triangles  a  b  c  and  B  S  T  are  similar, 


Or 


This  may  be  illustrated  by  an  apparatus  constructed  like  that  shown 
in  the  figure. 

If  the  direction  of  the  power  is  parallel  to  the  inclined  plane,  equili- 
brium will  obtain,  when  the  power  is  to  the  weight  as  the  height  of 
the  plane  is  to  its  length.  While  the  weight  is  raised  through  a  space 
equal  to  the  vertical  height  of  the  plane,  the  pow^r  must  move  through 
a  space  equal  to  its  length.  If  the  length  of  a  plane  is  10  feet,  and  its 
height  2  feet,  P  must  move  10  feet,  while  W  is  raised  2  feet ;  hence  the 
power  and  weight  are  inversely  as  their  velocities. 

123.  Application  of  the  power  parallel  to  the  base  of  the 
inclined  plane. — In  the  second  case,  gO 

let  the  power  act  in  the  direction  of  a  P, 
fig.  80,  parallel  to  B  C,  the  base  of  the 
plane ;  and  draw,  the  lines  6  a  and  b  c 
perpendicular  to  the  direction  of  the 
power  and  weight:  then  a  b  c  is  a 
bent  lever,  having  its  fulcrum  at  6,  and 
equilibrium  will  take  place  when 

and,  the  triangles  a  b  c  and  ABC  being  similar, 

P:  JF=AB:BC; 
Or 

•n 


AB 
BCT 


If  the  direction  of  the  power  is  parallel  to  the  base  of  the  plane, 
equilibrium  will-  obtain  when  the  power  is  to  the  weight  as  the  height 
of  the  plane  is  to  its  base. 

In  this  case  the  space  described  by  the  power  is  to  the  space  described 
by  the  weight  as  the  base  of  the  plane  is  to  its  height. 


THEORY   OP   MACHINERY. 


95 


124.  Application  of  the  power  in  some  direction  not  parallel 
to  any  side  of  the  plane. — Lastly,  let  the  power  act  in  some  direc- 
tion not  parallel  to  any  side  of  the  plane  ;  for  example :  in  the  direction 
aP,  fig.  81,  draw  the  lines  be  and  ba  perpendicular  to  the  directions 
of  the  two  forces ;  then,  as  before, 

P:  JF=  be:  ab. 

But  as  the  triangles  a  be  and  ABC  are  not  similar,  the  proportion 
between  the  arms  of  the  lever  cannot  81 

be  expressed  by  the  sides  of  the  plane. 

It  follows  from  what  has  been  said,  that 
the  effect  of  a  given  power  is  greater,  as  the 
height  of  the  plane  is  diminished  or  its 
length  increased ;  and  that  the  effect  is 
greatest  when  its  direction  is  parallel  to 
the  length  of  the  plane,  for,  if  the  power 
acts  in  any  other  direction,  a  part  of  its 

force  is  expended,  either  in  increasing  the    "**  YW 

pressure  of  the  body  on  the  plane,  or  in  lifting  the  weight  directly. 

125.  The  wedge. — Instead  of  lifting  a  load  by  moving  it  along  an 
inclined  plane,  the  same  result  may  be  obtained  by 

moving  the  plane  under  the  load.  When  used  in  this 
manner,  the  inclined  plane  is  called  a  wedge.  It  is 
customary,  however,  to  join  two  planes  base  to  base. 
In  fig.  82,  A  B  is  called  the  back  of  the  wedge,  A  C 
and  B  C  its  sides,  and  dC  its  length.  The  power  ia 
applied  to  the  back  of  the  wedge,  so  as  to  drive  it 
between  two  bodies,  and  overcome  their  resistance. 

The  resistance  may  act  at  right  angles  to  the  length  or  to 
the  sides  of  the  wedge.  In  the  first  case  it  resembles  an  inclined  plane,  when 
the  power  is  parallel  to  the  base ;  and  hence  the  forces  will  be  in  equilibrium 
when  the  power  is  to  the  resistance  as  the  back  of  the  wedge  is  to  its  length. 
In  the  second  case  it  is  similar  to  a  plane  when  the  power  is  parallel  to  the 
length ;  and  therefore  in  equilibrium  when  the  power  is  to  the  resistance  as 
the  back  of  the  wedge  to  its  side. 

The  power  is  supposed  to  move  through  a  space  equal  to  the  length  of  the 
wedge,  while  the  resistance  yields  to  the  extent  of  its  breadth. 

126.  Application  of  the  wedge. — As  a  mechanical  power,  the  wedge 
is  used  only  where  great  force  is  to  be  exerted  in  a  limited  space.     In  oil-mills, 
the  seeds  from  which  vegetable   oils   are  obtained  are  sometimes  compressed 
with  enormous  force  by  means  of  a  wedge.     It  is  everywhere  employed  to  split 
masses  of  stone  and  timber.     The  edges  of  all  cutting  tools,  as  saws,  knives, 
chisels,  razors,  shears,  <fec.,  and  the  points  of  piercing  instruments,  as  awls,  nails, 
pins,  needles,  <fec.,  are  modified  wedges.     Chisels  intended  to  cut  wood,  have 
their  edge  at  an  angle  of  about  30° ;  for  cutting  brass,  from  50°  to  60°  j  and  for 
iron,  about  80°  to  90°.     The  softer  or  more  yielding  the  substance  to  be  divided 


96  PHYSICS    OP    SOLIDS   AND    FLUIDS. 

the  more  acute  the  wedge  may  be  constructed.  In  general,  tools  which  are 
urged  by  pressure,  admit  of  being  sharper  than  those  which  are  driven  by  a 
blow. 

The  theory  of  the  wedge  gives  but  very  little  aid  in  estimating  its  effects,  as 
it  takes  no  account  of  friction,  which  so  largely  modifies  the  results,  and  the 
proportion  between  pressure  and  a  blow  cannot  be  defined. 

127.  The  screw.  —  This  machine  has  the  same  relation  to  the  ordi- 
nary inclined  plane  that  a  spiral  staircase  has  to  a  straight  one.  This 
relation  is  shown  in  fig.  83,  the  dotted  line  K  L  83 

marking  the  continuation  of  the  spiral.  The 
position  of  the  different  parts  of  an  inclined 
plane  upon  a  screw  is  shown  in  fig.  84.  a  b  c  d  efg, 
is  the  spiral  course  of  the  inclined  plane  upon  the 
screw,  and  a  c'  e'  g'  ate  points  in  the  straight 
inclined  plane  corresponding  to  similar  letters  on 
the  threads  of  the  screw,  as  would  be  seen  by 
winding  the  plane  around  the  cylinder.  The 
thread  of  a  screw  projects  from  the  surface  of  the  cylinder,  and  is 
designed  to  fit  into  a  spiral  groove,  cut  in  the  interior  of  a  block  called 
the  nut  ;  a  lever  is  also  84 

fixed  in  the  head  of  the 
cylinder  to  which  the 
power  is  applied.  The 
combination  of  these 
parts  forms  the  mecha- 
nical power  technically 
called  the  screw. 

In  working  the  screw,  the  resistance  acts  on  the  inclined  face  of  the 
thread,  and  the  power  parallel  to  the  base  of  the  screw.  This  cor- 
responds to  the  case  in  which  the  direction  of  the  power  is  parallel  to 
the  base  of  the  inclined  plane.  Equilibrium  will,  therefore,  take  place 
when  the  power  is  to  the  resistance  as  the  distance  between  the  threads 
of  the  screw  is  to  the  circumference  described  by  the  power. 


P:  W=h:2Rx,  andP=  ^X; 


Ji  being  the  distance  between  the  threads,  _K  the  radius  of  the  screw,  or 
of  the  length  of  the  lever  attached  to  it,  and  it  the  ratio  of  the  circum- 
ference of  a  circle  to  its  radius. 

During  each  revolution  the  power  describes  a  circle,  whose  circum- 
ference depends  on  the  length  of  the  lever,  but  the  end  of  the  screw 
advances  only  the  distance  between  two  threads  ;  thus  in  this,  as  in  all 
cases  of  the  use  of  machines,  what  is  gained  in  power  is  lost  in  velocity. 


THEORY    OF    MACHINERY. 


97 


128.  Mechanical  efficiency  and  applications  of  the  screw*— 

The  mechanical  efficiency  of  the  screw  85 

is  augmented,  either  by  increasing  the 

length  of  the  lever,  or  by  lessening  the 

distance  between  the  threads.     If  the 

threads  of  a  screw  are.  £  of  an  inch 

apart,  and  the  power  describes  a  circle 

of  5  feet  (120  half-inches)  circumfer- 

ence, a  power  of  1  Ib.  will  balance  a 

resistance  of  120  Ibs.  ;   if  the  threads 

are  J  inch  apart,  1  Ib.  will  balance  240 

Ibs.,  the  efficiency  being  doubled. 

Fine  screws  are  therefore  more  power- 
ful than  coarse  ones.  The  applications 
of  this  most  useful  mechanical  power 
are  too  numerous  to  mention,  but  no 
more  frequent  or  important  example  of  its  use  can  be  named  than  is 
seen  in  its  use  in  presses  of  nearly  all  kinds.  A  good  illustration  of 
which  is  seen  in  the  copying  press,  fig.  85. 

129.  The  endless  screw  is  a  contrivance  by  which  a  slow  motion 
is  imparted  to  a  wheel,  as  shown  in  fig. 

86.  The  threads  of  the  screw  act  upon 
the  cogs  of  the  wheel,  and  serve  to  move 
the  weight  Q,  attached  to  the  axis  M  L. 
If  we  call  the  radius  of  the  circle  de- 
scribed by  the  winch  D  B  =  r,  and  let 
7i  =  the  distance  between  the  threads  of 
the  screw,  we  shall  have  the  power  of  the 


screw  = 


Let  R  =  M  F,  and 


r> 

M  L,  and  the  power  of  the  wheel  and  axle  will  =  -777. 
Then  W :  P  =  2xr  X  R  :  h  X  R'; 


W=PX 


hR' 


Therefore  the  weight  is  to  the  power  as  the  circumference  of  the 
circle  described  by  the  winch  D,  multiplied  by  the  radius  of  the  wheel, 
is  to  the  distance  between  the  threads  of  the  screw  multiplied  by  the 
radius  of  the  axis. 

n* 


98  PHYSICS   OF   SOLIDS   AND   FLUIDS. 

g  3.  Strength  and  Power. 

130.  Animal  strength. — The  mechanical  effect  produced  by  men 
and  animals  is  subject  to  extreme  variation,  according  to  the  various 
circumstances  under  which  it  is  applied.     The  effect  produced  is  deter- 
mined by  multiplying  the  load  (or  weight)  by  the  speed.     There  is 
always  a  certain  relation  between  the  elements,  which  will  give  the 
maximum  effect ;  for  the  load  may  be  so  great  that  it  will  require  all 
the  strength  of  the  animal  to  support  it,  and  then  he  cannot  move ;  or, 
again,  the  animal  may  have  a  speed  of  motion  so  great,  that  he  cannot 
carry  any  load,  however  small. 

131.  Strength  of  men. — It  has  been  found  that  the  strength  of  a 
man  may  be  exerted,  for  a  short  time,  most  advantageously  in  raising  a 
weight  when  it  is  placed  between  his  legs.     The  greatest  weight  that 
can  be  raised  in  this  manner,  varies  from  450  to  600  Ibs. ;  its  average 
amount  does  not  however  exceed  250  Ibs. 

The  greatest  mechanical  effect  from  muscular  force  is  obtained  when 
the  animal  acts  simply  by  raising  his  weight  to  a  given  height,  and 
then  is  lowered  by  simple  gravity,  as  upon  a  moving  platform,  the 
animal  actually  resting  during  the  descent.  In  other  words,  the  animal 
affords  a  convenient  mode  of  raising  a  given  weight  (his  own)  to  a 
certain  height.  Thus,  if  two  baskets  are  arranged  at  each  end  of  a 
rope  hung  over  a  pulley,  and  a  weight"  to  be  raised  is  placed  in  one  of 
the  baskets,  one  or  more  men,  whose  weight  is  greater  than  that  of  the 
load  to  be  raised,  can,  by  getting  into  the  empty  basket,  raise  the 
weight  as  often  as  may  be  required.  It  has  been  found  by  experiment 
that,  in  this  way,  a  man  working  eight  hours  can  produce  an  effect 
equivalent  to  2,000,000  Ibs.  raised  one  foot ;  while  at  a  windlass  an 
effect  of  only  1,250,000  Ibs.  is  produced,  and  at  a  pile  engine,  only 
750,000  Ibs.  In  the  tread-mill,  the  daily  effect  of  men  of  the  average 
strength  is  1,875,000  Ibs.  raised  one  foot.  Spade  labor  is  one  of  the 
most  disadvantageous  forms  in  which  human  labor  can  be  applied;  the 
force  exerted  being  always  much  greater  than  the  weight  of  the  earth 
raised.  The  muscular  effect  of  the  two  hands  of  a  man  is  about  (50  k) 
110^  Ibs.,  and  for  a  female  about  two-thirds  of  this  quantity. 

132.  Horse-power  machines. — One   of   the    most   advantageous 
methods  of  applying  the  strength  of  animals,  is  by  machines   con- 
structed upon  the  principle  of  the  tread-mill.     In  practice,  however,  it 
has  been  found  more  convenient  to  apply  horse-power  to  machinery  by 
means  of  a  large  beveled  or  toothed  wheel,  fixed  horizontally  on  a 
strong  vertical  axis,  as  in  fig.  87.     The  horses  are  attached  to  project- 
ing arms  of  this  wheel,  and  as  they  move  in  their  circular  path,  they 


THEORY    OP    MACHINERY. 


99 


push  against  their  collars,  and  make  the  wheel  revolve.    This  beveled 
wheel  acts  on  a  beveled  pinion  attached  to  a  horizontal  shaft,  in  con- 
nection with  the  machinery  to  87 
be  set  in  motion.   The  maximum 
effect  which  a  horse  can  exert 
in  drawing  is  900  Ibs.,  but  when 
he   works    continuously,    it    is 
much  less.    In  the  machine  just 
mentioned,  a  horse  of  average 
strength  produces  as  much  effect 
as  seven  men  of  average  strength 
working  at  a  windlass.   Accord- 
ing to    experiments    made   by 
Predgold,  it   appears   that   the 

average  load  which  a  single  horse  can  draw,  at  the  rate  of  20  miles  per 
day,  in  a  cart  weighing  7  cwt.,  is  one  ton  of  1800  Ibs. 

133.  Table  of  the  comparative  strength  of  men  and  other 
animals. — The  following  estimates  of  the  relative  strength  of  man  and 
other  animals,  have  been  given  by  the  authorities  whose  names  are 
indicated,  Coulomb's  estimate  of  the  labor  of  a  man  being  in  each  case 
taken  as  the  unit. 

Carrying  loads  on  the  back,  on  a  level  road : 

Horse,  according  to  Brunacci, 

"  "  Wessemann, 

Mule,  "          Brunacci, 

In  drawing  loads,  on  a  level  road,  with  a  wheeled  vehicle : 

Man  with  a  wheelbarrow,  according  to  Coulomb,         10-0 
Horses  in  four-wheeled  wagon,      "  "  175-0 

"       in  two-wheeled  cart,  according  to  Brunacci,  243-0 
Mule,  "  "          «     "  " 

Ox,  "  "  "  " 

Hassenfratz  gives  the  following  comparative  estimate : 


4-8 
6-1 
7-6 


233-0 
122-0 


In  carrying  loads  on 

Man,    

a  level  road. 

...       1-0 

Man,     

.     .•    1-0 

.     .       7-0 

8-0 

Mule 

8-0 

Mule,     

.     .     7-0 

.     .     .         4-0 

Ass,     

^j7>,    ,  „  •  o  •      n   *  ^      •      • 

.     .      2-0 
.  4  to  7-0 
.     .       0-6 

Camel,,     r  ..   •.  -  . 
Dromedary,    ^   ;. 
Elephant1 

.v  .  .,,   Sir  3 

1  ?  147-0 

.     .     0-2 

->             •>          *       ° 

.  V-/    3-0- 

^  o  ;  •;   >  >    > 

134.  Steam-power.— Water  is'converted  into  steam  by  the  applica- 
M  of  heat.     Steam  is  an  elastic,  condensible  vapor,  capable  of  exert- 


100  PHYSICS   OF    SOLIDS   AND   FLUIDS. 

ing  great  force.  During  the  conversion  of  a  cubic  inch  of  water  into 
steam  a  mechanical  force  is  exerted,  which  may  be  stated,  in  round 
numbers,  as  equivalent  to  a  ton  weight  raised  one  foot  high.  The 
water  is  merely  the  medium  by  which  the  mechanical  effects  of  heat 
are  evolved.  The  real  moving  power  is  the  combustible,  the  coal  or 
wood,  consumed  in  the  evaporation  of  the  water. 

The  maximum  effects  from  a  given  weight  of  coal,  in  evaporating 
water,  and  consequent  mechanical  effect,  have  been  obtained  in  Corn- 
wall, England,  where  a  bushel  of  coal,  weighing  84  Ibs.,  has  produced 
a  mechanical  effect  equivalent  to  120,000,000  Ibs.  raised  one  foot. 
Probably  100,000,000,  is  the  maximum  mechanical  effect  attainable,  in 
regular  work,  by  the  consumption  of  a  bushel  of  coal. 

As  the  maximum  effect  produced  by  man  is  2,000,000,  and  that  of  a 
horse  10,000,000,  it  follows,  that  one  bushel  of  coal  consumed  daily 
may  perform  the  work  of  50  men  or  10  horses. 

In  the  chapter  on  heat  and  the  steam-engine,  this  subject  will  be 
more  fully  considered.  It  is  introduced  here  only  for  the  sake  of  the 
convenient  standards  of  force  it  gives  us. 

The  dynamometer,  already  described  (37),  is  employed  to  measure  the 
efficiency  of  any  given  mechanical  power. 

135.  Perpetual  motion. — Many  visionary  persons  have  convinced 
themselves  of  the  possibility  of  constructing  a  machine  to  work  con 
tinuously,  with  no  new  access  of  power.  That  such  a  machine  is  im 
possible,  in  the  nature  of  things,  is  88 

clear  from  the  fact  that  no  combina- 
tion of  parts  in  a  machine  can  create 
power.  A  machine  can  only  transmit 
force,  subject  to  the  various  losses 
incident  to  friction  and  other  resist- 
ances. 

Fig.  88  shows  one  of  the  numerous 
forms  of  apparatus  contrived  in  the 
vain  effort  to  elude  the  laws  of  nature 
and  produce  a  perpetual  motion.  The 
eight  balls  are  hinged  on  points,  in 
such  a  way  that  those  on  the  falling 
side  are  held  fartheV  frotfl  th'e  axis  than 'those*  on  fti3  -rising  side.  Not 
only  does  experiment  Sh^w  thai?  'such-a'Hiachme  "Jo^.U'riot  work,  but  it 
is  plain  that  the/'gunTrOf  the  resistances  (asule  froxr  friction,  &c.) 
must  equal  the  stfmrof  tire'  poyvers*.^  '  "  '  «  ••'••$*;•*  J 

Nature,  in  cataracts,  in  the  revolution  of  the  eartn  ancToth'er  heavenly 
bodies,  furnishes  us  examples  of  perpetual  motion.  But  in  mechanics 


THEORY   OF   MACHINERY.  101 

this  term  implies  the  assumed  capacity  of  a  machine  to  continue  the 
performance  of  its  work  by  some  renewing  force — as  of  a  clock  which 
should  wind  itself  up  in  proportion  as  by  gravity  it  runs  down — a 
thing  plainly  impossible. 

§  4.    Impediments  to  Motion. 

136.  Passive  resistances. — Besides  those  resistances  which  a  ma- 
chine is  designed   to  overcome,  there  are  certain  others  which  arise 
during  the  movement  of  the  machine,  and  oppose  its  useful  action  by 
destroying  more  or  less  of  the  moving  power.     These  forces  are  desig- 
nated by  the  general  name  of  passive  resistances,  or  impediments  to 
motion. 

Several  kinds  are  distinguished : 

1st. — When  we  attempt  to  cause  one  body  to  slide  over  another,  a 
resistance  is  experienced,  so  that  it  is  necessary  to  use  a  certain  degree 
of  force  to  commence  the  sliding,  and  also  to  continue  the  motion  after 
it  has  been  begun.  This  is  the  resistance  called  sliding  friction,  or 
simply  friction. 

2d. — When  a  cylindrical  body  is  rolled  on  a  plane  surface,  the  move- 
ment is  opposed  by  a  force  called  the  rolling  friction.  It  is  seen,  for 
example,  in  the  rolling  of  carriage  wheels  on  the  ground. 

3d. — The  ropes  and  chains  which  enter  into  the  composition  of  some 
machines,  are  supposed,  in  theory,  to  be  perfectly  flexible,  but  as  they 
are  not  so,  a  considerable  loss  of  power  is  caused  by  their  stiffness,  or 
imperfect  flexib  ility. 

4th. — The  movements  of  all  machines  take  place  either  in  air  or 
water,  and  the  particles  of  these  fluids  which  come  in  contact  with  the 
machine,  are  continually  set  in  motion,  which  can  only  happen  at  the 
expense  of  the  moving  power.  This  is  called  the  resistance  of  fluids. 

137.  Sliding  friction. — If  the  surfaces  of  bodies  were  perfectly  hard 
and  smooth,  they  would  slide  upon  each  other  without  any  resistance. 
But  the  most  highly  polished  surfaces  are,  really  (as  they  appear  under 
the  microscope),  full  of  minute  projections  and  cavities,  which  fit  in 
each  other  when  two  surfaces  are  brought  into  contact.     The  force 
required  to  overcome  the  roughness  and  consequent  adhesion  of  sur- 
faces is  the  measure  of  friction.     This  quantity,  divided  by  the  weight 
of  the  body,  forms  a  fraction  which  is  called  the  co-efficient  of  the 
friction. 

138.  Starting  friction — Friction  during  motion. — The  amount 
of  force  necessary  to  commence  the  motion  of  two  bodies,  sliding  on  each 
other,  is,  in  most  cases,  greater  than  the  force  required  to  continue  the 
movement  uniformly  after  it  has  been  begun ;  hence  this  resistance  is 


102 


PHYSICS    OF   SOLIDS   AND    FLUIDS. 


distinguished  into  two  kinds,  starting  friction,  and  friction  during 
motion.  They  are  also  called  statical  and  dynamical  friction.  Whewell 
proposes  to  name  the  former  striction,  reserving  the  word  friction  for 
the  latter.  However  named,  the  laws  of  each  can  be  determined  only 
by  experiment. 

Coulomb's  apparatus  for  determining  starting  friction. — Dif- 
ferent observers  are  by  no  means  agreed  in  respect  to  all  the  laws  of 
friction ;  we  shall  here  follow  the  results  obtained  in  1781,  by  the 
celebrated  French  philosopher  and  mathematician,  Coulomb.  In  1831, 
Morin,  by  command  of  the  French  government,  repeated  and  enlarged 
the  experiments  of  Coulomb,  usually  verifying  his  general  conclusions. 

The  principal  apparatus  used  by  Coulomb  is  represented  in  fig.  89. 

89 


It  consists  of  a  horizontal  table ;  a  box,  A,  to  receive  the  weights  used 
to  produce  the  different  pressures ;  a  pan,  D,  on  which  were  placed  the 
weights  to  drag  the  box  along  the  table  by  means  of  a  cord  passing 
over  a  pulley.  The  box  was  mounted  on  slides,  of  the  same  substance 
on  which  the  experiment  was  to  be  made,  and  corresponding  slips  of 
the  same,  or  a  different  substance,  were  placed  under  the  sliders  on 
the  table.  The  amount  of  the  weight  required  to  be  placed  in  D,  to 
move  the  box  from  a  state  of  rest,  is  the  measure  of  starting  friction  ; 
and  the  weight  necessary  to  continue  the  movements  uniformly,  is  the 
measure  of  friction  during  motion. 

Results  of  Coulomb's  experiments  on  starting  friction.— 
Without  detailing  the  experiments,  it  will  be  sufficient  to  state  their 
general  results  embraced  in  the  following  laws : — 

Friction  during  movement  is, 

1st. — Proportional  to  the  pressure  exerted  upon  the  sliding  surfaces 

2d. — Independent  of  the  extent  of  the  surfaces  in  contact. 

3d. — Independent  of  the  velocity  of  the  movement. 

4th. — Greater  between  surfaces  of  the  same  than  surfaces  of  different 
materials 


THEORY    OF    MACHINERY. 


103 


5th. — Greatest  between  rough  surfaces,  and  is  diminished  by  polish- 
ing, and  usually  by  the  use  of  suitable  unguents. 

Friction  at  starting  is, 

1st. — Proportional  to  pressure. 

2d. — Independent  of  extent  of  surface. 

3d. — Generally  increased  by  polishing  the  surfaces. 

The  friction  at  starting,  and  during  the  movement,  are  the  same, 
when  the  sliding  surfaces  are  hard,  like  the  metals ;  but  if  the  bodies 
are  compressible,  like  wood,  the  starting  friction  is  much  the  greatest. 
When  at  least  one  of  the  surfaces  is  compressible,  the  resistance  is  not 
always  the  same,  but  varies  according  to  the  time  the  surfaces  have 
been  in  contact.  If  wood  slides  on  wood,  the  starting  friction  attains 
its  greatest  intensity  in  two  or  three  minutes ;  but  if  the  sliding  sur- 
faces are  wood  and  metals,  the  greatest  intensity  is  not  reached  for  a 
much  longer  time,  several  hours,  and  sometimes  several  days.  But  after 
a  certain  time  has  elapsed,  the  starting  friction  is  no  longer  augmented 
by  lengthening  the  time  of  contact. 

It  appears  strange  at  first,  and  contrary  to  our  previous  ideas,  that 
the  friction  at  starting,  and  during  movement,  should  not  be  increased 
by  enlarging  the  surfaces  in  contact,  and  vice  versa.  The  explanation  is 
this.  Friction  is  proportional  to  pressure ;  if,  therefore,  two  bodies 
have  the  same  weight,  and  one  has  twice  the  surface  of  the  other,  the 
weight,  being  equally  distributed  on  each  surface,  will  be  twice  as 
great  on  each  point  of  the  surface  of  the  first  body  as  on  each  point  of 
the  second,  and  consequently  the  friction  at  each  point  of  the  first  is 
twice  the  friction  at  each  point  of  the  second,  and  the  whole  friction 
must  be  the  same  for  each  body.  This  law,  however,  does  not  hold  good 
in  extreme  cases. 

With  the  same  pressure,  the  friction  varies  exceedingly  according  to 
the  nature  of  the  surfaces  in  contact.  The  following  table  shows  the 
ratio  of  friction  in  several  cases,  the  pressure  being  100. 


Surfaces  in  contact. 

Ratio  of  friction  to  pressure. 

At  starting. 

In  motion. 

0-50 
0-36 
0-19 
060 
0-12 
0-63 
0-87 
0-18 
0-12 

0-36 
0-14 
0-07 
0-42 
0-08 
0-45 
0-33 
0-18 
0-07 

"        "        "      with  coating  of  soap,  .     . 
"        "        "        "          "        of  tallow,     . 

"         "         "         with  coating  of  tallow,  . 

«         "         "       with  coating  of  olive  oil, 

104 


PHYSICS    OF    SOLIDS    AND    FLUIDS. 


139.  Rolling  friction. — The  resistance  experienced  in  rolling  a 
cylinder  along  a  plane  surface  is  distinct  in  character  from  the  friction 
produced  in  sliding  the  cylinder,  and  very  much  less  in  amount.  In 
wood  rolling  on  wood  the  proportion  of  resistance  to  pressure  is  from 
16  to  1000,  or  6  to  1000,  while  the  sliding  friction  in  the  same  case  would 
be  as  5  to  10,  or  36  to  100,  according  to  the  kind  of  sliding  friction.  The 
resistance  of  rolling  friction  arises  from  a  slight  change  of  form  pro- 
duced in  the  body,  and  the  surface  on  which  it  moves,  and  correspond- 
ing to  the  amount  of  pressure.  The  cylinder  is  flattened,  and  the  plane 
depressed,  so  that  the  moving  force  is  exerted  in  continually  moving 
the  body  up  a  very  minute  inclined  plane. 

Coulomb's  apparatus  for  determining  rolling  friction. — The 
apparatus  employed  by  Coulomb,  consisted  of  two  bars,  horizontal  and 
parallel,  with  a  space  between  them,  fig.  90.  A  cylinder  of  the  same, 
or  a  different  substance,  was  placed  90 

transversely  across  the  bars,  and  loaded 
with  any  required  pressure  by  hanging 
strings  upon  it,  carrying  equal  weights 
at  their  extremities.  Another  string, 
wound  several  times  around  the  middle 
of  the  cylinder,  carried  a  pan  c  to  re- 
ceive the  weight  necessary  to  produce 
motion.  It  is  evident  that  this  weight 
acted  always  at  the  extremity  of  the 
radius  of  the  cylinder  as  a  lever. 

Results  of  Coulomb's  experi- 
ments on  rolling  friction. — From  the 
experiments  were  derived  the  following 
laws : — 

The  friction  of  rolling  bodies  is, 

1st. — Proportional  to  pressure. 

2d. — Independent  of  velocity,  of  the  diameter  of  the  cylinder,  and  of 
the  extent  of  the  surfaces  in  contact. 

3d.  Greater  when  the  substances  are  the  same  than  when  they  are 
different. 

4th. — Not  diminished  by  coatings  of  grease,  but  is  so  by  the  polish 
of  the  surfaces. 

If  the  force  which  produces  the  movement,  instead  of  being  applied 
always  at  the  sam.e  arm  of  the  lever,  fig.  90,  were  applied  horizontally 
at  the  centre  of  the  cylinder,  or  at  the  upper  extremity  of  its  vertical 
diameter,  it  would  be  inversely  proportional  to  the  diameter. 

The  friction  of  the  axle  of  a  wheel,  whether  the  axle  itself  turns,  or 


THEORY   OF   MACHINERY.  105 

the  wheel  on  the  axle,  is  somewhat  less  than  sliding  friction,  but  obeys 
the  same  laws.  The  friction  of  axles  may  be  reduced  one-half  or  one- 
quarter  its  original  amount  by  the  use  of  proper  unguents. 

140.  Mr.  Babbage's  experiment. — Mr.  Babbage  cites  an  instruc- 
tive experiment  to  illustrate  the  decrease  of  friction.    A  block  of  stone 
weighing  1080  Ibs.  was  drawn  on  the  surface  of  a  rock  by  a  force  of 
758  Ibs. ;  placed  on  a  wooden  sledge,  it  was  drawn  on  a  wooden  floor  by 
a  force  of  606  Ibs. ;  when  both  wooden  surfaces  were  greased,  182  Ibs. 
was  sufficient ;  and  when  the  block  was  mounted  on  wooden  rollers  of 
three  inches  diameter,  a  force  of  only  28  Ibs.  was  required  to  move  it. 

141.  Advantages  derived  from  friction. — The  advantages  arising 
from  friction    are   vastly  greater  than   the   loss   of  power  which  it 
occasions.   Without  this  property  of  matter  it  would  be  equally  impos- 
sible to  make  or  use  machines,  for  nothing  .could  be  nailed,  or  screwed, 
or  tied  together,  or  grasped  securely  in  the  hand.     From  the  difficulty 
of  walking  on  very  smooth  ice,  we  may  infer  how  useless  would  be  the 
effort  to  move,  if  our  feet  met  no  resistance  whatever. 

142.  Rigidity  of  ropes. — When  ropes  are  used  to  transmit  force, 
their  stiffness  occasions  a  considerable  loss  of  power,  amounting,  in 
some  combinations  of  pulleys,  to  two-thirds  of  the  whole  power.     The 
amount  of  the  loss  from  this  cause  is  modified  by  many  external  cir- 
cumstances, such  as  the  dampness  of  the  cordage,-its  quality,  and  the 
manner  in  which  it  is  made.     In  general,  the  resistance  of  ropes  is, 

1st. — Proportional  to  the  tension  to  which  they  are  subjected. 

2d. — It  increases  with  the  thickness,  and  is  greatest  in  those  that 
have  been  strongly  twisted. 

3d. — It  is  inversely  proportional  to  the  diameter  of  the  wheel  or 
cylinder  around  which  the  ropes  are  bent. 

143.  Resistances  of  fluids.— The  resistance  which  a  moving  body 
meets  in  air  and  water,  is  an  effect  of  the  transfer  of  motion  from  the 
solid  to  the  particles  of  the  fluid.    For  the  moving  body  must  constantly 
displace  a  pariof  the  fluid  equal  to  its  own  bulk,  and  the  motion  thus 
communicated  is  so  much  loss  of  the  motive  power.     When  other  cir- 
cumstances are  the  same,  the  denser  the  medium  the  greater  will  be 
the  resistance  which  it  offers.    Newton  demonstrated  that  if  a  spherical 
body  moves  in  a  medium  at  rest,  and  whose  density  is  the  same  as  its 
own,  it  will  lose  half  of  its  motion  before  it  has  described  a  space  equal 
to  twice  its  diameter.     The  resistance  encountered  by  a  body  moving 
in  water  is  800  times  greater  than  if  it  were  moving  with  the  same 
velocity  in  air ;  for  water  being  800  times  more  dense  than  air,  the 
body  must  displace  and  communicate  its  own  motion  to  800  times  as 
much  matter  in  the  same  time. 

12 


106  PHYSICS   OF   SOLIDS   AND   FLUIDS. 

The  resistance  also  depends  upon  the  extent  and  form  of  the  surface 
which  is  directly  opposed  to  the  resistance ;  i.  e.,  at  right  angles  to  the 
direction  of  the  motion.  A  body  with  a  pointed,  wedge-shaped,  or  curved 
surface,  is  less  opposed  than  one  whose  surface  is  flat  and  broad. 

The  resistance  increases  as  the  square  of  the  velocity ;  for  if  the 
velocity  is  doubled,  the  loss  of  motion  must  be  quadrupled,  because 
there  is  twice  as  much  fluid  to  be  moved  in  the  same  time,  and  it  has 
also  to  be  moved  twice  as  fast.  Again,  let  the  velocity  be  trebled,  then 
the  body  will  meet  three  times  as  many  particles  of  the  fluid  in  the 
same  time,  and  communicate  three  times  the  velocity ;  therefore  the 
resistance  is  3  X  3  =  9  =  32. 

Bodies  having  the  same  figure  and  density  overcome  the  resistance 
of  fluids  more  easily  in  proportion  to  their  size.  In  cannon-balls,  for 
example,  the  extent  of  surface  to  which  the  resistance  is  proportional 
increases  as  the  square  of  the  diameter,  while  the  weight,  or  power  to 
overcome  resistance,  increases  as  the  cube  of  the  diameter.  If  two 
balls  have  diameters  in  the  ratio  of  2 :  3,  the  resistances  which  they 
will  encounter  at  the  same  velocity  of  projection,  will  be  in  the  ratio 
of  4 :  9,  and  their  moving  force  in  the  ratio  of  8  :  27. 

144.  Actual  and  theoretical  velocities. — In  consequence  of  these 
impediments  to  motion,  the  actual  movements  of  bodies  are  materially 
different  from  the  theoretical  motions  explained  in  previous  sections. 
The  motion  of  falling  bodies  is  very  far  from  being  uniformly  accele- 
rated, nor  do  all  bodies  fall  with  equal  rapidity,  as  theory  requires, 
and  as  was  seen  to  be  true  in  the  guinea  and  feather  experiment.     The 
resistance  of  the  air,  which  is  very  small  at  first,  rapidly  increases,  and 
after  a  certain  time  becomes  equal  to  the  force  of  gravity,  when  the 
body  will  no  longer  be  accelerated,  but  move  uniformly  through  the 
remainder  of  its  descent.     The  descent  of  bodies  on  inclined  planes 
and  curves  deviates  still  more  from  uniformly  accelerated  motion,  since 
the  effect  of  friction  is  added  to  the  resistance  of  the  air. 

145.  Ballistic  curve. — A  still  greater  difference  is*observed  be- 
tween the  actual  and  theoretical  motions  of  pro-  91 
jectiles  (103).    Instead  of  describing  a  parabola, 

A  E  B,  fig.  91,  the  projectile  actually  describes 
the  curve  A  C  D,  called  the  ballistic  curve,  which 
never  attains  so  great  a  vertical  height,  or  so  long 
a  range  as  the  corresponding  parabola,  and 
which,  toward  the  end  of  its  course,  continually 
approaches  the  perpendicular,  E  F.  A  four- 
pound  shot,  which  fiies  6437  feet  in  the  air,  would  traverse  in  a  vacuum 
a  space  of  23,226  feet. 


THEORY   OF   MACHINERY.  107 

As  in  the  case  of  friction,  the  benefits  resulting  from  this  state  of  things 
overpay  the  disadvantages.  Fish  could  not  swim,  nor  birds  fly,  were  it  not  foi 
the  resistances  of  the  media  they  inhabit.  The  paddle-wheels  of  a  steamer 
would  not  move  it,  nor  its  rudder  guide  its  course,  if  they  met  no  resistance  to 
their  movements.  And  we  can  very  well  dispense  with  a  perfect  theory  of  pro- 
jectiles, if  thereby  the  rain  is  prevented  from  descending  with  the  destructive 
velocity  of  hail-stones. 


Problems. — Vis  Viva. 

47.  If  a  locomotive  and  train  move  20  miles  an  hour,  how  much  greater  force 
will  be  required  to  move  a  train  weighing  three  times   as   much  25  miles  an 
hour  ? 

48.  If  a  locomotive  weighing  30  tons  will  draw  a  train  weighing  90  tons  15 
miles   an  hour,  at  what  velocity  will  it  draw  a  train  weighing  30  tons  ?     The 
weight  of  the  locomotive  is  to  be  added  to^the  train  in  both  cases. 

49.  What  will  be  the  relative  destructive  power  of  a  hurricane  moving  60 
miles  an  hour,  and  another  moving  90  miles  an  hour  ? 

50.  If  a  pile-driver  weighing  1500  Ibs.  raised  20  feet  strikes  with  a  given  force 
to  overcome  resistance,  to  what  height  must  it  be  raised  to  give  a  shock  two  and 
a  half  times  as  great  ? 

51.  What  is  the  comparative  destructive  power  of  a  cannon-ball  weighing  64 
Ibs.  flying  1000  feet  per  second,  and  another  ball  weighing  200  Ibs.  flying  1500 
feet  per  second? 

The  Lever. 

52.  Two  weights,  3  and  4,  balance  on  the  extremities  of  a  lever  4  feet  long ; 
find  the  fulcrum. 

53.  Four  weights,  1,  3,  7,  5,  are  placed  at  equal  distances  on  a  straight  lever. 
Determine  the  position  of  the  fulcrum. 

54.  Two  men  carry  a  weight  of  2  cwt.  hung  on  a  pole,  the  ends  of  which  rest 
on  their  shoulders ;  what  part  of  the  load  is  borne  by  each  man,  the  weight 
hanging  6  inches  from  the  middle  of  the  pole,  the  whole  length  of  which  is  4 
feet? 

55.  A  beam,  18  feet  long,  is  supported  at  both  ends ;  a  weight  of  18  cwt.  is 
suspended  at  3  feet  from  one  end,  and  a  weight  of  12  cwt.  at  8  feet  from  the 
other  end ;  required  the  pressure  at  each  point  of  support. 

56.  A  uniform  beam,  40  feet  in  length,  the  weight  of  which  is  4  cwt.,  is  sup- 
ported by  two  props,  A  and  B,  30  feet  apart ;  a  weight  of  24  cwt.  is  then  sus- 
pended on  the  beam  at  the  distance  of  10  feet  from  B,  the  beam  projecting  8 
feet  over  the  prop  A,  and  2  feet  over  that  at  B  ;  required  the  pressure  on  each 
of  the  props. 

57.  On  a  lever  3  feet  in  length  a  weight  of  500  Ibs.  is  suspended  at  one  end, 
at  2$  inches  from  its  fulcrum ;  what  weight  at  the  other  end  will  keep  the  lever 
in  equilibrium,  the  lever  being  assumed  to  be  without  weight  ? 

"Wheel  and  Axle. 

58.  A  power  of  10  Ibs.  on  a  wheel  the  diameter  of  which  is  10  feet,  balances 
a  weight  of  300  Ibs.  on  the  axle ;  what  is  the  diameter  of  the  axle,  the  thickness 
of  the  rope  on  the  wheel  being  one  inch,  and  that  of  the  rope  on  the  axle  two 
inches  ? 


108  PHYSICS    OP    SOLIDS   AND   FLUIDS. 

59.  A  weight  of  2240  Ibs.  is  sustained  by  a  rope  of  2  inches  in  diameter,  going 
round  an  axle  4  inches  in  diameter ;  what  weight  must  be  suspended  at  the  cir- 
cumference of  a  wheel — radius  6  feet — by  a  rope  of  the  same  thickness,  to  obtain 
equilibrium  ? 

60.  In  a  combination   of  wheels  and  axles  there  are  given  the  radii  of  the 
wheels,  20,  26,  and  48  inches,  and  the  radii  of  the  pinions  and  axle,  4,  5,  and  8 
inches.     If  a  power  of  1  cwt.  be  applied  to  the  circumference  of  the  first  wheel, 
what  weight  will  it  be  able  to  sustain  at  the  circumference  of  the  axle,  or  last 
shaft  ? 

61.  The  number  of  teeth  in  each  of  three  successive  wheels  is  144,  and  the 
number  of  teeth  in  each  of  the  axles  or  pinions  is  6 ;  what  weight  will  this  ma- 
chine support  on  the  last  shaft  with  a  power  of  2  cwt.  on  the  first  wheel  ? 

The  Pulley. 

62.  In  a  system  of  pulleys,  such  as  is  shown  in  fig.  76,  the  number  of  mov- 
able pulleys  being  5 ;  required  the  weight,  the  power  being  500  Ibs.,  and  the 
weight  of  the  movable  block  and  pulleys  being  30  Ibs. 

63.  What  power  at  P,  fig.  77,  will  be  required  to  balance  a  weight,  W,  of  3 
tons,  the  number  and  arrangement  of  the  pulleys  being  as  shown  in  the  figure? 

Inclined  Plane. 

64.  What  power  acting  as  in  fig.  79,  will  balance  a  weight  of  300  Ibs.  on  the 
inclined  plane,  the  length  of  the  plane  being  25  feet,  and  the  vertical  height 
five  feet  ? 

65.  On  an  inclined  plane,  whose  base  is  10  feet  and  height  3  feet,  what  power 
acting  parallel  to  the  base  will  balance  a  weight  of  2  tons  ? 

66.  What  power  is  required  to   draw  a  train  of  cars,  weighing  40  tons,  up  a 
railway  grade  rising  1  foot  in  every  100  feet? 

The  Screw. 

67.  What  weight  can  be  raised  by  means  of  a  screw  having  its  threads  one 
inch  apart,  by  a  power  of  150  Ibs.  acting  at  a  distance  of  6  feet  from  the  axis 
of  the  screw  ? 

68.  Supposing  one-third  of  the  power  is  lost  in  overcoming  the  friction  of 
the  screw,  what  power  will  be  required,  acting  3  feet  from  the  axis  of  the  screw, 
to  raise  3  tons,  the  threads  of  the  screw  being  2  inches  apart  ? 

69.  What  power  at  the  winch  D,  fig.  86,  is  required  to  raise  a  weight  of  2  tons 
at  Q,  if  the  radius  of  the  axle  is  6  inches,  the  radius  of  the  wheel  3  feet,  the 
distance  between  the  threads  of  the  screw  yl^  part  of  the  circumference  of  the 
Wheel,  and  the  length  of  the  winch  D  B  =  2  feet  ? 

Resistance. 

70.  If  a  mass  of  iron  weighing  5  tons  slides  upon  iron  rails,  what  force  is 
required  to  start  it,  and  how  much  to  keep  it  moving  afterwards  ? 

71.  If  a  steam  vessel  of  1000  tons  is  moved  through  the  water  at  10  miles  an 
hour,  by  an  engine  of  300  horse-power,  what  is  the  power  of  an  engine  required 
to  propel  another  vessel,  of  the  same  model,  of  2000  tons  at  the  same  speed  ? 

72.  If  a  ball,   6   inches   in    diameter,  is  discharged   from  a  cannon  at  the 
rate  of  one  mile  in  7  seconds,  how  much  greater  force  would  be  required  to 
throw  a  ball  of  double  the  weight  with  the  same  velocity,  taking  into  account 
the  resistance  of  the  air  and  the  dimensions  of  the  balls  ? 

73.  If  an  engine  of  500  horse-power  propels  a  vessel  of  1500  tons  12  miles  an 
hour,  at  what  velocity  will  an  engine  of  600  horse-power  propel  a  vessel  of  2000 
tons,  built  on  the  same  model  as  the  preceding  ? 


PART   SECOND. 

THE  THREE  STATES  OF  MATTER. 


CHAPTER  I. 


MOLECULAR    FORCES. 

146.  Cohesion  and  Repulsion. — -The  three  states  of  matter  (15) — 
the  solid,  liquid,  and  gaseous — exist,  as  is  assumed,  in  virtue  of  cer- 
tain forces  inherent  in  the  particles  of  matter,  and  called  molecular 
forces.  These  forces  are  either  attractive  or  repulsive,  drawing  the  par- 
ticles of  bodies  toward  each  other,  or  tending  to  separate  them.  In 
solids  the  attractive  force  greatly  overpowers  the  repulsive,  and  the 
particles  of  matter  become  therefore  relatively  fixed  at  certain  distances 
from  each  other — not  being  in  actual  contact,  but  having,  as  we  have 
seen  (23),  numerous  pores  between  them.  Heat  may  enlarge  and  cold 
diminish  these  pores,  and  with  them  the  sensible  magnitude  of  the 
solid ;  but  the  integral  particles  of  the  solid  cannot  be  separated  with- 
out the  exercise  of  some  exterior  and  greater  force.  When  the  par- 
ticles of  a  body  are  not  separated  too  far,  they  return  again,  upon 
the  withdrawal  of  the  constraining  force,  to  their  original  position 
(Elasticity).  This  species  of  attraction  existing  between  particles  of 
the  same  kind  is  distinguished  by  the  term  cohesion,  and  when  existing 
between  particles  of  an  unlike  kind,  it  is  called  adhesion. 

Repulsion. — If  we  admit,  as  the  phenomena  of  porosity  demand 
(23),  that  in  spite  of  cohesive  attraction,  the  particles  of  bodies  do  not 
actually  touch  each  other,  it  follows  that  there  must  exist  in  the  mole- 
cules of  matter  a  second  and  counterbalancing  force  opposed  to  cohesion, 
12*  .  (109) 


110  THE    THREE    STATES    OF    MATTER. 

and — in  solids — in  equilibrium  with  it.     This  force  is  called  repulsion, 
We  shall  presently  revert  to  the  evidence  of  its  action  on  matter. 

While  the  existence  of  these  two  molecular  forces  is  in  many  cases 
capable  of  direct  proof,  the  exact  mode  of  their  action  is  chiefly  conjec- 
tural. It  is,  however,  certain  that  the  attractive  forces  act  only  at  insen- 
sible distances.  In  this  respect  the  molecular  forces  are  to  be  distin- 
guished from  gravitation, which  acts  at  all  distances.  Chemical  attraction 
is  also  distinguished  from  the  mechanical  forces  of  cohesion  and  adhesion, 
by  the  important  fact  that  its  exercise  is  invariably  attended  by  the 
loss  of  specific  identity  (7),  and,  of  course,  by  the  substitution  of  new 
qualities  in  the  compound  for  those  characteristic  of  its  constituents. 

Since  the  force  of  gravity  is  proportional  to  the  mass,  and  inversely  aa 
the  distance,  if  cohesion  were  merely  the  attraction  of  gravitation  acting  at 
insensible  distances,  the  particles  of  a  body  situated  at  the  centre  of  gravity  of 
a  large  mass,  should  cohere  more  strongly  than  particles  at  a  distance  from  the 
centre  of  gravity,  or  than  the  same  particles  when  the  mass  is  reduced  to  frag- 
ments, but  no  such  difference  has  been  observed,  we  must  therefore  conclude 
that  gravity  and  cohesive  attraction  are  essentially  different  forces. 

147.  Examples  of  cohesion  among  solids. — Cohesion,  when  once 
destroyed  by  mechanical  violence,  is  not  usually  brought  into  exercise 
again  by  mere  contact  of  the  separated  particles.  Thus  the  broken 
fragments  of  a  glass  vessel,  or  of  a  stone,  do  not  reunite  at  ordinary 
temperatures.  Two  hemispheres  of  tarnished  lead  will  not  adhere  by 
their  flat  surfaces  by  mere  pres-  92 

sure,  but  if  the  coating  of  oxyd  is 
first  removed  by  a  sharp  knife, 
and  the  two  clean  surfaces  are 
then  pressed  together,  with  a 
slight  wrenching  motion,  they 
will  cohere  strongly.  Arranged 
as  in  fig.  92,  two  surfaces  one 
inch  in  diameter  will  sustain  ten 
pounds  or  more.  This  is  only 
an  example  of  welding  at  com- 
mon temperatures,  a  process  suffi- 
ciently familiar  in  hot  iron.  Wax, 
dough,  india  rubber,  and  other 
similar  substances,  offer  examples 
of  a  like  nature,  provided  clean 
surfaces  be  pressed  together. 
Dust,  or  other  foreign  bodies, 
prevent  this  union.  Even  polished  glass  plates,  allowed  to  remain  long 


MOLECULAR    FORCES.  HI 

in  contact,  if  perfectly  clean,  and  under  pressure,  have  been  known  to 
cohere  so  strongly  as  to  separate  by  fracture  in  any  other  direction 
sooner  than  in  the  line  of  junction.  Boyle  demonstrated  that  this  fact 
is  not  accounted  for  by  attributing  the  action  to  atmospheric  pressure. 
He  suspended  a  pair  of  adhesion  plates  in  the  vacuum  of  an  air-pump, 
where,  in  the  absence  of  atmospheric  pressure,  it  required  still  a  con- 
siderable weight  to  detach  the  surfaces. 

Adhesion  is  distinguished  from  cohesion  by  the  fact  that  while  the 
latter  occurs  between  particles  of  a  like  kind,  producing  homogeneous 
bodies,  the  former  takes  place  between  particles  of  unlike  kinds,  pro- 
ducing heterogeneous  bodies.  Glue  binding  together  pieces  of  wood  is 
an  example  of  adhesion.  This  species  of  mechanical  attraction  is, 
however,  seen  in  its  most  important  relations  in  the  curious  phenomena 
of  capillarity,  to  be  discussed  hereafter. 

The  terms  cohesion  and  adhesion  are  often  used  interchangeably, 
and,  when  the  distinctions  here  pointed  out  are  borne  in  mind,  no  evil 
will  arise  from  this  use  of  terms. 

The  force  of  cohesion  among  the  particles  of  solids,  when  exerted 
under  favorable  conditions,  produces  the  regular  forms  of  crystals,  to 
which  we  shall  presently  revert. 

148.  Cohesion  in  liquids  and  between  liquid  gases  and 
solids. — The  force  of  cohesion  in  liquids  gives  the  spherical  form  to 
drops  of  rain  and  dew,  and  rounds  the  drop  of  water  suspended  from 
the  end  of  a  glass  rod.  If  two  drops  of  water  or  any  other  liquid 
approach  each  other  near  enough,  they  unite  to  form  a  larger  spherical 
drop.  A  soap-bubble  is  only  a  large  hollow  sphere  of  water,  whose 
outer  film  of  liquid  assumes  and  preserves  its  spherical  form  in  virtue 
of  cohesive  attraction  and  the  laws  of  liquid  equi- 
librium. The  soap,  while  it  adds  to  the  viscous  con- 
dition of  the  water,  really  diminishes  its  cohesive 
force,  as  was  shown  by  Prof.  Henry.  The  force  of 
cohesion  in  water  may  be  directly  measured  by  sus- 
pending a  counterpoised  disk  of  glass  or  metal  from 
a  scale  pan,  fig.  92*  adjusted  to  allow  the  disk  just  to 
touch  the  surface  of  the  water.  The  weight  required 
in  the  opposite  pan,  to  separate  the  disk  from  the  water,  then  becomes 
the  measure  of  cohesion  among  the  particles  of  water  forming  the  outer 
circle  of  contact. 

By  this  means  Gay  Lussac  found  that  a  disk  of  4'362  inches  in 
diameter  required  982  grains  to  separate  it  from  water,  while  from 
alcohol  (density  O819)  and  spirits  of  turpentine,  478'83  and  525 
grains,  respectively,  produced  separation ;  all  being  at  the  temperature 


112  THE    THREE    STATES    OP    MATTER. 

of  46°  Fahr.  The  thickness  and  material  of  the  disk  made  no  difference 
in  the  result,  showing  that  the  force  of  cohesion  was  the  only  force  to 
be  overcome,  and  that  this  force  was  exerted  at  a  distance  less  than  the 
thickness  of  the  film  of  liquid  necessary  to  moisten  the  surface  of  the 
disk.  It  is  also  evident  that  the  weights  obtained  do  not  represent  the 
whole  cohesive  force  in  each  case,  since,  from  the  circumstances  of  the 
trial,  it  can  be  only  the  outer  circle  of  particles  whose  cohesion  is  over- 
come, and  this  being  the  largest  circle,  each  succeeding  row  or  line 
of  particles  yields  readily  to  the  same  force. 

Between  liquids  and  solids  the  force  of  adhesion  is  modified  by  the 
phenomena  of  capillarity  and  surface  attraction. 

Between  gases  and  solids  cohesion  is  seen  to  exist  when  we 
attempt  to  wet  the  polished  surface  of  a  steel  blade,  or  a  clean  surface 
of  glass,  with  water.  The  liquid  fails  to  wet  the  polished  surface  of  the 
metal,  &c.,  owing  to  the  film  of  air  adhering  to  it,  due  to  the  attraction 
of  the  solid  for  the  air.  If  the  blade  is  slightly  heated,  or  its  surface 
is  roughened  mechanically  or  by  acids,  this  film  of  air  is  removed,  and 
the  blade  is  then  wetted.  (See  Smee's  battery :  Electricity.) 

Gases  do  not  manifest  cohesion  among  themselves,  because  the  repul- 
sive force  overcomes  it,  but  numerous  examples  of  its  exercise  may  be 
quoted  besides  that  just  named.  The  bubbles  of  gas  escaping  from 
aerated  water  adhere  to  the  sides  of  a  glass  vessel  from  this  cause. 
But  above  all  is  this  seen  in  the  power  of  recently  ignited  charcoal  to  ab- 
sorb and  retain  gases.  Owing  to  its  numerous  sensible  pores,  charcoal 
presents  a  very  large  surface  in  a  small  space.  The  more  compact  the 
wood  the  more  numerous  are  these  pores,  and  the  more  remarkable  the 
consequent  absorption  of  gas.  Different  gases  are  also  very  differently 
absorbed  by  it,  depending  on  their  condensibility  and  solubility.  Thus, 
while  only  four  or  five  volumes  of  common  air  are  absorbed  by  charcoal, 
thirty  volumes  of  carbonic  acid,  and  eighty  or  ninety  volumes  of  am- 
monia or  chlorohydric  acid  gas,  are  absorbed  by  charcoal  recently 
ignited.  This  curious  and  important  property  is  easily  illustrated  over 
the  mercurial  trough,  by  using  glass  cylinders,  filled  with  the  various 
gases,  to  cover  bits  of  charcoal  placed  on  the  mercury — the  absorption 
commencing  at  once  and  advancing  gradually  for  some  hours. 

We  will  consider  the  action  of  molecular  forces,  first,  between  mole- 
cules of  the  same  kind,  and,  second,  when  acting  between  molecules  of 
unlike  kinds,  to  which  are  referred  the  phenomena  of  capillarity. 


.       PROPERTIES   OF   SOLIDS.  113 

CHAPTER  II. 

OF  SOLIDS. 
MOLECULAR   FORCES   ACTING   BETWEEN    PARTICLES   OF   LIKE    KINDS. 

g  1.    Properties  of  Solids. 

149.  The   characteristic  properties  of  solids,   now  to  be  con 
sidered,  are,  1.  Crystalline  Form  ;  2.  Elasticity  ;  3.  Resistance  to  Frac- 
ture  (including   Strength  of  Materials) ;  4.  Hardness,  and  5.  Those 
properties  dependent  on  a  permanent  change  in  the  arrangement  of  the 
molecules — as  Ductility,  Malleability,  Temper,  &c. 

150.  Structure  of  solids. — In  solids  the  particles  of  matter  are 
held  in  fixed  relation  to  each  other  by  the  molecular  forces  (146)  JpFhe 
relative  disposition  of  the  molecules,  or  of  their  groups,  constitutes  what 
is  called  structure  in  solids.     This  structure  may  be  either  symmetrical 
or  regular,  as  in  living  beings  and  crystals,  or  amorphous,  as  in  most 
rocks  and  many  other  substances. 

There  exists  in  nature  a  plan,  which  cannot  be  mistaken,  to  combine 
matter  in  complete  and  symmetrical  wholes.  The  bodies  of  animals 
consist,  usually,  of  two  equal,  (or  nearly  equal),  and  similar  sets  of  limbs 
and  organs,  one  on  the  right  and  one  on  the  left  side.  The  organs  of 
most  flowering  plants  are  similarly  and  regularly  arranged  in  whorles  of 
three  members,  as  in  the  lily,  or  of  Jive,  as  in  the  rose,  or  in  some  other 
simple  numbers,  and  the  same  law  is  beautifully  exemplified  in  the 
arrangement  of  the  leaves  and  branches  of  all  plants  and  trees  (phyllo- 
taxy}.  In  the  animal  and  vegetable  world,  the  laws  which  direct  the 
aggregation  of  matter  are  those  of  VITALITY,  and  it  is  observed  that 
most  of  the  forms  thus  produced  are  bounded  by  curved  lines  and 
surfaces. 

In  the  inorganic  or  lifeless  world  different  laws  are  in  force,  and  in 
the  production  of  solids  the  atoms,  under  favorable  circumstances, 
arrange  themselves  in  forms  which  are  angular  and  bounded  by  plane 
surfaces.  The  geometrical  forms  thus  produced  are  analogous  to  the 
more  complicated  results  of  vitality  as  seen  in  animal  and  vegetable  life. 
These  forms  are  called  CRYSTALS,  and  the  laws  governing  the  aggrega- 
tion of  matter  into  such  forms,  are  called  the  laws  of  crystallization. 

When  solids  are  formed  in  a  manner  unfavorable  to  the  regular 
action  of  the  molecular  forces,  the  regular  forms  of  crystals  are  not 


114  THE   THREE    STATES    OF    MATTER. 

produced,  but  a  mass  which  has  perhaps  some  traces  of  crystalline 
structure  (as  in  marble),  or  which  is  entirely  amorphous(152),  according 
as  the  act  of  solidification  has  been  more  or  less  disturbed.  Thus,  in 
granite  we  easily  detect  the  crystalline  structure  of  some  of  the  con- 
stituents closely  aggregated,  while  in  slates  and  many  mechanical 
rocks  no  traces  of  crystalline  structure  can  be  seen. 

§  2.   Crystallography. 

151.  Conditions  of  crystallization. — In  order  that  crystals  may 
form,  it  is  a  necessary  condition  that  the  molecules  of  the  body  to  be 
crystallized  should  have  freedom  of  motion  among  themselves,  and 
ample  time  to  arrange  themselves  in  accordance  with  the  force  of  crys- 
tallogenic  attraction.  These  conditions  may  be  met  in  either  of  the 
following  methods :  1.  By  solution ;  2.  By  fusion ;  3.  By  sublimation 
or  evaporation ;  or,  4.  By  electrical  or  chemical  decomposition. 

(a)  By  solution. — Many  solids  dissolve  in  water ;  thus  most  salts,  as 
common  salt,  Epson*  salts,   saltpetre,  borax,  alum,  &c.,  form  a  clear 
sorwren  in  water,  in  which  all  crystalline  attractions  are  subordinated, 
until  by  gradual  evaporation,  or  by  cooling  from  a  saturated  hot  solu- 
tion, the   several  salts  reappear,  each  in  its   own  appropriate  form. 
Sulphur  and  phosphorus  also,  dissolved  by  heat  in  bisulphid  of  carbon, 
crystallize  by  the  cooling  of  the  solution.    Some  substances  are  equally 
soluble  in  cold  or  in  hot  water,  and  crystals  are  obtained  from  their 
solutions  only  by  evaporation,  with  or  without  the  aid  of  heat. 

Common  salt  is  an  example  of  such  a  substance;  when 
evaporated  very  gently,  as  by  solar  heat,  perfect  cubes 
are  formed ;  if  rapidly,  as  by  fire,  a  confused  mass  of 
irregular  crystalline  grains  result.  Sometimes  the  float- 
ing crystals,  as  they  grow  in  weight  continually,  but 
slowly,  sink,  giving  rise  to  the  curious  hopper-shaped 
forms  seen  in  fig.  93. 

Alumina  dissolves  in  melted  boracic  acid,  and  the  solution,  exposed 
for  a  time  to  the  highest  heat-of  a  porcelain  furnace,  loses  the  boracic 
acid  slowly  by  evaporation,  and  the  alumina  crystallizes  as  rubies  or 
sapphires.  Many  other  gems  have  thus  been  obtained,  of  microscopic 
size,  by  M.  Ebleman,  by  solution  in  boracic  or  phosphoric  acids,  or 
their  salts,  at  a  high  heat. 

(b)  By  fusion. — By  melting  sulphur,  bismuth,  and  many  other  sub- 
stances, in  crucibles,  and  allowing  them  to  cool  very  slowly ;  when  a 
crust  has  formed  on  the  surface  it  is  pierced,  and  the  contents  remain- 
ing fluid  are  turned  out,  the  interior  cavity  is  found  lined  with  crystals 
of  the  substance  experimented  on. 

(c)  By  sublimation. — By  heat  many  substances  rise  in  vapor,  and  on 


CRYSTALLOGRAPHY. 


115 


cooling  again,  in  a  proper  receptacle,  assume  their  appropriate  crystal- 
line forms — camphor,  sulphur,  arsenious  acid,  iodine,  arsenic,  sal-am- 
moniac, &c.,  can  be  thus  crystallized. 

(d)  By  electrical  or  chemical  decomposition. — By  adding  to  a  solution 
of  some  substances  some  other  dissolved  body,  which  causes  the  first 
to  become  insoluble,  a  crystalline  powder  often  falls  (this  is  true  in 
most  cases  of  precipitation),  due  to  the  formation  of  a  new  compound, 
of  a  less  solubility  than  either  of  the  substances  employed.  The  crystals 
of  metals,  e.  g.  of  copper,  gold,  silver,  &c.,  are  easily  formed  by  the 
processes  of  electro-metallurgy. 

152.  Amorphism. — Amorphism  is   that  state  of  a  solid  in  which 
there  is  no  trace  of  a  crystalline  structure ;  examples  of  such  a  state 
are  seen  in  common  glass,  gun-flint,  wax,  obsidian,  sugar-candy,  &c. 
An  amorphous  body,  having  no  planes  of  cleavage,  is  broken  in  one 
direction  as  easily  as  in  another.     Bodies   are  generally  more  soluble, 
less  hard  and  dense,  in  the  amorphous  than  in  the  crystalline  state. 

An  amorphous  body  may  be  produced  in  a  number  of  ways  j  for 
example,  by  fusion,  as  in  the  case  of  glass ;  by  evaporation  of  solu- 
tions, as  those  of  the  gums  and  glue  in  water ;  and  by  precipitation 
from  their  solutions,  as  is  the  case  with  alumina  and  phosphate  of  lime. 

The  property  of  toughness,  seen,  as  for  example,  in  emery  (amorphous  corun- 
dum), and  horn-stone  (amorphous  quartz),  is  much  more  highly  developed  in 
the  amorphous  than  in  the  crystalline  varieties  of  these  minerals. 

153.  Crystalline    forms.      Definitions. — The    crystalline    forms 
assumed  by  the  same  substance  are,  with  certain  limitations,  always 
the  same  ;  depending  on  the  nature  of  the  substance,  and  are  therefore 
essential  forms.    The  study  of  these  forms  and  the  laws  of  crystallogeny, 
reveal  to  us  all  that  we  know  of  the  ultimate  forms  of  matter. 

A  crystal  is  a  polyhedron,  and  the  terms  of  solid  geometry  are  used 
in  crystallography  without  change. 


94 


94* 


Replacement. — An  edge  or  angle  is 
replaced  when  cut  off  by  one  or  more 
secondary  planes.  Fig.  94,  i  i. 

Truncation. — An  edge  or  angle  is 
truncated  when  the  replacing  plane  is 
equally  inclined  to  the  adjacent  faces. 
Fig.  94. 

Bevelment. — An  edge  is  beveled  when  replaced  by  two  planes  which 
are  respectively  inclined  at  equal  angles  to  the  adjacent  faces  i2  i2,  fig. 
94*.  Truncation  and  beyelment  can  only  occur  on  edges  formed  by  the 
meeting  of  equal  planes. 


L16 


THE   THREE    STATES   OF   MATTER. 


The  axes  of  a  crystal  are  imaginary  lines  passing  through  its  centre, 
and  about  which  two  or  more  faces  are  symmetrically  arranged.  They 
connect  either  the  centres  of  opposite  faces,  fig.  95,  or  edges,  fig.  96,  or 
the  apices  of  opposite  solid  angles,  fig.  97,  or  of  both  edges  and  angles, 
fig.  98. 


95 


96 


97 


(I 

^ 

i 
io 

26 

0 

:    l^1 

2. 

c 

Three  axes  are  employed  for  the  different  systems  in  crystallography 
(excepting  the  sixth,  fig.  114),  whose  length  may  be  equal,  or  only  two 
alike,  or  all  unequal ;  they  may  also  be  at  right  angles  to  each  other,  or 
oblique. 

A  prism  is  a  column  having  any  number  of  sides.  In  crystal- 
lography we  have  four  and  six-sided  prisms,  which  may  be  either  right 
prisms,  that  is,  erect ;  or  oblique  prisms,  that  is,  inclined. 

Four-sided  prisms  occur  of  a  number  of  kinds ;  their  bases  may  be 
either  square,  rectangular,  rhombic,  or  rhomboidal.  If  the  base  is  a 
square,  or  a  rectangle,  and  the  prism  erect,  the  eight  solid  angles  are 
equal  and  rectangular;  the  edges  are  twelve,  and  may  vary;  for 
example, 

A  cube  is  bounded  by  six  equal  sides  (the  lateral  sides  being  equal 
to  the  bases),  and  the  twelve  edges  are  all  equal,  fig.  95. 

100 


A  right  square  prism,  fig.  99,  has  a  square  base  and  a  height  which 
may  be  either  greater  or  less  than  its  breadth  ;  its  sides  are  equal 
rectangles,  the  eight  basal  edges  (four  at  each  base)  are  equal  to  each 
other,  but  differ  from  the  four  lateral  edges. 

A  right  rectangular  prism,  fig.  100,  has  a  rectangular  base,  and  sides 
also  rectangular,  the  opposites  only  equal ;  two  edges  at  each  base  dif- 


CRYSTALLOGRAPHY. 


117 


fer  from  the  other  two,  while  the  lateral  edges  are  also  different;  hence 
there  are  three  sets  of  edges,  four  in  each  set. 

The  base  may  also  be  a  rhomb  or  rhomboid. 

A  right  rhombic  prism,  fig.  101,  has  a  varying  height  and  a  rhombic 
base.  Its  plane  angles  are  two  obtuse  and  two  acute,  with  correspond- 
ing solid  angles  and  lateral  edges  ;  the  four  lateral  faces  are  rectangles, 
and,  like  the  basal  edges,  are  equal. 


101 


102 


103 


An  oblique  rhombic  prism,  figs.  102,  103  (fig.  102  a  front  view,  and 
fig.  103  a  side  view)  ;  has  a  rhombic  base  and  a  varying  height,  the 
lateral  faces  are  rhomboids.  The  lateral  edges,  like  the  basal  edges, 
have  two  acute  and  two  obtuse  angles.  When  the  height  is  equal  to 
the  breadth  the  form  is  : — 

A  rhombohedron,  fig.  98,  composed  of  six  equal  rhombic  faces. 

A  right  rhomboidal  prism  has  a  rhomboidal  base  and  a  varying 
height,  only  the  two  opposite  sides  and  angles  are  equal,  the  lateral 
rectangular  faces  correspond  to  the  basal  edges ;  the  opposites  only  are 
equal.  This  form  is  similar  to  fig.  101. 

An  oblique  rhomboidal  prism,  fig.  104,  has  a  rhomboidal  base  and  a 
varying  height.  The  lateral  faces  are  rhomboids.  The  edges  of  each 
base  are  of  four  kinds  ;  for  two  opposite  are  longer  than  the  other  two, 
and  of  each  pair,  one  is  obtuse  and  the  other  acute.  In  this  solid, 
therefore,  only  diagonally  opposite  edges  are  similar,  and  only  opposite 
solid  angles  are  equal. 


105 


106 


An  hexagonal  prism,  fig.  105,  is  an  erect  six-sided  prism. 
An  octahedron  has  eight  triangular  faces ;  its  form  is  like  two  four 
sided  pyramids  united  base  to  base.     Three  octahedrons  are  described 
13 


118 


THE    THREE    STATES    OF    MATTER. 


The  regular  octahedron,  fig.  106,  has  a  square  base  and  eight  faces, 
equilateral  triangles ;  its  solid  angles  are  six,  and  equal,  as  also  are  its 
twelve  edges.  The  plane  angles  are  60°,  the  interfacial  angles  are 
109°  28'  16" ;  this  solid  is  symmetrical,  like  the  cube. 

The  right  square  octahedron,  fig.  107,  has  a  square  base,  but  a  verti- 
cal height,  greater  or  less  than  in  the  regular  octahedron.  Its  faces 
are  equal  isosceles  triangles.  Its  basal  edges  are  equal  and  similar, 
but  they  differ  in  length  from  the  eight  equal  pyramidal  edges.  The 
vertical  solid  angles  differ  from  the  basal 

The  right  rhombic  octahedron,  fig.  108,  has  a  rhombic  base  and  a 
varying  height;  its  faces  are  equal  triangles;  the  basal  edges  are 
equal ;  the  plane  angles  of  the  base  and  the  pyramidal  edges  are  of 
two  kinds,  two  obtuse  and  two  acute. 


107 


108 


109 


The  rhombic  dodecahedron,  fig.  109,  is  bounded  by  twelve  equal 
rhombs ;  it  has  twenty-four  similar  edges,  and  fourteen  solid  angles ; 
they  are  of  two  kinds :  Eight  obtuse,  formed  by  the  meeting  of  three 
obtuse  plane  angles,  and  six  acute,  formed  by  the  meeting  of  four  acute 
plane  angles. 

154.  Systems  of  crystals. — There  are  six  systems  of  axes,  pro- 
ducing the  same  number  of  systems  of  crystalline  forms,  by  the  sym- 
metrical arrangement  of  planes  about  these  axes.  They  are  called  the 
monometric,  dimetric,  trimetric,  monoclinic,  triclinic,  and  hexagonal 
systems. 

(a)  The  monometric  system  (from  monos,  one,  and  metron,  measure), 
includes  the  cube,  fig.  95,  the  regular  octahedron,  fig.  106,  and  rhombic 
dodecahedron,  fig.  109.  Each  of  these  forms  is  perfectly  symmetrical, 


NOTE. — In  studying  this  subject,  the  pupil  will  find  it  of  the  greatest  assist- 
ance to  his  easy  comprehension  of  the  forms  mentioned,  to  produce  them  with 
a  knife,  from  some  soft  substance  like  a  turnip  or  a  potato,  which  are  more 
easily  managed  than  chalk  or  wood,  and  neater  than  clay.  Sets  of  crystalline 
forms  and  cards,  with  the  outlines  of  the  various  forms  prepared  for  cutting 
up,  are  furnished  cheaply  by  the  German  chemical  dealers,  for  the  use  of 
schools. 


CRYSTALLOGRAPHY. 


119 


being  equal  in  height,  length,  and  breadth.  Their  axes  are  three  in 
number,  of  equal  length,  and  at  right  angles  to  each  other.  In  the 
cube,  the  axes  connect  the  centres  of  opposite  faces,  in  the  octahedron, 
the  apices  of  opposite  soKd  angles,  and  in  the  dodecahedron,  the  apices 
of  opposite  acute  solid  angles.  The  relation  of  the  axes  in  these  solids 
to  each  other,  may  be  understood  by  deriving  one  form  from  the  other. 
If  in  the  cube  (its  faces  are  indicated  by  o)  we  truncate  each  of  its 
eight  solid  angles,  fig.  110  is  first  produced,  and  as  the  truncation  pro- 
ceeds, fig.  Ill,  and  finally  a  perfect  octahedron.  It  will  be  noticed  that 
the  centres  of  o,  the  ends  of  the  axes  in  the  cube,  correspond  to  the 
apices  of  the  solid  angles  in  the  octahedron,  which  are  also  the  ends 
of  axes. 

110 


(6)  The  dimetric  system  (from  dis,  two-fold,  and  metron,  measure] 
includes  the  square  prism,  fig.  99,  and  square  octa- 
hedron,  fig.  107,  bearing  the  same  relation  to  each  other 
as  the  cube  does  to  the  regular  octahedron.  In  this 
system  there  are  three  axes,  all  at  right  angles  to  each 
other,  but  only  the  two  lateral  are  equal,  the  third,  or 
vertical  axis,  being  of  varying  length.  In  the  prism, 
the  axes  connect  the  centres  of  opposite  faces,  in  the 
octahedron  the  apices  of  opposite  solid  angles.  If  a  square  prism 
has  each  of  its  solid  angles  truncated,  we  shall  have  first,  fig.  112,  and, 
finally,  the  square  octahedron  is  produced. 

(c)  The  trimetric  system  (from  tris,  three-fold,  and  metron,  measure), 
includes  the  rectangular  prism,  fig.  100,  the  rhombic  prism,  fig.  101, 
and  the  rhombic  octahedron,  fig.  108.     Each  of  these  forms  has  its 
three  axes  at  right  angles  to  each  other,  and  all  are  unequal  in  length. 
In  a  rectangular  prism   (the  base  a  rectangle),  the  axes  connect  the 
centres  of  opposite  faces.     In  the  rhombic  prism  (base  a  rhomb),  the 
vertical  axis  connects  the  centres  of  the  bases,  the  two  lateral  axes  con- 
nect the  centres  of  opposite  edges.     In  the  rhombic  octahedron  (base 
a  rhomb)  the  axes  connect  the  apices  of  opposite  solid  angles. 

(d)  The  monodinic  system  (from  monos,  one,  and  klino,  to  incline), 
includes  the  right  rhomboidal  prism,  fig.  101,  and  the  oblique  rhombio 


120 


THE    THREE    STATES    OF    MATTER. 


114 


prism,  fig.  102.     In  this  system  the  three  axes  are  unequal,  the  two 

lateral  axes  are  at  right  angles  with  one  another,  the  vertical  is  inclined 

to  one  of  the  lateral  axes  and  at  right  angles  with 

the  other.     In  the  right  rhomboidal  prism  the  axes 

connect  the  centres  of  opposite  faces.    In  the  oblique 

rhombic  prism  the  vertical  axis  connects  the  centres 

of  the  bases,  and  the  two  lateral  axes,  the  centres  of 

opposite  lateral  edges.     The  truncation  of  the  lateral 

edges  of  one  prism  finally  produces  the  other.     The 

relation  of  these  prisms  to  each  other  is  seen  in  fig.  103. 

(e]  The  triclinic  system  (from  iris,  three,   and  klino,   to  incline), 
includes  the  oblique  rhomboidal  prism,  fig.  104.     All  the  axes  are  un- 
equal and  oblique,  the  vertical  axis  connects  the  centres  of  the  bases ; 
the  lateral  axes  connect  the  centres  of  the  lateral  edges. 

(f)  The  hexagonal  system  includes  the  hexagonal 
prism,  fig.  105,  and  rhombohedron,  fig.  114.     In  the 
hexagonal  prism,  fig.  105,  the  vertical  axis  connects 
the  centres  of  the  bases,  the  three  lateral  axes  connect 
the  centres  of  opposite  lateral  faces  or  edges,  and  cross 
each  other  at  an  angle  of  60°,  at  right  angles  to  the 
vertical  axis. 

In  the  rhombohedron,  two  diagonally  opposite  solid  angles  consist  of  three 
equal  obtuse  or  three  equal  acute  plane  angles ;  the  diagonal  connecting  these 
solid  angles  is  called  the  vertical  axis ;  placed  with  this  axis  in  a  vertical  posi- 
tion, the  rhombohedron  is  said  to  be  in  position,  and  looking  from  above,  it 
will  be  noticed  that  the  lateral  edges  are  at  an  equal  distance  from  the  vertical 
axis;  the  three  lateral  axes  connect  the  centres  of  the  lateral  edges  intersecting 
each  other,  as  do  the  lateral  axes  of  the  hexagonal  prism,  at  an  angle  of  60°. 
Placing  the  rhombohedron  in  position,  if  we  remove  the  six  lateral  edges,  re- 
placing them  by  planes  parallel  to  the  vertical  axis,  there  is 
produced  a  regular  hexagonal  prism,  terminated  by  three-sided 
pyramids.  If  their  vertical  solid  angles  are  also  removed  the 
regular  hexagonal  prism  results.  If  we  remove  from  an  hex- 
agonal prism  three  alternate  basal  edges,  and  at  the  other  ex- 
tremity also,  three  edges,  alternating  with  the  first,  as  shown 
in  fig.  115,  and  continue  the  removal  until  the  original  form 
is  obliterated,  a  rhombohedron  is  produced ;  it  also  results  by 
removing,  in  a  corresponding  manner,  the  alternate  solid 
angles  from  the  hexagonal  prism.  When  the  plane  angles  forming  the  vertical 
solid  angles  are  obtuse,  the  rhombohedron  is  called  obtuse,  and  if  acute,  the 
solid  is  called  an  acute  rhombohedron. 

155.  Modified  forms.— If  bodies  in  crystallizing  assumed  only  the 
fundamental  forms,  there  would  be  but  comparatively  little  variety 
and  beauty  in  crystalline  solids ;  it  is  to  the  modification  of  the  funda- 
mental forms  that  we  owe  that  endless  variety  of  crystalline  figures 


115 


CRYSTALLOGRAPHY. 


121 


which  we  observe  in  nature,  and  that  are  produced  in  the  laboratory. 
These  modified  forms  are  called  secondary  or  derivative  forms,  and  are 
produced  by  the  replacing  of  the  edges  and  angles  of  the  fundamental 
forms  by  planes,  which  are  called  secondary  planes.  The  modifica- 
tions of  crystals  take  place  according  to  two  simple  laws. 

1st.  All  the  similar  parts  of  a  crystal  may  be  simultaneously  and  simi- 
larly modified.  The  forms  thus  resulting  are  called  holohedral  forms 
(from  holos,  whole,  and  edra,  face). 

2d.  Half  the  similar  parts  of  a  crystal  may  be  simultaneously  and 
similarly  modified.  The  forms  thus  resulting  are  called  hemihedral 
forms  (from  kemisa,  half,  and  edra,  face). 

[It  is  beyond  the  design  of  this  elementary  work  to  enter  into  more  detail 
concerning  the  different  systems  of  crystallography,  and  of  modified  forms. 
For  further  information  the  student  is  referred  to  Dana's  Mineralogy,  from 
which,  by  permission,  this  chapter  has  been  condensed.] 

156.  Compound  crystals. — Sometimes  we  find  two  or  more  crystals 
united  regularly  and  symmetrically  together.  The  form,  if  composed 
of  two  individuals,  is  called  a  twin  crystal.  Fig.  116  is  a  simple  crystal 


117 


118 


119 


of  gypsum  ;  if  it  be  bisected  along  the  imaginary  line  a  b,  and  the 
right  half  be  inverted  and  applied  to  the  other  half,  it  will  form  fig. 
117.  If  an  octahedron,  as  fig.  118,  be  bisected  through  the  dotted  line, 


120 


121 


and  the  upper  half  revolved  half  way  around  be  then  united  to  the 
lower,  it  produces  fig.  119.    Both  figs.  117  and  119  are  twin  crystals. 
13* 


122  THE    THREE    STATES    OF    MATTER. 

The  imaginary  axis,  on  which  the  revolution  of  half  the  crystal  is 
made,  is  termed  the  axis  of  revolution  and  the  imaginary  section,  the 
plane  of  revolution.  Compound  crystals,  composed  of  more  than  two 
individuals,  are  frequently  observed,  as  in  the  case  of  the  snow-flake,  a 
not  unusual  form  of  which  is  represented 'by  fig.  120,  composed  of  six 
crystals  meeting  at  a  point,  or  of  three  crossing  each  other  at  an  angle 
of  60°.  Fig.  121  represents  a  compound  crystal  of  chrysoberyl. 

157.  Cleavage. — By  the  application  of  mechanical  force  to  crystals 
we  observe  that  they  often  split  in  certain  directions,  leaving  even  and 
polished  surfaces.     The  production  of  such  surfaces,  in  causing  the 
separation  of  the  particles  of  the  crystals,  is  called  tneir  cleavage  ;  the 
planes  along  which  the  separation  takes  place  are  called  cleavage  joints. 
Cleavage  is  often  obtained  with  great  ease,  as,  for  example,  with  mica, 
which  may  be   separated  by  means  of  the  fingers  into  thin  leaves. 
Galena,  also,  cleaves  easily,  and  as  the  three  cleavage  planes  are  at 
right  angles  to  each  other,  a  cube  results.     Calc  spar  splits  in  three 
oblique  directions,  and  thus  a  rhombohedron  is  obtained ;  while  in  fluor 
spar  a  cleavage  of  its  solid  angles  produces  an  octahedron.    The  cleav- 
age of  many  crystals  is  obtained  with  great  difficulty,  as,  for  example, 
in  quartz   and  tourmaline ;  in  others  no  cleavage  can  be  produced, 
owing  to  the  strong  cohesion  among  the  laminae.     In  some  crystals  but 
one  cleavage  is  visible,  as  with  mica  ;  several  have  two ;  others  three, 
as  galena  and  calc  spar ;  fluor  spar  has  four,  blende  has  six,  while 
others  have  even  more.     We  obtain,  by  the  cleavage  of  a  crystal,  some 
one  of  the  thirteen  fundamental  forms.     Varieties  of  the  same  mineral 
have  the  same  cleavage.    .Cleavage  occurs  parallel  to  the  faces  of  the 
fundamental  form,  or  along  the  diagonals  ;  the  facility  of  cleavage  and 
lustre  of  the  surfaces  is  always  the  same,  parallel  to  similar  faces. 

158.  Determination  of  crystalline  forms. — In  order  to  determine 
a  crystal,  it  is  essential  to  refer  it  to  the  system  to  which  it  belongs, 
and  to  determine  the  simple  forms  of  which  it  consists,  with  the  rela- 
tive lengths  and  inclination  of  the  axis. 

§3.  Elasticity. 

159.  Elasticity  of  solids. — Elasticity,  already  mentioned  as  one 
of  the  properties  of  matter,  has  a  peculiar  importance  in  solids,  because 
it  is  itself  a   moving  force,  and  serves  to  measure  the  intensity  of 
other  forces.     All  bodies  offer  a  resistance  to   compression  and   ex- 
tension, which  is  due  to  elasticity.     It  is  shown  in  the  effort  of  a  com- 
pressed spring,  or  a  bent  bow,  to  recover  from  its  forced   state  of 
flexion. 

Tension,  flexure,  and  torsion  are  also  at  once  evidence  and  measures 


ELASTICITY.  1 23 

of  the  force  of  elasticity  in  solids  ;  while  in  fluids  compression  is  the  only 
evidence  of  its  presence,  and  hence  compressibility  alone  is  a  general 
property  of  matter. 

Every  body  has  a  limit  of  elasticity  beyond  which  it  cannot  be  car- 
ried without  a  permanent  derangement  of  its  particles,  or  fracture.  A 
perfectly  elastic  body  is  one  which  returns  completely  to  its  original 
form  when  pressure  is  removed ;  and  every  body  does  this,  each  withio 
its  own  limit  of  elasticity.  Hence  every  body  may,  in  a  restricted  sense, 
be  said  to  be  perfectly  elastic.  The  return  of  an  elastic  body  to  its 
primitive  position  is  usually  made  with  several  oscillations,  called  oscil- 
lations of  elasticity.  This  is  familiarly  seen  in  the  recoil  of  a  bent  blade 
or  spring  of  steel. 

It  is  evident  that  in  bending  the  steel  its  molecules  are  deranged  from  their 
position  of  equilibrium  by  compression  on  one  side  and  extension  on  the  other, 
and  that  it  is  the  force  with  which  they  tend  to  replace  themselves  which  pro- 
duces the  elasticity  of  the  blade. 

There  is  a  similar,  although  less  perceptible,  change  of  figure  in  an  ivory  ball, 
which,  dropped  upon  a  hard  surface,  will  rebound  nearly  to  the  height  from 
which  it  fell.  It  does  not  immediately  recover  its  spherical  shape,  but  is  for 
several  times,  alternately,  an  oblate  and  prolate  spheroid. 

160.  Elasticity  of  tension  and  compression. — By  tension  is  to 
be  understood  the  action  of  a  force  exerted  in  the  direction  of  the  length, 
of  a  wire,  for  example.  The  laws  of  elasticity  of  tension  have  been  ex- 
perimentally deduced,  by  suspending  weights  from  the  lower  end  of  a 
rod  or  wire,  sustained  at  top  by  a  firm  support.  The  elongation  occa- 
sioned by  each  addition  of  weight  is  measured  by  a  telescope  mounted 
on  a  graduated  bar,  parallel  to  the  wire  (the  apparatus  is  called  a 
cathetometer}.  If  the  limit  of  elasticity  is  not  passed,  the  rod  or  wire 
returns  to  its  original  length  on  removing  the  weights  ;  but  if  the  strain 
is  continued  too  long,  or  too  great  a  tension  is  brought  to  bear,  a  per- 
manent change  of  length  results.  When  the  limits  of  elasticity  are  not 
passed,  the  following  laws  are  developed  by  this  mode  of  experiment. 

1.  For  the  same  substance  the  elongation  caused  by  each  unit  of  tension 
is  the  same,  whatever  may  have  been  the  original  tension.     Thus,  with  a 
wire  loaded  with  ten  or  twenty  pounds,  the  elongation  for  each  succes- 
sive pound  is  the  same  as  for  the  first  pound. 

2.  The  elongation  is  proportional  to  the  tension  employed.    This  follows 
from  the  first  law,  and  signifies  that  if  the  rod  or  wire  is  elongated  one 
unit  by  one  pound,  it  will  be  elongated  ten  units  by  ten  pounds,  &c. 

3.  The  elongation  with  a  given  tension  is  proportional  to  the  length  of 
the  rod.     That  is  to  say,  if  a  rod  of  a  given  length  is  elongated  a  unit 
of  length  by  a  given  tension,  a  rod  two  units  long  is  elongated  twice  as 
much  by  the  same  tension. 


124  THE    THREE    STATES    OF    MATTER. 

4.  The  elongation  is  inversely  proportional  to  the  area  of  the  section  of 
the  rod.  That  is,  if  of  two  rods  of  the  same  substance,  of  equal  length, 
and  subject  to  the  same  tension,  one  has  twice  the  area  of  the  other,  it 
will  be  elongated  only  half  as  much. 

Experiment  has  shown  that  in  the  case  of  the  compression  of  a  metallic 
bar,  or  rod,  in  the  direction  of  its  length,  by  an  endwise  force,  the  bar 
is  shortened  just  as  much  as  it  would  be  lengthened  if  the  same  forco 
had  been  used  to  stretch  it.  Hence  the  laws  for  the  elasticity  of  com- 
pression are  quite  the  same  with  those  for  tension. 

These  laws  may  be  demonstrated  mathematically  as  well  as  experi- 
mentally, but  it  is  not  requisite  here  that  we  should  do  more  than 
enunciate  and  illustrate  them. 

161.  Coefficient  of  elasticity. — From  the  laws  of  elasticity,  of 
tension,  and  compression,  just  enunciated,  it  follows  that  the  elongation 
(1}  of  a  given  rod  is  proportional  to  a  constant  quantity,  C,  depending 
on  the  nature  of  the  substance ;  secondly,  to  the  weight,  W,  by  which 
it  is  stretched;  thirdly,  to  its  length,  Z/;  and,  fourthly,  that  it  is 
inversely  proportional  to  the  area  of  its  section,  S:  i.  e. 


1=0.  JF.li.-i-; 


'=*¥•  «  *=- 


hence, 


Putting  K=  -77-  in  these  equations,  they  become 
C 

1     WL  LW 


If  in  the  last  equation  we  make  I  =  L,  and  /S  =  1,  it  becomes  K=  W. 

The  quantity  K  is  called  the  coefficient  of  elasticity.  In  other  words, 
the  coefficient  of  elasticity,  in  any  homogeneous  substance,  is  equal  to 
the  weight  required  to  double  the  length  of  a  bar  of  that  substance 
having  a  given  area,  assuming  such  an  elongation  physically  possible, 
which  it  is  not,  unless  in  the  case  of  caoutchouc. 

We  are  indebted  to  Wertheim  for  most  of  our  experimental  knowledge 
of  this  subject.  The  following  table  shows  the  mean  coefficient  of  elas- 
ticity of  a  number  of  metals,  as  deduced  by  him,  with  various  weights, 
at  different  temperatures,  from  1°  to  392°  Fahrenheit. 


ELASTICITY. 


125 


METALS.* 

IO_HO  p. 

Value  of  K  at  the  temperature  of— 

50°  F. 

590_68o  F. 

212"  F. 

SB23  F. 

Gold  hammered, 

9,351 

8,603 

"     annealed, 

5,585 

5,408 

5,482 

Silver  hammered, 

7,800 

7,411 

"       annealed, 

7,140 

7,274 

6,374 

Palladium  hammered, 

10,659 

10,289 

Platinum  hammered, 

16,224 

15,647 

"          annealed, 

15,518 

14,178 

12,964    i 

Copper  hammered, 

13,052 

12,200 

"        annealed, 

10,519 

9,827 

7,862 

Iron-wire  (ordinary), 

17,743 

18,613 

19,995 

"         annealed, 

20,794 

21,877 

17,700 

Steel-wire  annealed  blue, 

17,690 

18,045 

18,977 

English  steel-wire  annealed, 

17,278 

21,292 

19,278 

Cast-steel  annealed, 

19,561 

19,014 

17,926 

Berlin-brass  hammered, 

9,782 

9,005 

An  inspection  of  this  table  shows  that  the  coefficients  of  elasticity  of 
the  metals,  generally  diminish  as  the  temperature  rises  from  1°  to 
392°  F.  But  for  iron  and  steel,  the  coefficients  augment  up  to  212°  F., 
and  then  diminish,  until  at  392°  F.,  they  have  the  same  tenacity  as  at 
common  temperatures. 

Wertheim  has  also  determined  by  experiment  that  the  coefficient  of 
elasticity  in  the  metals  is  increased  by  all  means  which  produce  an 
increase  of  density,  and  decreased  by  the  contrary  means.  He  found, 
also,  that  the  passage  of  an  electric  current  in  a  conductor  momentarily 
diminishes  this  coefficient,  independent  of  the  alteration  of  temperature 
produced  by  the  electricity.  In  alloys  the  coefficient  is  nearly  the 
mean  of  the  coefficients  of  the  several  metals  compounded,  even  when 
there  is  a  difference  of  bulk  between  the  mass  of  the  alloy  and  the  sum 
of  its  ingredients. 

162.  Elasticity  of  flexure.— Let  A  B,  fig.  122,  be  a  rectangular 
beam,  fixed  horizontally  by  one  of  its  ends.  If  the  free  end  of  such  a 
beam  is  acted  on  by  any  force  tending  to  bend  it  in  the  direction  B  D', 
the  bar  will,  in  virtue  of  its  elasticity,  return  again  to  its  horizontal 
position  when  the  flexing  force  ceases  to  act,  after  performing  a  certain 
number  of  oscillations. 

The  elasticity  of  flexure  is  due  chiefly  to  the  united   effect  of  the 


*  The  rods  employed  in  these  experiments  had  each  a  section  of  one  square 
millimetre,  and  the  values  of  K  are  the  weights,  in  kilogrammes,  that  would  be 
required  to  stretch  the  rods  to  double  their  original  length.  These  values,  in 
general,  greatly  exceed  the  limit  of  elasticity. 


126 


THE    THREE    STATES    OF    MATTER. 


elasticity  of  tension  and  compression.  For  the  molecules  on  the  upper 
side  of  the  curve  are  extended,  while  those  on  its  under  side  are  com- 
pressed, and  the  united  effort  of 
these  two  forces — which  are  equal — 
is  to  restore  the  beam  to  its  first 
position.  The  conversion  of  a 
straight  line  into  a  curve,  as  in  this 
case,  is  also  accompanied  by  a  dis-  b 

turbance  in  the  equilibrium  of  the  molecules,  independent  of  the 
change  due  to  their  separation  and  compression ;  and  such  a  change 
develops  elasticity. 

The  laws  of  elasticity  of  flexure  are  comprised  in  the  following  formulae  : 
Wl*  Dabd* 

UO  «  =  -vr,-5-o'  w=— rS~. 


In  which  a  is  the  arc  7?  B',  described  by  the  flexure ;  W,  is  the  flexing  weight 
acting  in  a  perpendicular ;  b,  the  horizontal  breadth  of  the  bar  ;  d,  its  thickness  ; 
I,  the  length  of  the  bar,  and  D,  a  constant  quantity,  depending  on  the  nature  of 
the  substance  used.  If  in  the  above  we  make  each  of  the  quantities  a,  b,  d,  and 
I,  equal  unity,  it  follows  that  D  =  W,  or  D,  is  a  weight  which  will  bend  a  given 
bar  one  unit  long,  and  of  a  given  diameter  (say  one  centimetre),  through  a  unit 
of  arc  (say  one  degree).  This  quantity,  D,  is  called  the  coefficient  of  elasticity 
of  flexure,  and  in  any  case  the  value  of  a,  b,  d,  and  I,  being  known  experi- 
mentally, the  value  of  D  is  readily  ascertained  by  calculation. 

If  a  beam  is  supported  at  its  two  extremities,  A,  B,  fig.  123,  and  the  weight  ia 
applied  in  the  middle,  the  formula  becomes 

IQDabd* 
(2.)    W— 3 — ,  where  a  is  the  flexure  and  I  the  distance 


from  the  supports. 


123 


The  following  laws  are  deduced  from  the  first  formula : 

1.  The  displacement  of  the  free  end  of  the  bar  is  proportional  to  the 
load. 

This  is  equally  evident  from  the  experiments  of  Coulomb  and  from 
an  analysis  of  the  isochronism  of  the  oscillations  accompanying  the 
effort  to  restore  the  equilibrium. 

2.  The  load  requisite  to  produce  a  given  flexure  is  proportional  to  the 
breadth  of  the  beam  or  bar. 


ELASTICITY. 


127 


124 


This  is  evident  if  we  consider  a  beam  two  or  three  times  as  broad, 
composed  of  two  or  three  separate  beams,  each  requiring  the  same  load 
as  the  first  bar  to  flex  it  through  the  same  arc. 

3.  The  load  is  also  proportional  to  the  cube  of  the  depth  or  thickness  of 
the  bar. 

4.  The  load  is  in  the  inverse  ratio  of  the  cube  of  the  length  of  the  bar. 

If  the  section  of  the  beam  is  not  a  rectangle,  with  one  side  perpen- 
dicular to  the  direction  of  the  flexing  force,  these  laws  cannot  be 
directly  applied.  It  is  assumed  in  all  the  cases  that  the  bar  returns  to 
its  first  position  when  left  to  itself;  or,  in  other  words,  that  the  pressure 
has  not  exceeded  the  limit  of  elasticity. 

Applications. — Constant  use  is  made  of  the  elasticity  of  flexure. 
The  dynamometer  of  Reynier  has  already  been  named  (37).  Springs 
of  all  kinds,  for  balances,  carriages,  time-pieces,  bows,  &c.,  employ  this 
agency.  The  aneroid  barometer  of  Vidi,  and  the  metallic  manometer 
and  thermometer  of  Bourdon  are  familiar  and  most  useful  applications 
of  this  force. 

163.  M.  Bourdon's  metallic  barometer. — M.  Bourdon,  of  Paris, 
has  applied  the  principle  of  elas- 
ticity of  flexure  to  the  construction 
of  a  metallic  barometer,  which,  with 
great  simplicity  of  construction,  has 
all  the  advantages  of  the  aneroid. 
The  essential  part  of  the  instrument, 
fig.  124,  consists  of  a  very  thin  and 
elastic  brass  tube,  A,  bent  into  the 
form  of  an  arc  of  a  circle,  whose  cross 
section  is  a  flattened  ellipse,  with 
its  longer  diameter  perpendicular 
to  the  plane  of  curvature.  This  tube, 
exhausted  of  air,  and  hermetically 
closed,  is  attached  only  at  its  centre, 
so  that  the  ends  are  free  to  move. 
With  a  diminished  atmospheric  pres- 
sure, the  ends  separate  from  each  other.  If  the  atmospheric  pressure 
increases,  the  ends  come  nearer  together.  By  means  of  the  metallic 
wires,  a,  b,  and  the  spring,  c,  these  movements  of  the  ends  of  the  tube 
are  communicated  to  a  needle  moving  over  a  graduated  plate. 

The  same  principle  Bourdon  has  applied  to  the  construction  of 
manometers  for  locomotives  and  other  steam-boilers,  which  are  now 
extensively  used  in  all  countries. 


128 


THE    THREE    STATES    OF    MATTER. 


164.  The  aneroid  barometer.* — The  construction  of  this  instru« 
ment,  invented  by  Vidi,  of  Paris,  depends  upon  the  elasticity  of  flexure. 
Being  of  small  size,  and   containing  no  125 
mercury,  it  is  very  portable,  and  it  gives 

results  sufficiently  accurate  for  all  ordinary 

purposes.     It  consists  of  a  circular  copper 

box,  the  cover  of  which  is  very  thin,  and 

hermetically  sealed,  after  the  air  is  partly 

exhausted  from  its  interior.     This  chest  is 

contained  in  an  outer  case,  fig.  125,  about 

four  inches  in  diameter,  and  which  has  a 

dial-plate  like  that  of  a  watch.   Variations 

in   the  pressure   of  the   atmosphere  will 

cause  the  cover  of  the  exhausted  box  to 

move  with  the  change  of   tension.     By 

means  of  a  combination  of  levers  and  springs,  the  movements  of  the 

centre  of  this  cover  are  communicated  to  a  pointer  which  moves  over 

the  graduated  plate. 

Fig.  126  shows  the  interior  construction  of  this  instrument.  To  the  cover  M 
of  the  exhausted  box,  are  attached  two 

uprights,  S,  which  act  upon  a  lever,  P,  126 

by  means  of  a  pin  uniting  them.  This 
lever,  P,  is  attached  to  a  bar,  moving 
freely  on  two  pivots  placed  at  its  ex- 
tremities. A  lever,  B,  unites  the  bar, 
K,  to  the  plate,  A,  pressing  on  two 
springs,  D.  By  means  of  a  spring, 
represented  on  the  side  of  the  figure,  the 
rod  E,  in  connection  with  A,  commu- 
nicates movement  to  the  bent  lever,  H, 
causing  a  metallic  wire  to  uncoil  itself 
from  the  axis,  0,  of  the  pointer,  thus 
transmitting  to  it  the  movement. 

Excellent  aneroid  barometers  are  now  made  at  Lebanon  Spa,  N.  Y.,  by  E. 
Kendall,  at  a  moderate  cost. 

The  theory  of  the  barometer  and  the  mode  of  observing  atmospheric 
pressure  with  the  aneroid  barometer,  is  explained  in  the  chapter  on 
gases. 

165.  Elasticity  of  torsion. — When  a  metallic  rod  or  wire  is  twisted 
by  a  force  applied  at  one  extremity,  while  the  other  remains  fixed,  it 
has  a  constant  tendency  to  return  to  its  first  position,  and  if  the  force 


*  Aneroid  is  derived  from  the  Greek  alpha  (a),  privative,  and  ipiu,  to  flow 
(a  barometer  without  a  fluid),  in  allusion  to  the  absence  of  quicksilver. 


OF   SOLIDS. 


129 


is  withdrawn,  when  left  to  itself,  the  wire  makes  a  number  of  oscilla- 
tions before  it  comes  to  a  state  of  rest. 


Let  a  b,  fig.  127, 
127 


We  can  easily  see  how  torsion  is  developed  from  elasticity. 
be  a  metallic  wire,  made  tense  by  a  weight,  W,  and 
twisted  by  a  force  applied  at  d,  acting  in  a  circle  of 
which  d  b  is  the  radius.  Let  m  n  represent  an  enlarged 
view  of  a  row  of  molecules  on  the  surface  of  the  wire 
parallel  to  the  axis.  If  the  length  of  the  wire  remains 
unchanged  during  torsion,  and  the  line  m  n  takes  the 
position  of  the  spiral  mn',  it  is  evident  that  the  distances 
between  the  molecules  in  this  line  must  be  increased.  The 
elasticity  of  torsion,  therefore,  depends  upon  the  force 
with  which  the  particles  tend  to  preserve  their  respective 
distances  from  each  other.  By  the  same  force  with  which 
the  molecules  on  the  surface  of  the  wire  tend  to  resist 
separation,  the  molecules  in  the  axis  of  the  wire  are  com- 
pressed, and  there  is  a  tendency  to  dimmish  the  length 
of  the  wire.  Torsion,  therefore,  tends  to  separate  the 
molecules  on  the  surface  of  the  wire,  and  to  compress 
those  situated  in  the  axis. 

The  angle  of  torsion  is  the  angular  distance, 
d  b  d',  through  which  the  movable  end  of  the  wire  is 
rotated  about  its  axis.  The  force  of  torsion  is  the  power  applied  at  the 
extremity  of  a  lever  whose  length  is  unity,  placed  perpendicular  to 
the  axis  of  the  wire,  to  produce  the  deviation  indicated  by  the  angle 
of  torsion  ;  this  force  is  called  the  coefficient  of  torsion. 

166.  Coulomb's  laws  of  torsion.  —  For  our  knowledge  of  the  laws 
of  torsion  we  are  indebted  to  Coulomb,  who  has  reduced  these  laws  to 
the  following  formula  : 


=  *";  or'(2)  f   - 


When  a  cylindrical  weight,  W,  is  suspended  to  a  wire,  as  shown  in 
fig.  127,  so  that  its  axis  corresponds  with  the  axis  of  tl»e  wire,  W  is  the 
suspended  weight,  a  its  radius,  g  the  accelerating  force  of  gravity  (71), 
f  the  coefficient  of  torsion  for  the  extended  wire,  and  t  the  time  of  an 
oscillation  when  the  force  of  torsion  is  removed,  and  the  wire  is  left 
free  to  vibrate.  The  following  laws  were  deduced  by  Coulomb  from 
the  preceding  formula  : 

(1.)    The  force  of  torsion  is  proportional  to  the  angle  of  torsion. 

To  prove  this  law,  Coulomb  caused  the  weight  to  oscillate  around  its  axis  by 
the  torsion  of  the  wire,  and  found  that  the  times  of  oscillation  were  the  same 
whatever  their  amplitude.  This  result  corresponds  with  the  formula  in  which 
the  time  of  oscillation  is  independent  of  the  amplitude. 

Based  upon  this  law,  Coulomb  invented  a  very  delicate  torsion  balance  which 

14 


130  THE    THREE    STATES    OF    MATTER. 

bears  his  name.  This  instrument  will  be  described  when  speaking  of  its  use  in 
electrical  experiments  (820). 

(2.)  The  force  of  torsion  remains  the  same  whatever  may  be  the  tension 
of  the  wire. 

Experiments  prove  that  the  squares  of  the  times  of  oscillation  are  proportional 

W 

to  the  weights  employed,  whence  it  follows  that  — ,  in  formula  (2),  is  constant 

whatever  may  be  the  value  of  W,  therefore  it  is  evident  from  the  formula  that 
the  coefficient  of  torsion,  /,  is  constant,  and  that  the  force  of  torsion  agrees 
with  the  preceding  law. 

(3.)  The  coefficient  of  torsion  is  inversely  proportional  to  the  length  of 
the  wire. 

Experiments  prove  that  the  square  of  the  time  of  oscillation  is  proportional  to 
the  length  of  the  wire,  and  the  formula  shows  that  f  is  inversely  proportional 
to  <2,  therefore  it  must  also  be  inversely  proportional  to  the  length  of  the  wire. 

(4.)  The  coefficient  of  torsion  is  proportional  to  the  fourth  power  of  the 
diameter  of  the  wire. 

According  to  experiment,  the  time  of  oscillation  is  inversely  proportional  to 
the  square  of  the  diameter,  and  the  formula  shows  that  the  coefficient  of  torsion 
is  inversely  proportional  to  the  square  of  the  time  of  oscillation,  hence  the 
coefficient  of  torsion  is  proportional  to  the  fourth  power  of  the  diameter  of  the 
wire. 

167.  Torsion  of  rigid  bars. — Savart  found  by  experiment  that  the 
laws  of  Coulomb,  which  had  been  previously  determined  for  flexible 
wires  of  cylindrical  form,  were  equally  applicable  to  rigid  bars  of 
brass,    copper,    glass,  or  wood,   wrhether   the   sections  were   circular, 
square,  rectangular,   or  triangular,  provided   that   comparisons  were 
made  only  between  bars  of  the  same  form. 

More  recently  Poisson  has  demonstrated  these  laws,  in  case  of  cylindrical 
rods,  by  means  of  the  calculus,  and  M.  Cauchy  has  obtained  the  same  result  by 
the  calculus  for  bars  having  a  rectangular  section. 

168.  Limit  of  elasticity. — When  a  wire  or  rod  has  been  stretched 
by  a  weight  which  is  very  great  in  proportion  to  the  diameter  of  the 
wire  or  rod,  the   elongation  and  the  diminution  of  diameter   do  not 
entirely  disappear  when  the  tension  is  removed.     The  bar  is  then  said 
to  have  been /breed,  or  to  have  been  stretched  beyond  its  limit  of  elasti- 
city.    Similar  effects  are  seen  when  elasticity  has  been  developed  by 
compression,  flexion,  or  torsion. 

These  results  are  explained  by  supposing  that  the  molecules  com- 
posing the  wire  or  rod  have  been  forced  into  new  relations  with  each 
other,  so  that  elasticity  no  longer  acts  on  all  the  particles  in  the  same 
direction  as  before,  and  therefore  a  permanent  change  of  form  is 


OF    SOLIDS.  131 

developed.  It  follows,  therefore,  that  after  a  rod  or  wire  has  thus  been 
forced,  there  should  be  a  new  state  of  elasticity  similar  to  the  first ;  and 
such  experiment  shows  to  be  the  case. 

If  a  degree  of  tension,  sufficient  to  produce  permanent  elongation, 
acts  for  a  long  time,  a  rod  will  be  gradually  drawn  out  into  wire. 

M.  Vicat  has  observed  a  wire,  placed  where  it  was  free  from  any  sudden  shock, 
extended  by  a  weight  exceeding  its  limit  of  elasticity  (equal  to  about  one-third 
what  would  be  required  to  produce  instantaneous  rupture),  and  which  continued 
to  be  elongated  for  years  without  attaining  its  limit  of  extension. 

Thin  plates  of  glass  or  steel  placed  obliquely,  or  supported  only  at  the  ends, 
will,  after  a  time,  contract  a  permanent  curvature. 

The  limit  of  elasticity  is  rapidly  diminished  by  heat. 

At  temperatures  of  59°  F.,  212°  F.,  and  392°  F.,  Wertheim  found  that  the 
limits  of  elasticity  for  copper  varied  as  the  numbers  3,  2,  1  j  and  for  platinum 
as  14^,  13,  11J.  Annealing  diminishes  the  limits  of  elasticity,  but  Wertheim 
found  that  a  temperature  of  392°  F.  made  no  sensible  difference  in  the  elasticity 
of  those  metals  which  had  been  previously  annealed. 

169.  Change  of  density    produced    by   tension. — In   general, 
metals  that  are  forced  by  excessive  tension  increase  in  density  by  a 
lateral  approach  of  their  molecules,  but  the  contrary  effect  is  produced 
by  tension  in  bars  of  iron  or  lead.     Annealing  restores  the  density  of 
metals  which  have  been  forced  by  tension. 

I  4.  Strength  of  Materials. 

170.  Laws  of  tenacity. — The  absolute  strength  or  tenacity  of  a 
body  is  its  power  of  resisting  a  force  applied  in  the  direction  of  its 
length,  and  tending  to  draw  it  asunder.    The  following  are  the  laws  of 
tenacity : 

1st.  The  tenacity  of  a  bar,  or  rod,  or  the  resistance  it  is  able  to  sustain, 
is  proportional  to  the  area  of  its  transverse  section. 

2d.  The  tenacity  is  independent  of  the  length  of  the  bars. 

The  resistance  which  a  rod  can  sustain  is  evidently  proportional  to  the 
transverse  section  of  the  body,  for  the  cohesion  of  two,  three,  or  four  times  as 
many  particles  must  be  destroyed,  if  the  area  of  the  section  is  increased  two, 
three,  or  four  times.  If  a  wire  supports  a  certain  weight,  two  such  wires,  or 
one  of  double  size  of  the  same  quality,  will  support  a  double  weight.  Tenacity 
is  not  modified  by  length,  except  that  the  probability  of  casual  defects  increases 
with  the  length.  Tenacity  is  measured  experimentally  by  securing  one  end  of 
the  body  to  a  fixed  point,  and  hanging  gradually  increasing  weights  to  the  other, 
until  it  is  broken.  The  breaking  weight  measures  the  absolute  strength.  To 
compare  the  strength  of  different  bodies,  we  must  assume  a  unit  of  area;  the 
one  usually  chosen  is  one  square  inch. 

The  following  table  gives  the  absolute  strength  of  some  of  the  more 


132 


THE    THREE    STATES    OF    MATTER. 


important  bodies,  expressed  in  pounds,  for  one  square  inch  area  of  the 
transverse  section. 

2d.  WOODS  :  — 

Sycamore,      ....  9,630 

Birch,  ...%...  12,225 

Elm,      ......  9,720—15,040 

Larch,        .....  12,240 

Oak,      ......  10,367—25,851 

Box,      ......  14,210—24,043 

Ash,      ......  13,480—23,455 

Pine,     ......  10,038—14,965 

Fir,       ......  6,991—12,876 

3d.  Conns  :— 


1st.  METALS:— 

Steel  untempered,    . 

110,690—127,094 

"    tempered,   .     . 

114,794—153,741 

"     cast,        .     .     . 

134,256 

Iron,  bar,  .... 

53,182—  84,611 

"     wire,      .     .     . 

58,730—112,905 

"     cast,       .     .     . 

16,243—  19,464 

Silver,  cast,    .     .     . 

40,997 

Copper,    "... 

20,320—  37,380 

Brass,      "... 

17,947_  19,472 

"       wire,     .     .     . 

47,114—  58,931 

Gold,      

20,490—  65,237 

Tin,  cast,    .... 

4,736 

Zinc, 

2,820 

Lead. 

887—     1.824 

Hemp  twisted,  i  to  1  inch, 
"  "       1—3       " 


5—7 


8,746 
6,800 
5,345 

4,860 


Wrought  metals  are  more  tenacious  than  cast,  and  alloys  are  sometimes 
stronger  than  either  of  their  constituents.  The  strength  of  metals,  as  a  rule, 
diminishes  as  they  are  heated  ;  and  sudden,  frequent,  and  extreme  changes  of 
temperature  always  impair  tenacity. 

Johnson's  results.  —  From  an  extensive  series  of  carefully  conducted 
experiments,  the  late  Professor  Walter  R.  Johnson  ascertained  that,  if 
either  bars  or  plates  of  malleable  iron  are  subjected  to  a  high  degree  of 
tension,  whilst  heated  to  550°  or  600°  F.,  and  are  then  gradually  cooled, 
the  maximum  tenacity  of  the  iron  is  sensibly  increased  over  fifteen 
(15Tyff)  per  cent.  From  the  maximum  thus  obtained,  the  tenacity 
gradually  diminishes  by  heating,  but  the  tenacity  will  remain  greater 
than  before  the  first  heating,  unless  the  temperature  is  raised  above 
700°  F.  (Report  to  Franklin  Institute  on  strength  of  materials  for 
steam-boilers,  1837.) 

The  strength  of  cords  is  in  proportion  to  the  fineness  of  the  strands,  and  also 
to  the  fineness  of  the  flax  or  hemp  fibres  of  which  the  strands  consist.  They 
are  weakened  by  overtwisting.  Damp  hempen  cords  are  stronger  than  dry  ones, 
twisted  than  spun,  tarred  than  untarred,  and  unbleached  than  bleached.  Silk 
cords  are  three  times  stronger  than  those  of  flax. 

Tenacity  of  vegetable  and  animal  substances.  —  Woods  are  sub- 
ject to  great  inequalities.  Trees  grown  on  mountains  are  much  stronger  than 
those  of  the  same  kind  from  the  plains. 

Animal  and  vegetable  substances,  converted  from  the  liquid  to  the  solid  state, 
as  gums,  varnish,  glue,  Ac.,  possess  extraordinary  strength.  Rumford  found  that 
a  solid  cylinder  of  paper,  glued  together,  whose  sectional  area  was  one  square 
inch,  would  support  30,000  Ibs.;  and  a  similar  cylinder  of  hempen  strings,  glued 
together  lengthwise,  supported  92,000  Ibs.  —  a  tenacity  greater  than  that  observed 
in  iron. 

171.  Resistance  to  pressure  in  columns.  —  The  resistance  of  a 


OF    SOLIDS  133 

column  to  a  vertical  force  which  tends  to  crush  it,  depends  on  its  form, 
its  sectional  area,  and  its  height.  Of  two  columns  of  the  same  mate- 
rial, having  the  same  form  and  equal  heights,  the  one  which  has  the 
larger  sectional  area  will  be  the  stronger,  but  the  exact  ratio  of  increase 
in  strength  is  unknown. 

According  to  Euler :  When  the  base  remains  the  same,  the  strength  of  a 
column  diminishes  as  the  square  of  the  height;  that  is,  when  the  height  is 
trebled,  the  strength  is  diminished  nine  times. 

The  resistance  of  a  right  prism  is  in  the  inverse  ratio  of  the  square  of  the 
height,  and  directly  as  the  width,  and  the  square  of  the  thickness. 

A  prism,  whose  base  is  a  parallelogram,  has  less  strength  than  one  of  the  same 
height  and  volume,  whose  base  is  a  square ;  and  the  latter  less  than  a  cylinder 
of  equal  height  and  volume. 

A  solid  cylinder  resists  less  than  a  hollow  one  of  equal  height  and  mass ;  and 
lastly,  a  solid  cylinder  less  than  an  equivalent  cone.  A  column  of  one  piece  is 
stronger  than  one  composed  of  several. 

Solids  do  not  offer  the  same  resistance  in  all  positions  :  stones  in  the  position 
of  their  natural  bed  are  stronger  than  when  placed  otherwise ;  and  wood  is 
stronger  in  the  direction  of  its  fibres  than  across  them. 

The  strength  of  rectangular  columns  is  directly  as  the  product  of  the  longer 
side  of  the  section  into  the  cube  of  the  shorter  side,  and  inversely  as  the  square 
of  the  height. 

172.  The  lateral  or  transverse  strength  of  materials  is  their 
power  to  resist  a  breaking  force  applied  at  right  angles  to  their  length. 

Let  a  b  c,  fig.  128,  be  a  beam  secured  at  one  end,  and  supporting  at 
the  other  extremity  a  weight,  W,  128 

acting  at  right  angles  with  its 
length.  It  is  evident  that  while 
the  suspended  weight  tends  to 
produce  extension  and  rupture 
at  the  upper  surface,  a,  the  par- 
ticles at  the  opposite  or  under 
surface,  o,  will  be  compressed. 

Between  these  two  points  there  will  be  a  certain  plane,  m  n,  called  the 
neutral  axis,  where  there  is  neither  extension  nor  compression. 

Suppose  the  power  of  the  beam  to  resist  compression  is  the  same  as 
its  power  of  resisting  extension,  then  the  neutral  axis  will  divide  the 
transverse  section  into  two  equal  parts,  an  area  of  compression  and  an 
area  of  extension.  When  the  fibres  on  the  surface  a  are  extended  to 
their  limit  of  tenacity,  the  fibres  at  o  will  be  compressed  with  an  equal 
force,  while  no  force  is  exerted  on  the  neutral  axis,  therefore  the  entire 
force  required  to  be  overcome  to  produce  rupture  is  equal  to  one-half 
the  longitudinal  tenacity  of  the  beam.  If  t  represents  the  absolute 
tenacity  of  a  unit  of  area  (See  Table,  |  170),  6  the  breadth  of  the  beam, 


134  THE    THREE    STATES    OF    MATTER. 

and  d  its  depth,  then  the  resistance  to  be  overcome;  7?,  =  ^tbd.     The 

effect  of  the  breaking  force  tends  to  turn  the  section  a  o  about  the  neutral 

axis.   The  sura  of  all  the  extending  forces,  128  a 

H  h,  fig.  128  a,  will  be  represented  by  the 

area  of  the  triangle  a  G  a/.    These  forces 

act  at  different  distances  from  the  neutral 

axis,  G,  but  their  entire  effect  will  be  the 

same  as  if  they  were  all  concentrated  at 

the  centre  of  gravity  of  aGa',  which  is 


at  a  distance  from  G  equal  to  §  a  G  = 

£  a  o  =  ^d.   The  statical  moment  of  the  extending  force  will  therefore  be 

itbd  X  %d  =  -fetid?. 

The  statical  moment  of  the  compressing  force  is  also  -fetid*.  Hence  the 
sum  of  the  moments  of  the  statical  forces  opposed  to  fracture  is  %tbd*. 
To  overcome  this  moment  of  resistance,  the  weight,  W,  acts  at  the  end 
of  the  beam,  the  length  of  which  we  represent  by  I;  then,  since  at  the 
moment  of  fracture  the  statical  moment  of  the  weight  must  equal  the 
statical  moment  of  the  resistance,  we  shall  have 

Wl  =  tfbd\    or,    W=t^.. 

The  lateral  cohesion  of  the  beam  prevents  the  different  laminae  from  sliding 
on  each  other,  and  thus  tends  to  prevent  fracture,  but  this  element  of  strength 
is  neglected  in  the  preceding  analysis. 

To  find  the^reight  required  to  break  a  beam  supported  at  one  end, 
we  have  the  following  — 

RULE  :  Multiply  the  absolute  tenacity  of  a  beam  of  the  same  dimensions, 
by  its  depth,  and  divide  the  product  by  six  times  the  length  ;  the  quo- 
tient is  the  weight  suspended  at  the  extremity  required  to  break  the  beam. 

Practical  applications.  —  To  apply  this  rule  to  practical  purposes, 
it  is  necessary  to  take  into  consideration  the  weight  of  the  beam  itself. 
This  weight  may  be  considered  as  acting  at  its  centre  of  gravity,  con- 
sequently the  strain  produced  by  it  will  be  only  half  as  much  as  if  it 
acted  at  the  extremity  of  the  beam,  we  must  therefore  subtract  from  the 
breaking  weight  one-half  the  weight  of  the  beam.  Calling  the  weight 
of  the  beam  w,  the  formula  becomes, 


~   Ql        2* 

If  we  would  estimate  the  load  which  a  beam  can  sustain  without  danger  of 
breaking,  we  must  consider  that  beams,  of  whatever  material  they  may  be 
constructed,  are  liable  to  be  more  or  less  imperfect.  To  afford  security  from 
accident,  it  is  customary  to  estimate  the  working  load  as  only  J,  J,  or,  .in  some 
cases,  only  fe  part  what  would  be  required  to  produce  fracture. 


OF    SOLIDS. 


135 


For  a  cylindrical  beam  supported  at  one  end,  the  breaking  weight,  diminished 
by  the  weight  of  the  beam  itself,  is 

<7Tr3        w 
W  =  —  --  —  ,     r     being  the  radius  of  the  beam. 

For  a  tube  whose  external  and  internal  radii  are  r  and  r',  the  breaking  weight 
will  be 

(f7T/-3          10    \  /tTtr'3          w'\  tit/  \  W—Wf 

—  i  )-(—•,-)  =  «M-  -5- 

For  a  rectangular  tube  supported  at  one  end, 
t 


If  a  ^pectangular  beam  is  supported  at  the  centre,  and  the  weight  is 
divided  into  two  parts,  rest- 
ing upon  opposite  ends  of  the 
beam,  as  shown  A,  fig.  129,  we 
must  replace  W,  w,  and  I  in  the 
preceding  formula  by  £W,  %w, 
and  %L  Making  these  substi- 
tions,  and  reducing  : 

w      4tbd? 


The  weight  which  a  beam 
can  support  when  it  rests  upon 
its  centre,  and  the  weight  is  \ 
equally  divided  at  its  extremi-  < 
ties,  is  four  times  as  great  as  if  the  beam  were  supported  only  at  one  end, 
and  the  weight  was  suspended  from  the  other  end. 

One-half  of  the  beam  is  included  as  a  part  of  the  breaking  weight. 

If  the  beam  is  supported  at  its  two  extremities,  and  the  weight  is 
suspended  at  the  centre,  as  shown  at  B,  fig.  129,  the  breaking  weight 
will  obviously  be  the  same  as  the  sum  of  the  two  weights  in  the  pre 
ceding  case. 

If  the  beam  is  secured  at  both  extremities,  as  shown  at  D,  fig.  129, 
and  the  weight  is  placed  at  the  centre,  three  fractures  are  to  be  pro- 
duced simultaneously.  To  produce  the  fracture  at  the  centre  separately 
will  require  the  same  weight  as  in  the  preceding  case,  and  the  fractures 
at  C  and  C'  will  each  require  one-half  as  much  more  force,  while  one- 
half  of  the  weight  of  the  beam  is  to  be  included  Therefore, 


136  THE    THREE    STATES    OF    MATTER. 

General  estimate  of  the  strength  of  beams. — If  the  weight  is 
evenly  distributed  over  the  whole  beam,  it  will  support  twice  as  much 
as  if  the  whole  pressure  were  placed  in  the  centre.  If  a  rectangular 
beam  has  two  or  three  times  the  breadth  of  another,  the  depth  and 
length  being  the  same,  it  will  have  two  or  three  times  the  lateral 
strength ;  and  if  the  length  is  increased  two  or  three  times,  other 
things  being  equal,  the  power  of  suspension  will  become  one-half 
or  one-third  respectively.  When  the  length  and  breadth  remain  the 
same,  the  strength  increases  with  the  depth,  but  in  a  higher  pro- 
portion. A  beam  having  the  same  length  and  breadth  as  another,  but 
twice  or  three  times  the  depth,  will  bear  a  four  or  nine  times  greater 
weight.  A  thin  board  or  beam  is  therefore  much  stronger  when  placed 
on  its  edge  than  on  its  side  ;  on  this  principle,  the  rafters  ssd  floor 
timbers  of  buildings  are  made. 

In  round  timber,  the  power  of  suspension  is  in  proportion  to  the 
cubes  of  the  diameters,  and  inversely  as  the  length ;  a  cylinder  whose 
diameter  is  two  or  three  times  greater  than  that  of  another,  will  carry 
a  weight  8  or  27  times  heavier.  The  lateral  strength  of  square  timber 
is  to  that  of  the  tree  whence  it  is  hewn  as  10  :  17  nearly. 

The  strongest  rectangular  beam  that  can  be  sawn  from  a  piece  of 
round  timber  is  one  whose  breadth  is  equal  to  the  square  root  of  one- 
third  multiplied  by  the  diameter,  and  its  depth  is  equal  to  the  square 
root  of  two- thirds  multiplied  by  the  diameter. 

A  tube  is  the  form  which  combines  the  least  weight  of  materials 
with  the  greatest  lateral  strength.  ^Galileo  was  the  first  who  remarked 
that  the  bones  of  animals,  the  quills  of  birds,  the  stalks  of  plants  which 
bear  a  heavy  weight  of  seed  at  their  summit,  and  other  similar  hollow 
cylinders,  offer  a  much  greater  resistance  than  solid  cylinders  of  the 
some  length,  and  constructed  of  the  same  quantity  of  matter. 

A  round  tube  whose  external  and  internal  diameters  are  to  each 
other  as  10  :  7  has  (according  to  Tredgold)  twice  the  lateral  strength 
of  a  solid  cylinder  containing  the  same  amount  of  material. 

A  rectangular  tube,  whose  height  is  considerably  greater  than  the 
breadth,  will  sustain  a  greater  amount  of  lateral  pressure  than  a  hollow 
cylinder  of  the  same  thickness,  and  containing  the  same  amount  of 
material,  because  a  much  greater  amount  of  material  is  placed  at  a 
remote  distance  from  the  neutral  axis.  Hollow  rectangular  beams  of 
iron  are  used  in  architecture,  and  the  same  form  of  construction  was 
selected  by  Stephenson  for  the  Britannia  and  Victoria  Bridges. 

The  Britannia  Tubular  Bridge,  across  the  Menai  Straits,  is  an 
immense  rectangular  iron  tube,  or  corridor,  17  feet  wide,  22  feet  high 
at  the  ends,  30  feet  at  the  centre,  and  1834  feet  long,  through  whicb 


OF    SOLIDS.  137 

the  English  Western  Railroad  passes  from  "Wales  to  the  inland  of 
Anglesea,  104  feet  above  high  water  mark.  Two  of  the  openings 
between  the  piers  are  each  460  feet,  and  the  other  two  each  230  feet. 
The  ordinary  pressure  of  the  railroad  trains  which  pass  this  bridge 
produces  a  depression  of  merely  one-eighth  of  an  inch,  or  less ;  discerni- 
ble only  by  the  aid  of  instruments. 

The  Victoria  Tubular  Bridge,  for  the  passage  of  the  Grand  Trunk 
Railway  across  the  St.  Lawrence,  at  Montreal,  is  6600  feet,  or  a  mile 
and  a  quarter  in  length.  It  has  24  openings  of  242  feet  each,  and  a 
centre  span  of  330  feet.  The  abutments  are  36  feet,  and  the  central 
piers  60  feet  above  summer  water.  The  breadth  of  these  immense  iron 
tubes  is  16  feet,  the  height  at  the  ends  of  the  bridge  19  feet,  and  at  the 
centre  21  feet  8  inches.  The  tubes  are  constructed  of  boiler  iron, 
varying  from  \  to  £  an  inch  in  thickness,  strongly  braced  with  lateral 
irons  placed  at  distances  of  from  3  to  6  feet.  The  cost  of  this  stupen- 
dous bridge  was  $7,000,000. 

173.  Limits  of  magnitude. — The  materials  of  all  structures  must 
support  their  own  weight,  and  therefore  their  available  strength  is  the 
excess  only  of  their  absolute  strength  above  what  is  necessary  to  sup- 
port themselves. 

When  all  the  dimensions  of  materials  are  increased,  the  absolute 
strength  augments  as  the  square  of  the  ratio  of  increase,  but  at  the 
same  time,  the  weight  of  the  materials  augments  as  the  cube  of  the 
increase. 

If  the  dimensions  of  a  beam  are  doubled,  it  is  four  times  stronger, 
and  eight  times  heavier;  or  if  its  magnitude  is  multiplied  4  times,  its 
strength  will  be  multiplied  16  times,  and  its  weight  64  times. 

In  consequence  of  unequal  ratio  in  increase,  the  strength  of  a  struc- 
ture of  any  kind  cannot  be  estimated  from  its  model  alone,  which  is 
always  much  stronger  in  proportion  to  its  size  than  the  structure.  In 
enlarging  a  structure,  a  limit  is  soon  reached  at  which  it  has  no  avail- 
able strength,  its  total  absolute  strength  being  required  to  support 
itself;  and  if  this  limit  is  passed,  it  will  fall  to  pieces  by  its  own  weight. 

All  works,  natural  and  artificial,  have  such  limits  of  magnitude  which 
they  cannot  surpass  while  their  materials  remain  the  same. 

In  conformity  to  this  principle,  small  animals  are  stronger  than  large  ones, 
and  insects  and  animalculae  are  capable  of  feats  of  strength  and  agility,  which 
seem  miraculous  when  translated  into  the  proportions  of  man,  The  operation 
of  the  same  law  may  be  seen  by  comparing  the  unwieldy  movements  of  the 
elephant,  with  the  lithe  and  active  tiger,  or  the  easy  motion  of  song-birds,  and 
the  arrowy  swoop  of  the  hawk,  with  the  laborious  and  measured  flight  of  the 
swan,  and  the  condor  of  the  Andes.  For  the  same  reason,  the  gigantic  saurians, 
whose  bones  are  mentioned  by  geologists,  had  their  home  in  the  ocean,  where, 


188  THE    THREE    STATES    OF    MATTER. 

in  rnoderff  times,  are  found  sea-weeds  of  interminable  length,  and  animals, 
whose  ponderous  mass  would  be  incapable  of  motion,  if  they  were  not  floated 
buoyantly  by  the  element  they  inhabit. 

§  5.  Properties  of  Solids  depending  on  a  permanent  displace- 
ment of  their  Molecules. 

174.  Malleability,   or  the  property  of  being  wrought  under  the 
hammer,  belongs  to  many  of  the  metals  in  an  eminent  degree,  and 
upon,  it  their  utility  iu  a  great  measure  depends. 

The  following  is  the  order  of  malleability  of  the  principal  metals, 
when  extended  under  the  hammer ;  viz.,  lead,  tin,  gold,  zinc,  silver, 
copper,  platinum,  iron.  This  order  represents  the  facility  of  extension 
depending  on  relative  hardness,  but  gold  may  be  beaten  thinner  than 
any  other  metal  (compare  $  19). 

The  property  of  extending  into  plates  in  the  rolling-mill  is  somewhat 
different  from  the  facility  of  extending  under  the  hammer,  and  is  pos- 
sessed by  the  metals  in  the  following  order;  viz.,  gold,  silver,  copper,  tin, 
lead,  zinc,  platinum,  iron.  Malleability  varies  with  the  temperature. 

Iron  is  most  malleable  when  it  first  attains  a  white  heat,  and  in  that  state 
huge  masses  of  it  are  taken  from  the  furnace  to  be  forged,  the  metal  yielding 
like  wax  to  the  pressure  of  the  rolling-mill,  or  the  blows  of  the  hammer.  Zinc 
is  most  malleable  at  300°  or  400°,  and  lead  and  copper  when  they  are  cold. 
Glass,  which  is  very  brittle  when  cold,  becomes  malleable  at  a  high  temperature. 
Gold  may  be  hammered  into  leaves  so  thin  that  a  million  of  them  are  less  than  an 
inch  thick.  Metals  lose  their  malleability  by  constant  hammering,  but  recover 
it  again  by  being  heated  and  slowly  cooled — a  process  called  annealing. 

175.  Ductility,  or  the  property  of  being  drawn  into  wire,  must  not 
be  confounded  with  malleability,  for  the  same  metals  are  not  always 
both  ductile  and  malleable,  or  do  not  possess  these  properties  to  an 
equal  extent.     In  general,  ductility  increases  with  the  temperature. 

The  following  is  the  order  of  ductility  in  the  principal  metals ;  viz., 
platinum,  silver,  iron,  copper,  gold,  zinc,  tin,  lead. 

Iron  may  be  drawn  into  the  finest  wire,  but  it  cannot  be  rolled  into  plates  of 
proportional  thinness.  Tin  and  lead  possess  these  qualities  in  the  reverse 
order. 

176.  Hardness  has  no  relation  to  density,  or  the  number  of  particles 
within  a  given  space,  but  depends  only  on  the  nature  of  the  particles, 
their  mutual  arrangement,  and  cohesion. 

The  metals  may  be  scratched  by  glass,  which  is  far  lighter  than  most  of  them, 
and  among  metals,  density  is  not  connected  with  relative  hardness.  Alloys  are 
often  harder  than  either  of  their  constituents,  and  -some  metals,  as  steel,  may 
have  their  hardness  modified  by  heat  at  pleasure. 

The  following  table  gives  the  scale  of  hardness  used  by  mineralogists, 
commencing  with  talc,  the  softest  crystalline  solid,  and  ending  with 


OF    SOLIDS. 


139 


diamond,  which  is  esteemed  the  hardest,  since  it  cuts  all  other  bodies, 
but  cannot  be  cut  by  any  but  itself. 


Deg. 

Substance. 

Deg. 

Substance. 

1 

2 
3 
4 
5 

Talc. 
Gypsum. 
Calc  spar. 
Fluor  spar. 
Apatite. 

6 
7 
8 
9 
10 

Feldspar. 
Quartz. 
Topaz. 
Sapphire. 
Diamond. 

The  terms  hard  and  soft  are  seen  by  an  inspection  of  this  table  to 
be  entirely  relative,  since  each  succeeding  body  is  harder  than  the  one 
preceding,  and  vice  versa,  the  extremes  only  being  respectively  softer 
and  harder  than  all  others. 

We  employ  hardened  steel  to  cut  wood,  and  even  iron  ,•  emery  (the  rough 
sapphire)  is  required  to  cut  and  polish  steel  and  glass.  The  diamond,  set  in  a 
staft'  of  metal,  is  an  efficient  tool  for  cutting  plates  of  glass  into  any  required  size. 
Even  the  hardest  rocks,  as  porphyry  and  jasper,  are  readily  turned  into  any 
required  form  in  the  lathe,  by  the  use  of  a  diamond  properly  set  as  a  turning 
tool. 

177.  Erittleness. — Bodies  which   are  easily  broken  in  pieces  and 
pulverized  are  said  to  be  brittle.     Such  are  hard  bodies  generally,  and 
also  many  highly  elastic  substances. 

178.  Hardening;  Temper;  Annealing. — When  certain  metals  are 
heated  to  redness  or  to  a  higher  temperature,  and  then  are  suddenly 
cooled,  by  plunging  into  cold  water,  oil,  or  mercury,  they  become  hard, 
brittle,  and  more  elastic  than  before.    This  process  is  called  hardening. 

The  effects  of  this  method  of  hardening  are  most  important  in  the  case  of 
steel,  since  it  is  in  virtue  of  this  quality  that  its  application  to  a  great  variety 
of  purposes  depends. 

When  steel  is  raised  to  a  high  heat  and  slowly  cooled,  it  becomes 
soft,  ductile,  flexible,  and  much  less  elastic  than  before.  This  process 
is  called  softening  or  annealing,  although  the  latter  term  is  more  fre- 
quently employed  to  denote  a  similar  process  of  removing  the  hardness 
produced  by  hammering,  and  other  mechanical  means. 

Softened  steel  may  be  hammered,  rolled  into  sheets,  drawn  into  wire, 
or  wrought  into  any  form  required  in  the  arts.  If  hardness  or  great 
elasticity  is  required,  the  steel  is  then  heated  to  redness  and  plunged 
into  cold  water,  oil,  mercury,  or  some  other  fluid,  by  which  it  is  rapidly 
cooled.  If,  as  is  generally  the  case,  it  is  then  too  hard  for  the  use  to 
which  it  is  to  be  applied,  a  portion  of  the  hardness  is  removed  by  what 
is  called  drawing  the  temper,  'by  heating  to  a  lower  temperature,  and 


140  THE    THREE    STATES   OF   MATTER. 

allowing  the  article  to  cool  gradually.  The  proportion  of  hardness 
removed  depends  on  the  temperature  to  which  the  articles  are  heated. 
This  process  of  reheating  and  cooling,  by  which  the  degree  of  hardness 
is  modified  to  suit  any  special  purpose,  is  called  tempering. 

Colors  of  tempered  steel. — The  workmen  carefully  observe  the  color 
of  the  steel,  as  it  is  reheated,  and  determine,  from  the  tint,  when  a  degree  of 
heat  is  obtained  sufficient  to  produce  the  temper  desired.  The  tints  which  cor- 
respond approximately  to  the  different  temperatures  are  as  follows : — 

Light  straw,       428°  F.         Violet  yellow,  509°  Blue,  560° 

Golden  yellow,  446°  Purple  violet,  530°  Deep  blue,  603° 

Orange  yellow,  464°  Feeble  blue,      550°  Sea-green,  626° 

Dies  used  in  coining  require  to  be  made  of  the  hardest  steel.  Files  have  but 
a  very  little  of  the  hardness  removed  by  tempering.  Razors  and  fine  cutlery 
are  reheated  to  a  pale  yellow ;  penknife  blades  to  a  light  straw  color ;  table 
cutlery,  where  flexibility  is  required  more  than  hardness,  is  reheated  to  violet ; 
watch-springs  to  a  full  blue;  coach-springs  to  a  deep  blue. 

Tempering  by  a  bath. — In  many  manufactories  the  requisite  heat  for 
tempering  is  obtained  by  immersing  the  hardened  steel  articles  in  a  bath  of 
metallic  alloys,  mercury,  or  oil,  the  temperature  of  which  can  be  exactly  regu- 
lated by  a  thermometer.  The  articles  to  be  tempered  are  placed  in  the  bath, 
which  is  then  heated  to  the  required  temperature,  and  then  allowed  to  cool 
slowly.  In  this  way  a  great  number  of  articles  of  the  same  kind  can  be  made 
to  assume  a  uniform  temper  at  small  expense. 

It  is  a  remarkable  property  of  steel  that  when  it  is  heated  to  a  temperature 
that  allows  it  to  begin  to  harden,  by  rapid  cooling  it  receives  its  full  degree  of 
hardness.  It  cannot  be  partially  hardened  at  any  lower  temperature.  A  bar 
of  steel,  heated  at  one  end  while  the  other  remains  cold,  will  be  found,  after 
rapid  cooling,  hardened  at  one  end,  with  a  sharp  line  o;f  demarkation  between 
the  hard  and  soft  parts.  Where  it  has  been  heated  to  a  temperature  insufficient 
for  hardening,  and  is  then  rapidly  cooled,  it  is  sensibly  softened. 

Temper  of  glass. — Glass  undergoes  the  same  changes  by  tempering 
as  steel.  It  becomes,  by  rapid  cooling,  more  brittle,  harder,  and  less 
dense.  A  specimen  of  glass,  examined  by  Chevandier  and  Wertheim, 
having  a  density  of  2*513,  acquired  by  annealing  a  density  of  2'523. 
For  hardening  glass  it  is  sufficient  to  allow  it  to  cool  rapidly  in  the 
open  air,  by  moving  it  about.  Glass-ware  is  annealed  by  passing  it 
slowly  through  a  very  long  oven,  called  a  "  leer,"  the  end  where  it 
enters  being  nearly  a  red  heat,  and  the  other  extremity  nearly  cold. 
Without  the  process  of  annealing,  glass  utensils  would  be  almost 
worthless. 

Prince  Rupert's  Drops. — A  beautiful  illustration  of  the  properties  of 
'anannealed  glass  may  be  seen  in  the  scientific  toy  called  Prince  Rupert's  Drops, 
or  Dutch  Tears.  They  are  made  by  dropping  nielted  glass  into  water,  by  which 
means  it  is  suddenly  cooled  and  becomes  very  hard  and  brittle.  They  have  a 


OF   SOLIDS.  141 

long  oval  form  tapering  to  a  point  at  one  end,  fig.  130.     The  body  of  these 
glass  drops  will  bear  a  smart  stroke  from  a  hammer  without  break- 
ing,  but  if  a  portion  of  the  smaller  end  is  broken  off  the  whole  mass 
will  be  broken  into  an  almost  impalpable  powder,  with  -a  violent 
shock.     The  Bologna  vial  is  another  similar  example. 

Tempering  copper  and  bronze. — Most  metals  are  acted 
on  by  heat  and  cold  in  the  same  manner  as  steel,  but  to  a 
less  extent.  Copper  is  a  remarkable  exception,  since  its 
properties  in  this  respect  are  exactly  the  reverse  of  those  manifested 
by  steel.  When  copper  is  rapidly  cooled  it  becomes  soft  and  malleable, 
but  when  it  is  slowly  cooled  it  becomes  hard  and  brittle. 

Bronze,  which  is  an  alloy  of  copper  and  tin,  undergoes,  by  change 
of  temperature,  the  same  changes  as  copper,  but  in  a  more  remarkable 
degree. 

A  recent  fracture  of  bronze,  which  has  been  rapidly  cooled,  presents 
a  yellow  color ;  but  after  it  has  been  slowly  cooled  the  color  is  a  bril- 
liant white,  like  pure  tin.  It  is  thus  evident  that  hardening  and  anneal- 
ing cause  different  arrangements  of  the  particles  of  copper  and  tin  of 
which  the  bronze  is  composed. 

179.  Hammering. — By  hammering,  the  molecules  of  many  bodies 
are  brought  nearer  to  each  other,  so  that  their  density  is  increased. 
By  rolling,  wire-drawing,  extension,  compression,  bending,  twisting, 
or  any  mechanical  means  by  which  the  limits  of  elasticity  are  passed, 
changes  are  effected  similar  to  those  produced  by  hammering. 

Lead  yields  under  the  hammer  or  rolling-mill  without  increasing  its  density, 
but  its  density  may  be  increased  by  compressing  in  dies,  or  in  any  situation 
whore  it  has  no  room  to  spread  out  under  the  action  of  the  compressing  force. 

By  such  mechanical  means  the  physical  properties  of  solid  bodies  undergo 
changes  analogous  to  those  produced  by  tempering.  They  become  dense,  tena- 
cious, hard,  brittle,  and  their  limit  of  elasticity  (168)  is  increased,  although  their 
elastic  force  is  unchanged,  as  was  shown  by  Coulomb,  from-the  fact  that  their 
vibrations  in  either  condition  are  accomplished  in  the  same  time. 

Annealing  restores  the  metals  to  the  same  condition  as  before  they  were  sub- 
mitted to  mechanical  force.  Iron  and  platinum  require  to  be  frequently  annealed 
during  the  process  of  drawing  into  wire. 

The  ancients  gave  to  the  bronze  plates  of  their  armor  the  necessary  hardness 
by  hammering. 

When  zinc  and  iron  have  been  hardened  by  rolling,  the  tenacity  and  elasticity 
are  not  the  same  in  both  directions  of  the  plates,  and  rolling  does  not  increase 
the  tenacity  in  so  great  a  degree  as  drawing  into  wire.  M.  Navier  found  that  a 
rod  of  forged  iron,  having  a  section  of  one  square  millimetre,  required  to  break 
it  a  weight  of  40  kilogrammes.  When  it  had  been  rolled  into  thin  plates,  a 
strip  cut  in  the  direction  of  its  length,  having  the  same  sectional  area,  required 
a  weight  of  41  kilogrammes  to  break  it ;  but  only  36  kilogrammes  if  cut  in  a 
transverse  direction. 

Fine  wire  twisted  into  cables  is  used  to  support  suspension  bridges,  because 

15 


142  THE   THREE   STATES   OF    MATTER. 

such  cables  are  much  stronger  than  the  same  amount  of  iron  in  the  form  of  rod» 
or  coarse  wire. 

180.  Changes  of  structure,  affecting  the  mechanical  proper- 
ties of  metals,  take  place  spontaneously  by  the  lapse  of  time,  or  more 
rapidly  by  the  influence  of  heat  or  vibrations. 

These  changes  have  been  principally  observed  in  iron.  When  this 
metal  is  recently  forged  it  is  very  strong  and  flexible,  and  its  fracture 
is  fibrous  and  of  a  dull  color ;  but  when  it  becomes  old,  or  has  been 
subjected  to  frequent  vibrations,  or  changes  of  temperature,  it  becomes 
hard  and  brittle,  and  its  fracture  is  coarsely  granular,  presenting  many 
brilliant  facets.  This  change,  often  seen  in  the  axles  of  railway  car- 
riages, is  produced  by  vibration  combined  with  the  heat  of  friction, 
especially  in  the  severe  weather  of  northern  winters.  These  facts,  well 
known  to  engineers  upon  railroads,  explain  the  necessity  of  running 
trains  at  but  moderate  speed  when  the  thermometer  indicates  a  tempe- 
rature near  to  zero. 

Similar  changes,  diminishing  the  tenacity,  take  place  in  chains  and  anchors, 
•which  have  been  for  a  long  time  imbedded  in  ice.  Gay  Lussac  has  observed  bars 
of  iron,  which  became  almost  as  brittle  as  glass  by  remaining  for  a  long  time 
at  a  high  temperature  in  an  oven. 

Some  curious  results  produced  by  vibration  were  discovered  by 
Savart,  who,  having  caused  strips  of  glass  and  bars  of  metal,  drawn 
into  wire,  to  vibrate  in  the  direction  of  their  length,  found  that  they 
gave  out  at  first  very  indistinct  and  confused  sounds,  but  on  continuing 
the  experiments  for  a  long  time  this  confusion  gave  place  to  clear  and 
distinct  tones,  which  were  obtained  with  ease. 

Brass  wire  strained  like  the  strings  of  a  piano,  where  it  is  exposed 
to  atmospheric  changes  and  constant  vibration  from  currents  of  air,  in 
a  few  months  loses  its  tenacity  and  becomes  completely  friable,  show- 
ing in  its  cross  fracture  a  radiated  structure. 

Annealing  produces  the  same  effect,  in  this  respect,  as  vibration.  Substances 
cast  in  the  form  of  plates  do  not  resound  well  until  after  the  lapse  of  several 
days.  Sulphur,  cooled  in  the  form  of  a  disc,  does  not  at  first  give  out  a  clear 
sound,  but  after  a  time  it  vibrates  readily,  and  after  the  lapse  of  some  months 
the  sound  emitted  is  very  much  changed.  This  proves  that  there  has  been  some 
modification  of  structure. 

§  6.  Collision  of  Solid  Bodies. 

181.  Motion  communicated  by  collision. —  When  two  solid  bodies 
come  into  collision,  the  motion  is  redistributed  through  them,  whether  one 
or  both  bodies  are  in  motion. 

1.  If  the  bodies  are  soft  and  tenacious,  or  if  the  shock  is  not  so 


OP    SOLIDS.  143 

great  as  to  overcome  the  tenacity  of  one  or  both  bodies,  they  acquire  a 
uniform  motion,  and  move  in  contact  as  one  body,  as  stated  under 
impact,  §  112. 

2.  If  the  bodies  are  hard  and  inelastic,  and  the  collision  takes  place 
at  only  a  small  portion  of  the  surfaces,  and  if  the  shock  is  so  great  as  to 
overcome  the  tenacity  of  one  or  both  bodies  before  motion  is  uniformly 
distributed  through  the  masses,  they  will  be  broken  in  pieces,  and  the 
fragments  scattered  in  different  directions, 

3.  If  the  bodies  are  so  elastic  that  motion  may  be  distributed  through 
the  mass  before  the  limit  of  elasticity  is  passed,  a  reaction  will  take 
place,  and  the  elasticity  will  modify  the  distribution  of  motion. 

182.  Direct  impact  of  elastic  bodies. — When  two  elastic  spheri- 
cal bodies  m  and  M',  fig.  131,  come  into  collision,  while  moving  in  the 
same  straight  line,  they  will  undergo  compression  or  flattening,  as  shown 
in  the  figure,  and  their  centres  will  continue  to  approach  each  other 
until  they  acquire  a  common  velocity  (112).     This  velocity  is  repre- 
sented by  x  = ; ,  u  and  u'  being  the  velocities  before  impact, 

m  +  m' 

and  x  the  common  velocity  of  their  centres  of  gravity  at  the  instant  of 

greatest  compression.    If  the  limit  of  elasticity  has  131 

not  been  passed,  the  elasticity  of  the  two  bodies  _._      -''"M  m' 

will  now  act  as   an   internal  force,  causing  their  m 

centres  of  gravity  to  recede  from  each  other,  until 

the  bodies  recover  their  original  forms,  when  they 

separate,  and  the  shock  terminates. 

183.  Modulus  of  elasticity. — When  two  elastic  bodies  meet,  the 
force  with  which  they  are  urged  towards  each  other  is  called  the  force 
of  compression ;  the  force  of  elasticity  causing  their  centres  to  recede 
during  the  second  interval  of  the  shock  is  called  the  force  of  restitution  ; 
the  ratio  of  these  two  forces  is  called  the  modulus  of  elasticity.     When 
this  ratio  is  unity,  or  the  force  of  restitution  is  equal  to  the  force  of 
compression,  the  bodies  are  said  to  be  perfectly  elastic.    When  this 
ratio  is  zero,  the  bodies  are  said  to  be  inelastic.     For  any  value  of  this 
ratio,  between  these  extremes,  the  bodies  are  said  to  be  imperfectly 
elastic. 

There  are  no  bodies  known  that  are  perfectly  elastic,  or  perfectly 
inelastic  ;  hence,  in  considering  the  collision  of  solid  bodies,  it  is  neces- 
sary to  take  into  account  the  degree  of  elasticity  which  they  possess. 

The  following  table  exhibits  the  degree  of  elasticity  of  several  com- 
mon substances,  perfect  elasticity  being  taken  as  unity. 


144 


THE    THREE    STATES    OF    MATTER. 


Substances. 

Degree  of  elasticity. 

Substances. 

1 

Degree  of  elasticity. 

Glass,      .... 

0-94 

Bell  metal,  .     .     . 

0-67 

Hard-baked  clay, 

0-89 

Cork,       .... 

0-65 

Ivory,      .... 

0-81 

Brass,      .... 

0-41 

Limestone,  . 

0-79 

Lead,       .... 

0-20 

Steel,  hardened,    . 

0'79 

Clay  just  yielding  ) 

0-17 

Cast-iron,     . 

0-73 

to  the  hand,         J 

Steel,  soft,  .     .     . 

0-67 

J 

184.  Velocity  of  elastic  bodies  after  direct  impact. — If  two 

imperfectly  elastic  bodies,  m  and  m',  move  in  the  same  straight  line 
with  velocities  u  and  u',  u  being  greater  than  wx,  the  first  body  will 
overtake  and  strike  against  the  second  with  the  same  force  as  if  the 
second  body  were  at  rest,  and  the  first  body  were  moving  with  a  velo- 
city equal  to  M  —  wx.  The  two  bodies,  being  elastic,  will  suffer  com- 
pression until  they  acquire  a  common  velocity, 

mu  -}-  m'u' 

m  +  mf 

The  velocity  lost  by  m  at  this  instant  will  be  u  —  x,  and  the  velocity 
gained  by  m/  will  be  x  —  u' 

Let  e  be  the  modulus  of  elasticity,  and  v  and  v'  the  velocities  of  the  two  bodies 
after  they  recover  their  original  forms  at  the  close  of  the  second  period  of  the 
shock. 

Since  the  forces  of  compression  and  restitution  are  in  proportion  to  the  velo- 
cities they  generate  or  destroy,  the  velocity  destroyed  in  m,  by  the  force  of 
restitution  will  be  e  (u  —  #),  and  the  velocity  gained  by  m',  by  the  force  of  resti- 
tution, will  be  e  (x  —  u'). 

Hence  the  whole  velocity  lost  by  m  will  be  (1  -f-  e)  (u  —  »),  and  the  whole 
velocity  gained  by  m'  will  be  (1  -f-  e)  (x  —  u').  The  velocity  of  m  after  impact 
will  be 

v  =  u  —  (1  -|-  €)  («  —  x)  =  x  —  e(  u  —  05).  (a) 

The  velocity  of  m'  after  impact  will  be 

«'=«'  +  (1  -f  e)  (*  —  «')=*  +  e(x  —  t*').  (6) 

Substituting  the  value  of  x  in  the  formula  (a)  and  (6),  and  reducing,  we 
obtain 

mu  -j-  m'u'        tn'e(n  —  «') 

m  -}-  m' 
mu  -f-  m'u' 


m  -f  m' 


m  -f-  m' 

me(u  —  «') 

m  -f  mf 


I*) 


If  the  two  bodies  move  in  opposite  directions  before  impact,  we  must  make 
either  u  or  u'  negative  in  the  preceding  formulae.    If  one  of  the  bodies  is  at  rest 


OF    SOLIDS.  145 

before  impact,  «'  becomes  zero.  If  e  =  1,  the  formulas  represent  the  conditions 
of  perfectly  elastic  bodies,  and  if  e  =  0,  the  formulae  will  apply  to  inelastic 
bodies. 

From  the  preceding  formulae  we  may  deduce  the  following  general 
conclusions : 

1.  If  two  bodies  are  perfectly  elastic,  their  relative  velocities  before  and 
after  impact  are  the  same. 

Making  e  =  1  in  (a)  and  (6),  and  subtracting  the  latter  from  the  former,  we 
have, — 


2.  If  the  bodies  are  perfectly  elastic  and  equal,  they  will  interchange 
velocities  by  impact. 

Making  m  =  m't  and  e  —-  I  in  (c)  and  (d), 


V  =  *(u  +  u')  +  i(«  -  u')  =  u. 

3.  By  the  impact  of  bodies,  whether  elastic  or  otherwise,  no  motion  is 
lost. 

Multiplying  (c)  by  m,  and  (d)  by  m',  and  adding  and  cancelling  similar  terms, 
we  have 

mv  -\-  m'vf  =  mu  -j-  m'u', 

in  which  the  first  member  of  the  equation  is  the  sum  of  the  momenta  of  the 
two  bodies  after  impact,  and  the  second  member  the  sum  of  their  momenta  before 
impact. 

4.  The  velocity  which  one  body  communicates  to  another  at  rest,  when 
perfectly  elastic,  is  equal  to  twice  the  velocity  of  the  former,  divided  by  one 
plus  the  ratio  of  the  masses  of  the  two  bodies. 

In  formula  (d)  let  m'        rm,     u'  =  0,     and  e  =  1,  we  shall  then  obtain 

2w 


5.  When  a  body  in  motion  strikes  another  equal  body  at  rest,  both 
bodies  being  perfectly  elastic,  the  first  body  comes  to  a  state  of  rest,  and 
the  second  flies  off  with  the  previous  velocity  of  the  first. 

If  the  two  masses  are  equal,  r  .-  1  in  the  last  formula,  and  «'  =u. 

Scholium. — If  a  series  of  perfectly  elastic  balls  are  arranged  in  a 
line,  and  all  are  in  contact  before  impact,  except  the  first,  which  is 
made  to  strike  against  the  second,  all  the  balls  except  the  last  will 
remain  in  contact,  and  at  rest,  after  impact,  and  the  last  will  move  off 
with  the  velocity  of  the  first. 
15* 


146 


THE   THREE    STATES   OF   MATTER. 


185.  Transmission  of  shock  through  a  series  of  elastic  balls. 
Experimental  illustration  of  elasticity. — If  several  equal  ivory 
balls  are  suspended,  as  shown  in  fig. 
132,  when  1  is  drawn  back  to  a,  and 
let  fall  against  2,  only  the  last  in  the 
series,  7,  will  move;  this  will  start 
with  the  velocity  which  1  had  at  the 
instant  of  striking  against  2,  and  it  '• 
will  fly  off  to  the  position  b,  at  a  dis- 
tance equal  to'  the  limit  to  which  the  first  had  been  drawn  back ;  it  will 
then  return  striking  against  6,  which  will  again  be  set  in  motion,  all 
the  others  remaining  at  rest.  This  alternate  movement  of  the  extreme 
balls  of  the  series  will  continue  until  friction,  and  the  resistance  of  the 
air  conspiring  with  the  slightly  imperfect  elasticity  of  the  balls,  at  length 
causes  the  action  to  cease. 


Problems. — Elasticity  of  Tension. 

74.  A  rectangular  bar  of  iron  whose  transverse  section  is  one  square  centi- 
metre, and  whose  length  is  three  feet,  is  suspended  with  its  upper  extremity 
attached  to  a  firm  support :  what  weight  must  be  suspended  at  its  lower  extremity 
to  cause  a  temporary  elongation  of  one-fourth  of  an  inch  when  the  temperature 
la  14°  F.,  50"  F.,  212°  F.,  392°  F.  ? 

This  problem  may  be  solved  for  rods  of  any  of  the  metals  mentioned  in  the 
table  (161). 

75.  A  rectangular  bar  of  hammered  brass  2£  feet  in  length,  suspended  by  its 
upper  extremity,  supports  a  weight  of  75  kilogrammes :  how  much  will  it  be 
temporarily  elongated  when  the  temperature  ia  raised  to  50°  F.  ? 

Elasticity  of  Flexure. 

76.  If  a  beam  10  feet  long,  3  inches  wide,  and  6  inches  in  depth,  suffers  a 
certain  amount  of  flexure  when  one  end  is  firmly  supported  in  a  wall,  what 
weight  will  be  required  to  give  an  equal  flexure  to  another  beam  of  the  same 
material,  15  feet  long,  6  inches  wide,  and  9  inches  in  depth  ? 

77.  What  weight  suspended  at  the  middle  of  the  last-mentioned  beam  will  be 
required  to  produce  an  equal  amount  of  flexure  when  the  beam  is  supported  at 
both  ends  ? 

Tenacity. 

78.  How  many  pounds  weight,  suspended  by  a  steel  wire  hanging  vertically, 
will  be  required  to  break  it  when  the  wire  is  one-fourth  of  an  inch  in  diameter  ? 

Calculate  for  both  tempered  and  untempered  steel. 

79.  In  a  pendulum  experiment,  it  is  required  to  suspend  a  weight  of  64  Ibs. 
by  a  copper  wire.     What  must  be  the  diameter  of  the  wire,  when,  for  the  sake 
of  security,  |  is  deducted  from  its  strength  as  given  by  the  table  ? 

Transverse  Strength. 

80.  If  a  beam  of  oak,  6  inches  wide  by  9  inches  in  depth,  projects  20  feet 


OF    SOLIDS.  147 

from  a  wall  in  which  it  is  secured,  what  weight  suspended  at  the  end,  as  in  fig. 
128,  will  be  required  to  break  it,  no  account  being  taken  of  the  weight  of  the 
beam  itself? 

81.  What  weight  will  be  required  to  break  a  cylinder  of  cast  iron  25  feet  long, 
having  an  external  diameter  of  2  feet,  and  an  internal  diameter  of  20  inches,  the 
weight  being  supported  at  the  extremity  ? 

82.  What  weight,  placed  at  the  centre  of  the  greater  span  of  the  Britannia 
Tubular  Bridge,  would  be  required  to  break  it,  calling  the  breadth  of  the  tube 
17  feet,  height  30  feet,  calculating  for  a  single  thickness,  J  of  an  inch  of  plate 
iron,  and  estimating  the  tenacity  equal  to  a  force  of  60,000  Ibs.  to  the  square 
inch? 

83.  Deducting  from  the  weight  found  in  the  last  problem,  the  weight  of  one- 
half  the  length  of  tube  spanning  the  greater  opening,  and  estimating  the  work- 
ing load  as  £  the  breaking  weight,  how  heavy  a  train  might  safely  cross  the 
Britannia  Bridge  ? 

84.  How  heavy  a  train  may  safely  cross  the  Victoria  Bridge  (172),  if  the 
thickness  of  the  tube  at  the  centre  is  i  an  inch,  and  if,  disregarding  the  weight 
of  the  tube  itself,  the  train  is  limited  to  &  the  absolute  tenacity  of  the  structure  ? 

85.  What  weight  can  be  sustained  at  the  middle  of  the  strongest  rectangular 
beam  that  can  be  sawn  from  a  birch  log  2  feet  in  diameter,  and  30  feet  long, 
reckoning  the  weight  of  the  timber  nine-tenths  that  of  water  ? 

Impact  of  Elastic  Bodies. 

86.  Two  glass  spheres  weighing  12  oz.  and  7  oz.  respectively,  move  in  the 
same  direction  with  velocities  of  8  feet  and  5  feet  in  a  second.    Find  the  respec- 
tive velocities  of  the  two  balls  after  impact,  and  their  common  velocity  at  the 
instant  of  greatest  condensation. 

This  problem  may  be  varied  by  substituting  for  glass,  balls  made  of  each 
substance  whose  degree  of  elasticity  is  given  in  the  table  (183). 

87.  A  perfectly  elastic  body  m,  moving  with  a  velocity  of  12,  impinges  on 
another  perfectly  elastic  body,  m',  moving  in  the  opposite  direction  with  a  velo- 
city of  5 ;  by  impact  m  loses  one-third  of  its  momentum.   What  are  the  relative 
weights  of  the  masses  m  and  m'  ? 

88.  A  body,  m  (=  3m'),  impinges  on  m'  at  rest.     The  velocity  of  m  after 
impact  is  f  of  its  velocity  before  impact.    Required  the  value  of  e,  the  modulus 
of  elasticity. 

89.  Two  bodies  m  and  m',  whose  elasticity  is  §,  moving  in  opposite  directions 
with  velocities  of  25  and  26  feet  per  second  respectively,  impinge  directly  upon 
each  other.     Find  the  distance  between  them  4£  seconds  after  impact. 

90.  A  number  of  perfectly  elastic  balls  are  placed  in  a  right  line.    The  first  is 
made  to  start  with  a  given  velocity;  determine  the  ratio  of  the  balls  so  that  its 
momentum  may  be  equally  divided  among  the  remainder. 

91.  An  elastic  ball  falls  from  a  height  of  40  feet.     How  high  will  it  rebound, 
supposing  that  one-fifth  of  the  final  velocity  is  lost  at  the  impact  in  consequence 
of  imperfect  elasticity  ? 

92.  An  ivory  ball  falls  from  an  elevation  of  100  feet.   With  what  velocity  must 
another  similar  ball  be  projected  upward  in  the  same  vertical  line,  that  after 
the  two  balls  meet,  the  first  ball  may  return  to  the  same  elevation  from  which 
it  fell  ? 


148  THE    THREE    STATES    OF    MATTER. 


CHAPTER  III. 

OF  FLUIDS. 

HYDRODYNAMICS. 

I  1.    Hydrostatics. 

I.     DISTINGUISHING    PROPERTIES  OF    LIQUIDS. 

186.  Definitions. — Fluids — Hydrodynamics. — Fluids  are  bodies 
in  which  the  attractive  and  repulsive  forces  (146)  are,  1st,  either  in  per- 
fect equilibrium,  producing  liquids  or  inelastic  fluids ;  or  2d,  in  which 
the  repulsive  force  holds  sway,  producing  gases  or  elastic  fluids. 

Hydrodynamics  treats  of  the  peculiarities  of  state  and  motion  among 
fluid  bodies,  both  liquids  and  gases  (15).  It  is  subdivided  into  hydro- 
statics, or  fluids  at  rest,  and  hydraulics,  or  fluids  in  motion. 

187.  Mechanical  condition  of  liquids. — Liquids,  owing  to  the 
slight  cohesive  attraction  among  their  particles,  possess  no  definite  form, 
but  adapt  themselves  to  the  shape  of  the  containing  vessel.     This  is  a 
necessary  consequence  of  the  perfect  freedom  of  motion  among  the  par- 
ticles of  a  liquid.     Liquids  vary  very  much,  however,  in  the  degree  of 
their  fluidity,  as  between  thin  mobile  liquids  like  alcohol  or  water,  and 
thick,  viscous,  bodies  like  oils  and  tar.    In  viscous  bodies,  the  imperfect 
fluidity  is  a  consequence  of  the  only  partial  ascendency  of  the  repulsive 
force,  leaving  still  a  notable  amount  of  cohesion  among  the  particles. 
Heat  serves  to  increase  the  repulsive  force,  and  so  converts  viscous  into 
thin  liquids. 

Liquids  and  gases  are  conveniently  distinguished  as  non-elastic  and 
elastic  fluids,  but  this  distinction  is  not  absolute,  since  all  liquids  possess 
some  elasticity,  more,  usually,  than  belongs  to  the  solid  state  of  the  same 
bodies. 

188.  Elasticity  of  liquids.— Compressibility.— We  have  already, 
in  sec.  21,  illustrated   the  compressibility  of  water.     The  researches 
of  Canton,  in  1761,  Oersted,  in  1823,  and  others  of  later  dates,  have 
proved  that  all  liquids  are  slightly  compressible.     The  piezometer 
(rtif|w,  to  press,  and  petpov,  a  measure)  is  an  instrument  designed  to 
measure  the  compressibility  of  liquids.     Oersted's  apparatus,  fig.  133, 
consists  of  a  strong  glass  cylinder ;  twenty-four  or  twenty-five  inches 


OF   FLUIDS. 


149 


in  height,  mounted  on  a  stand :  the  upper  part  is  accurateiy  closed  by  a 
brass  cap,  through  which  passes  the  funnel  tube,  R,  to  supply  the  vessel 
with  water,  and  a  cylinder,  furnished  with  a  piston,  moving  by  the 
screw  P.  In  the  interior  is  a  vessel  A,  containing  the  liquid  to  be 
compressed,  having  a  capillary  tube  at  its  upper  part,  which  bends  and 
descends  to  the  mercury  0,  contained  in  the  lower  part  of  the  vessel. 
This  capillary  tube  is  subdivided  into  133 

equal  parts,  and  the  number  of  these 
parts  the  vessel  A  can  contain,  is  accu- 
rately determined.  There  is  also  in  the 
interior  of  the  cylinder,  a  tube  of  glass, 
B,  furnished  with  a  graduated  scale,  C ; 
this  tube  is  closed  at  its  upper  end,  and 
has  its  lower  end  immersed  in  the  mer- 
cury, 0.  This  tube  is  called  a  mano- 
meter (280),  and  is,  when  at  rest,  nearly 
filled  with  air. 

In  order  to  experiment  with  this  apparatus, 
fill  the  vessel,  A,  with  the  liquid  to  be  com- 
pressed, and  by  means  of  the  funnel,  R,  fill 
the  cylinder  with  water,  having  previously 
placed  mercury  in  its  lower  part.  Turning 
the  screw,  P,  the  piston  descends ;  in  conse- 
quence, the  air  in  the  tube,  B,  is  compressed, 
and  the  mercury  is  elevated ;  the  degree  of 
elevation  shows  the  amount  of  pressure ;  at 
the  same  time,  the  mercury  rises  in  the  capil- 
lary tube,  and  gives  the  measure  of  the  com- 
pression of  the  liquid  in  A. 

Supposing  each  division  of  the  capillary 
tube  held  but  a  millionth  part  as  much  as 
the  vessel  A,  then  if  the  liquid  to  be  com- 
pressed was  water  (at  the  pressure  of  one  atmosphere),  we  should 
observe  the  mercury  to  rise  between  49  and  50  divisions. 

There  is  one  correction  to  be  made  in  the  observations  obtained  by 
this  instrument ;  it  might  be  supposed  that  the  capacity  of  A  would  be 
invariable,  the  exterior  and  interior  walls  being  compressed  equally  by 
the  liquid,  but  it  is  not  so ;  the  interior  capacity  of  the  vase  undergoes 
the  same  diminution  as  would  a  body  of  glass  of  the  same  form  and 
volume,  submitted  to  the  same  pressure.  This  diminution  amounts 
to  about  33  ten  millionths  (Tff,ir§iUff<j)»  of  the  primitive  volume,  for 
«ach  atmosphere  of  pressure. 

This  quantity  can  be  calculated  in  any  case,  as  well  for  glass  as  for 


150 


THE    THREE    STATES   OF    MATTER. 


copper  and  brass  (the  three  materials  used  in  the  improved  piezometer 
of  Regnault),  from  the  known  elongation  of  rods  of  these  substances 
at  the  same  tension,  according  to  the  laws  of  Wertheirn  (160).  M. 
GRASSI  (Ann.  de  Chimie  et  Phys.,  3'  Strie.  Tom.  XXXI.,  p.  437)  has 
lately  revised  the  results  of  Oersted,  Canton,  and  of  Messrs.  Colladon  and 
Sturm,  on  a  great  number  of  liquids,  and  at  different  temp.eratures. 
The  compressibility  of  water  diminishes  with  increasing  temperatures. 
On  the  other  hand,  heat  increases  the  compressibility  of  alcohol,  ether, 
chloroform,  and  wood  spirit. 

Salt  or  sulphuric  acid  diminishes  the  compressibility  of  water  in  pro- 
portion to  the  quantity  dissolved,  but  for  a  given  density  these  solu- 
tions obey  the  same  order  as  pure  water. 

Grassi's  principal  results  are  given  in  the  following  table,  the  com- 
pressibility being  parts  in  a  million  at  a  pressure  of  one  atmosphere : 


Liquid*  used. 

Temperature. 

Compressibility. 

Pressure  in  atmos- 
pheres employed. 

Mercury,  

32°  F 

0-000  002-95 

Water 

32° 

0-000  050-3 

Do  

77° 

0-000  045-6 

Do  

128° 

0-000  044-1 

Ether 

32° 

0-000  111-0 

3-408 

Do  

57° 

0-000  140-0 

1-580 

Alcohol,    

45° 

0-000,082-8 

2-302 

Do  

55i° 

0-000  090-4 

1-570 

Wood  spirit,       .     .     . 
Chloroform,  .... 
Do  

56° 
47° 
54° 

0-000,091.3 
0-000,062-5 
0-000,064-8 

1-309 

It  appears,  that  of  all  liquids  tried,  mercury  has  the  least,  and  ether 
the  greatest,  ratio  of  compressibility.  The  pressures  were  carried  to 
the  great  extent  of  220  atmospheres. 

Elasticity. — It  is  hardly  requisite  to  remark  that  the  return  of  com- 
pressed liquids  to  their  original  bulk,  on  removal  of  pressure,  is  proof 
of  an  elastic  force  in  them  equal  to  their  ratio  of  compressibility. 

Consequences. — It  follows  from  what  has  been  said, — 

First.  That  the  molecules  of  liquids,  owing  to  the  entire  freedom  of 
motion  among  themselves,  are  in  equilibrium. 

Second.  That  liquids  possess  perfect  elasticity,  and  a  slight  degree  of 
compressibility. 

Let  us  now  farther  consider  the  necessary  consequences  of  these  mechanical 
conditions  of  liquids,  both  independent  of  gravity,  and  also  with  reference  to 
that  force. 


OF   FLUIDS. 


151 


134 


II.    TRANSMISSION  OF  PRESSURE  IN  LIQUIDS. 

189.  Liquids  transmit   pressure   equally  in  all   directions. — 

Liquids  transmit  in  all  directions,  and  with  the  same  intensity,  the  pres- 
sure exerted  on  any  point  of  their  mass. 

This  important  theorem  was  first  clearly  announced  by  B.  Pascal. 
Let  fig.  134  be  a  vessel  filled  with  a  liquid,  and  furnished  with  a  num- 
ber of  equal  cylinders,  in  each  of  which  is  a  well-fitting  piston.  The 
vessel  and  liquid  are  both  assumed  to  be  without  weight,  consequently 
none  of  the  pistons  have  any  tendency  to  move.  If  pressure  is  applied 
to  the  piston  A,  it  will  be  forced  inwards,  and  the  other  pistons  B,  C,  D, 
and  E,  of  equal  area,  will  each  be  forced  outwards  with  the  same  pres- 
sure, so  that  if  the  piston  A  was  pressed  inwards  with  a  force  of  one  pound, 
it  would  be  found  necessary  to  apply  a  force 
of  one  pound  to  each  of  the  other  pistons, 
in  order  to  keep  them  in  their  place.  If 
the  area  of  B  and  C  was  two  or  three  times 
that  of  A,  then  the  pressure  upon  them 
would  be  two  or  three  times  as  great.  We 
cannot  perfectly  demonstrate,  that  liquids 
transmit  pressure  equally  in  all  directions 
(because  we  cannot  obtain  for  experiment, 
as  would  be  necessary,  liquids  without 
weight,  and  pistons  working  without  fric- 
tion), but  that  this  pressure  is  exerted  in  all  directions,,  is  sbown  by  the 
simple  apparatus,  fig.  135,  consisting  of  a  cylinder,  furnished  with  a 
piston  and  terminated  by  a  sphere;  on  this  135 

sphere  are  placed  small  tubes,  jutting  out  in 
all  directions;  upon  filling  the  sphere  and 
cylinder  with  water,  and  pressing  upon  the 
piston,  the  water  is  forced  out  from  each  of  the 
jets  with  equal  energy.  This  is  a  necessary 
consequence  of  the  mechanical  constitution  of 
liquids  (187). 

Let  A  represent  the  area  of  any  portion  of 
the  inner  surface  of  a  vessel,  and  A'  that  of  any 
other  portion  of  the  same  vessel,  while  P  and 
P/  are  the  pressures  exerted  on  these  surfaces 
respectively  by  any  force  of  compression  on 
the  liquid,  and  we  have 

P:  P/  =  A:  A'. 

It  also  follows  that  this  expression  represents  correctly  the  pressure 


152 


THE    THREE    STAGES    OF    MATTER. 


exerted  on  any  solid  body  plunged  in  the  liquid,  as  well  as  for  any  part 
of  the  sectional  area  of  the  liquid  itself.     Hence : — 

The  entire  pressure  sustained  by  any  surface  is  proportional  to  its  area, 
"  and  thus,"  says  Pascal  in  his  Treatise  on  the  Equilibrium  of  Fluids, 
it  appears  that  a  vessel  full  of  water  is  a  new  Principle  in  Mechanics, 
and  a  new  Machine  which  will  multiply  force  to  any  degree  we  choose." 
Pascal  also  referred  the  equilibrium  of  fluids  to  the  principle  of  virtual 
velocities  which  regulates  the  equilibrium  of  other  machines  (105). 

190.  The  Bramah  Hydrostatic  Press.— This  powerful  apparatus 
depends  upon  the  principle  just  announced.  136 

Want  of  good  workmanship  alone  prevented 
Pascal  from  realizing  his  conception  of  this 
machine  (in  1653),  as  was  long  afterwards 
(A.D.  1796),  done  by  Bramah,  at  London. 

As  the  form  of  the  vessel  has  no  influence 
on  the  equal  transmission  of  pressures,  and 
the  point  of  application  of  force  may  be 
situated  at  any  convenient  distance  from  the 
press,  it  is  plain  that  the  mechanician  can  use 
this  principle  as  circumstances  demand.  Thus,  in  fig.  136,  the  piston  a 
may  be  to  the  larger  one  b  c  as  1  :  20,  and  hence  a  pressure  of  one  pound 

137 


exerted  on  a  will  raise  b  c  with  a  force  of  twenty  pounds,  and  cony 
any  pressure  exerted  on  b  c  will  be  diminished  twenty  fold  at  a. 


or  FLUIDS.  153 

The  main  parts  of  the  Bramah  hydrostatic  press,  fig.  137,  consist  of  a  small 
forcing-pump,  A,  in  which  is  a  piston  worked  by  a  lever.  This  pump  communi- 
cates with  a  large  and  strong  cylindrical  reservoir,  B,  by  a  tube  indicated  by  the 
dotted  lines  in  the  figure.  In  this  cylinder  a  water-tight  piston  moves,  bearing 
at  its  upper  end  a  flat  metallic  plate,  between  which  and  the  top  of  the  frame, 
D,  the  substance,  M,  to  be  compressed,  is  placed. 

The  cylinders  are  filled  by  means  of  the  curved  tube  H,  one  end  of  which 
rests  in  a  vessel  containing  water,  or  oil,  the  other  terminates  in  the  barrel  A, 
and  has  a  valve  at  its  end  opening  upwards.  This  valve  opens  when  the  piston 
is  raised,  thus  drawing  in  water,  and  closes  when  the  piston  descends.  By 
working  the  piston,  the  barrels  A  and  B  are  completely  filled  with  water.  The 
orifice  0  is  in  connection  with  a  stop-cock,  by  which  the  water  can  be  drawn 
off  when  the  pressure  is  to  be  reduced. 

If  the  cylinder  B  has  an  area  of  200  square  inches,  and  the  small  cylinder  an 
area  of  half  a  square  inch,  the  pressure  of  the  water  on  the  piston  above  B,  will 
be  400  times  that  applied  at  the  lever.  But  let  the  arms  of  the  lever  be  to  each 
other  as  one  to  fifty,  then  when  a  force  of  fifty  pounds  is  applied  at  the  long 
arm,  the  piston  will  descend  with  a  force  of  2500  pounds  (50  X  ^  =  2500), 
and  there  will  be  exerted,  theoretically,  a  force  of  1,000,000  pounds  upon  the 
piston  in  B  (50  X  50  X  40°  =  1,000,000),  or,  deducting  one-fourth  for  the  loss 
occasioned  by  the  different  impediments  to  motion,  a  man  would  still  be  able  to 
exert  a  force  of  750,000  pounds. 

This  enormous  result  is  gained,  of  course,  very  slowly,  in  accordance 
with  the  well-known  relation  of  power  to  weight  (109). 

Uses  in  the  arts.— The  hydrostatic  (often  called  hydraulic)  press  is  of 
extensive  use  in  the  industrial  arts.  It  is  employed  for  compressing  cloth,  oil- 
cake, paper,  hay,  gunpowder,  candles,  vermicelli,  and  for  numerous  other  arti- 
cle?, to  which  the  proper  form  or  condition  is  imparted  by  severe  pressure; 
also  for  testing  steam-boilers  and  chain  cables.  The  tubes  of  the  famous 
Britannia  tubular  bridge  over  the  straits  of  Menai  (172)  were  raised  to  their 
place  by  means  of  powerful  hydraulic  presses. 

191.  Pressure  of  a  liquid  on  the  bottom  of  a  vessel.— The 

pressure  exerted  by  a  liquid  on  the  horizontal  base  of  a  containing  vessel, 
is  1st,  independent  of  the  shape  of  the  vessel,  and  2d,  is  equal  to  the 
weight  of  a  column  of  this  liquid,  whose  base  is  that  of  the  vessel,  and 
whose  height  equals  the  depth  of  the  liquid. 

In  a  conical  vessel,  standing  on  its  base  and  filled  with  liquid,  con- 
ceive any  number  of  horizontal  planes,  dividing  the  contents  of  the 
vessel  into  a  series  of  frustums,  so  thin  that  each  frustum  may  be 
considered  a  cylinder.  It  is  evident  that  the  pressure  exerted  by  each 
cylindrical  mass  on  its  own  base  is  equal  to  its  own  weight.  But  by 
the  principle  of  Pascal  each  succeeding  section  will  have  to  support 
a  pressure,  as  much  greater  than  the  weight  of  the  superincumbent 
masses  as  the  area  of  its  base  is  greater  than  the  area  of  the  base  of 
16 


154  THE   THREE   STATES   OF   MATTER. 

that  preceding  it.      Hence,  the  base  of  the  conical  vessel       133 
will  support  a  pressure  equal  to  the  weight  of  a  column  of 
water  whose  base  and  height  are  respectively  those  of  the 
vessel. 

Evidently,  from  this  reasoning,  if  the  conical  vessel  is  in- 
verted, or  its  form  is  in  any  way  modified,  the  same  law  holds 
good. 

The  truth  of  this  principle  may  be  experimentally  demon- 
strated by  means  of  the  apparatus  in  fig.  138.  If  this  instru- 
ment is  placed  in  a  liquid,  the  piston  C  is  forced  in  with  a 
pressure  equal  to  the  weight  of  a  column  of  the  liquid,  whose 
base  has  the  area  of  the  piston,  and  whose  height  is  equal  to 
the  depth  of  the  liquid  above  the  surface  of  the  piston. 

To  demonstrate  that  the  pressure  is  independent  of  the  form  of  the 
vessel,  M.  Haldat  has  contrived  the  apparatus,  fig.  139.  It  consists  of 
a  tube,  A  B  c,  bent  twice  at  right  angles.  On  A,  may  be  placed  the 
vessels  M  and  P,  of  equal  height,  but  of  different  forms.  The  tube 
A  B  c  is  filled  with  mercury,  which  rises  to  an  equal  height  in  A  and  c ; 
M  is  then  placed  on  A,  and  filled  with  water ;  the  mercury  immediately 
rises  in  c,  to  a  certain  point,  as  a.  We  then  replace  M  by  P,  and  fill 
with  water  to  the  same  height  as 
before.  The  mercury  again  rises 
to  the  point  a,  as  it  did  with  the 
vessel  M ;  it  is  evident  that  the 
pressure  transmitted  to  the  mer- 
cury in  the  direction  AB,  was  the 
same  in  both  cases,  proving,  most 
conclusively,  that  the  pressure  does 
not  depend  upon  the  quantity  of 
liquid,  for  the  vessels  M  and  P  differ 
greatly  in  capacity.  The  area  of  the 
base  formed  by  the  surface  of  the 
mercury,  and  the  vertical  height  formed  by  the  column  of  water,  were, 
however,  the  same  in  both  cases,  and  upon  these,  as  before  stated,  the 
pressure  depends.  In  the  case  of  a  vessel  having  vertical  walls,  the  pres- 
sure would  be  equal  to  the  weight  of  the  liquid  the  vessel  contained. 

192.  Upward  pressure. — Having  shown  that  pressure  in  liquids  is 
exerted  from  above,  downwards ;  it  follows,  from  the  law  of  equality 
of  pressure,  that  a  corresponding  force  is  exerted  from  below,  upwards. 
This  pressure  is  made  very  manifest  by  the  buoyancy  experienced  when 
we  plunge  the  hand  into  a  liquid  of  great  density,  as  into  mercury  In 


OF   FLUIDS. 


155 


order  to  demonstrate  this  upward  pressure  experimentally,  a  tube  of 

glass  is  taken,  open  at  both  ends,  fig.  140,  having  at  the  lower  end  a 

disk  of  glass,  B,  which  is  supported  by  means  of  a  thread  from  its 

centre :  the  whole  is  then  placed  in  a  vessel  140 

of  water  and  abandoned  to  itself;  the  disk 

remains  attached  to  the  end  of  the  cylinder, 

owing  to  the  upward  pressure  of  the  water. 

If  now  the  interior  tube  be  carefully  filled, 

the  disk  will  not  fall  until  the  level  of  the 

water  within  the  tube  is  nearly  the  same  as 

that  in  the  outer  vessel,  proving  that  the 

upward  pressure  is  equal  to  the  weight  of 

the  interior  column,  and  therefore  that : — The 

upward  pressure,  in  any  vessel,  is  equal  to  the 

weight  of  a  column  of  liquid  having  the  same 

base  as   the  cylinder,  A,  and  whose  height 

equals  the  depth  of  the  section  below  the  surface  of  the  liquid. 

193.  Pressure  on  the  sides  of  a  vessel. — The  141 

pressure  of  a  liquid  on  any  portion  of  a  lateral  wall,  is  f 

equal  to  the  weight  of  a  column  of  liquid,  which  has  for 
its  base  this  portion  of  the  wall,  and  for  its  height  the 
vertical  distance  from  its  centre  of  gravity  to  the  surface 
of  the  liquid.  Thus,  in  fig.  141,  the  pressure  at  the 
height,  C  D,  of  the  wall  is,  by  §  191,  equal  to  the  weight 
of  the  column  A  B,  since  the  pressure  of  this  is  com- 
municated laterally  to  all  the  particles  lying  on  the 
same  horizontal  plane. 

This  lateral  pressure  increases,  of  course,  with  the  depth  of  liquid  in 
the  vessel.  Thus,  in  fig.  142,  the  column  of  liquid  A  C 
pressing  with  a  certain  force  on  Z,  the  column  E  F 
will  press  on  G,  with  a  force  as  much  greater,  as  E  F  is 
deeper  than  A  C.  This  may  be  further  illustrated  by 
plunging  the  apparatus,  fig.  138,  at  various  depths  and 
in  a  horizontal  position,  the  piston  will  be  forced  in 
with  a  pressure  corresponding  to  the  depth ;  also,  if  it 
is  placed  in  any  position  intermediate  between  the 
horizontal  and  vertical,  the  piston  will  be  similarly 
pressed  in,  thus  showing  that  pressure  is  exerted 
equally  in  all  directions. 

194.  Pascal's  experiment  with  a  cask. — Pascal  made  a  striking 
experiment  at  Rouen,  in  1647,  to  illustrate  the  enormous  pressure 


142 
E        A 

L 

P 

it 

156 


THE    THREE    STATES    OP    MATTER. 


exerted  by  a  lofty  column  of  water  contained  in  a  small  tube.  A 
strong  cask,  filled  with  water  and  arranged  as  in  fig.  143,  was  fitted 
with  a  small  tube  about  forty  feet  high.  When  this  tube  was  filled 
with  water,  the  effect  of  the  pressure  transmitted  to  all  parts  of  the 
cask  was  sufficient  to  burst  the  vessel. 


144 


195.  The  water  bellows,  or  hydrostatic  paradox. — This  familar 
experiment  is  only  a  modification  (in  form)  of  Pascal's  cask. 

The  hydrostatic  bellows,  fig.  144,  consists  of  two  boards,  B  C,  and  E  D,  con- 
nected with  leather  or  India-rubber  cloth,  A,  in  such  a  manner  that  the  upper 
board  can  rise  and  fall,  like  the  common  air  bellows.  The  tube  T  E  communi- 
cates with  the  interior  of  the  apparatus.  Supposing  the  tube  to  have  a  cross 
section  of  one  square  inch,  and  the  top  of  the  bellows  to  have  a  surface  of  100 
square  inches,  one  pound  of  water  in  the  tube  would  lift  100  pounds  on  the  bel- 
lows, the  weight  of  the  water  acting  with  a  pressure  equal  to  one  pound  on  each 
square  inch  of  the  surface.  The  pressure  is  proportioned  to  the  height  of  the 
column  of  water ;  for  if  we  use  a  smaller  tube,  for  the  same  bulk  of  fluid,  the 
height  of  the  column  of  water  will  be  greater,  and  will  raise  a  greater  weight ; 
if  the  tube  be  larger,  the  column  will  not  be  so  high,  and  will  not  raise  so  large 
a  weight. 

196.  Total  pressure  on  the  walls.— In  the  vessel  ABCD    6g. 


OF    FLUIDS. 


157 


145 


145,  divide  the  side  AB  into  10  equal  parts.  Supposing  the  pressure 
at  1  to  be  one  pound,  then  the  pressure  at  2  would  be  two  pounds, 
at  3  three  pounds,  &c.,  as  the  intensity  of  the  pressure  increases  directly 
with  the  depth.  The  average  intensity  of  pressure  would  be  found  at 
the  5th  division  (or  a  point  midway  between  the  1st  and  10th),  and  the 
total  pressure  on  the  walls  would  be  the  same  as  if  it  sustained  the 
average  intensity  over  the  whole  lateral  surface,  and  therefore  the  total 
pressure  upon  a  wall  of  such  a  vessel,  is  equal  to  the  weight  of  a  column 
nfthe  liquid  whose  base  is  equal  to  the  area  of  the  side,  and  whose  height 
is  equal  to  one-half  of  the  depth  of  the  liquid 
in  the  vessel.  This  is  true,  whether  the  vessel 
be  vertical  or  inclined  in  any  direction.  In 
the  case  of  a  cubical  vessel,  this  pressure  on 
one  side  would  be  equal  to  one-half  the 
weight  of  the  liquid  contained  in  the  vessel. 

Total  pressure  on  the  bottom  and  sides  of  a  vessel. — The 

total  pressure  exercised  on  the  bottom  and  sides  of  a  vessel,  is  much 
greater  than  the  weight  of  the  liquid  contained  in  the  vessel.  In  the 
case  of  a  cubical  vessel,  the  pressure  exerted  on  the  bottom  is  equal  to 
the  whole  weight  of  the  liquid  (191),  the  pressure  exerted  on  each  side 
being  equal  to  half  the  weight  of  the  liquid  on  the  four  sides,  it  is  equal 
to  twice  its  weight,  consequently,  in  a  cubical  vessel  the  entire  pres- 
sure exerted  on  the  bottom  and  sides  is  equal  to  three  times  the  weight  of 
the  contained  liquid. 

Table,  showing  the  pressure  in  pounds,  per  square  inch,  and  square  foot,  produced 
by  water  at  various  depths. 


Depth  in  feet. 

Pressure  per  square  inch. 

Pressure  per  square  foot. 

1 

8-4328 

623232 

2 

0-8656 

124-6464 

3 

1-2984 

186-9696 

4 

1-7312 

249-2928 

5 

2-1640 

311-6160 

6 

2-5968 

373-9392 

7 

3-0296 

436-2624 

8 

3-4624 

498-5856 

9 

3-8952 

560-9088 

10 

4-3280 

623-2320 

By  aid  of  the  above  table,  the  pressure  of  water  on  any  surface  of  a  vessel 

containing  it,  can  be  determined.     As,  for  example,  the  pressure  of  water  on  a 

square  foot,  at  the  bottom  of  a  vessel  twenty-three  feet  in  depth ;  at  two  feet, 

the  pressure  is  124-6464;  at  twenty  feet,  ten  times  as  much;  —  1246-464;  at 

16* 


158 


THE    THREE    STATES    OF    MATTER. 


three  feet,  186-9696,  and  1246-464  -f  186-9696  —  1433-4336,  the  pressure  of  water 
on  a  square  foot  of  surface,  at  a  depth  of  twenty-three  feet. 

That  the  pressure  produced  at  great  depths  is  really  immense,  can  be  shown 
by  confining  a  piece  of  wood  at  great  depths  in  the  sea.  The  pressure  forces 
the  water  into  the  pores,  so  that  it  will  not  be  capable  of  floating  afterwards. 
A  bottle,  the  body  of  which  is  square,  if  tightly  corked  and  lowered  into  the 
sea,  will  be  broken  by  the  pressure.  If  the  body  of  the  bottle  is  strong  and 
cylindrical,  the  cork  will  be  forced  in.  Below  a  certain  depth,  divers  cannot 
penetrate,  and  the  same  may,  perhaps,  be  true  of  fishes. 

197.  The  centre  of  pressure  upon  any  surface  immersed  in  a 
fluid  is  the  point  of  application  of  the  resultant  of  all  the  pressures 
acting  upon  it. 

If  the  pressure  of  a  fluid  upon  an  immersed  surface  were  the  same 
at  all  depths,  the  centre  of  pressure  would  be  at  the  centre  of  gravity 
of  the  surface.  But  as  the  pressure  increases  with  the  depth,  the  centre 
of  pressure  will  always  be  below  the  centre  of  gravity. 

The  centre  of  pressure  in  an  immersed  surface,  or  in  the  side  of  a 
vessel  containing  a  fluid,  is  a  point  to  which  a  force  equal  and  opposite 
to  the  resultant  of  all  the  pressures  must  be  applied  to  keep  the  surface  at 
rest. 

The  position  of  this  point,  for  various  regular  surfaces,  has  been 
determined  by  the  calculus. 

The  centre  of  pressure  of  a  rectangular  surface,  vertically  or  obliquely 
immersed,  so  as  to  have  one  side  in  the  surface  of  the  liquid,  is  in  a  line 
joining  the  centres  of  the  superior  and  inferior  bases,  and  at  a  distance 
from  the  inferior  base,  equal  to  one-third  the  height  of  the  rectangle. 
In  fig.  146  the  point  C,  in  the  line  A  B,  distant  from  B  one-third  of 
A  B,  is  the  centre  of  pressure. 


146 

A 


148 
A 


When  the  immersed  surface  is  a  triangle  having  one  side  horizontal, 
and  the  apex  in  the  surface  of  the  fluid,  the  centre  of  pressure  is  in  a 
line  joining  the  apex  and  the  centre  of  the  horizontal  base  at  a  distance 
from  the  centre  of  the  base  equal  to  one-fourth  the  bisecting  line. 
The  centre  of  pressure  in  the  triangle,  fig.  147,  is  at  c,  distant  from  B 
one-fourth  of  the  line  A  B. 

When  the  base  of  the  triangle  lies  in  the  surface  of  the  fluid,  the 


OF    FLUIDS.  159 

centre  of  pressure  is  midway  between  the  apex  and  the  centre  of  the 
base,  as  at  c,  fig.  148,  which  is  equidistant  between  A  and  B. 

198.  Pressures  vary  as  the  specific  gravities  of  liquids.— Two 
liquids  press  on  the  same  area  and  at  the  same  depth,  directly  in  the  ratio 
of  their  specific  gravities.    We  have  seen  (191)  that  the  pressure  exerted 
on  the  base  of  a  vessel  having  vertical  walls  is  equal  to  the  weight  of 
the  liquid  the  vessel  contains.    Plainly,  therefore,  the  pressures  exerted 
on  the  base  of  two  equal  vessels  filled  with  equal  volumes  of  liquid  of 
unlike  density  will  vary  directly  with  their  specific  gravities ;  or  repre- 
senting the  pressures  in  the  two  cases  by  P  and  P/,  and  the  specific 
gravities  by  (Sp.  Gr.)  and  (Sp.  Gr.y,  we  have 

P:P'=  (Sp.  Gr.)  :  (Sp.  Or.)' 

III.     EQUILIBRIUM   OF   LIQUIDS. 

199.  The  conditions  of  equilibrium  in  liquids. — The  joint  effect 
of  gravitation,  and  of  the  perfect  mobility  of  the  particles  of  a  liquid,  is : — 

1.  That  the  surface  of  a  liquid  at  every  point  must  be  perpendicular  to 
the  direction  of  gravity,  i.  e.,  it  must  be  horizontal  or  level. 

This  principle,  first  distinctly  enunciated  by  Archimedes,  follows  from 
the  nature  of  gravitation,  which  acting  on  a  body  free  to  move,  causes 
its  centre  of  gravity  to  descend  as  low  as  possible.  It  is  only  when  the 
surface  is  horizontal  that  all  the  particles  of  the  fluid  mass  are  equally 
solicited  by  the  force  of  gravity. 

The  inequalities  of  the  solid  surface  of  the  earth  exist,  because 
cohesion  is  opposed  to  gravitation.  Otherwise  the  mountains  would 
sink,  and  the  valleys  rise,  until  the  whole  mass  had  a  uniform  level. 

By  this  principle  a  surface  of  water  is  perfectly  horizontal  only  when 
its  area  is  so  limited  that  the  direction  of  the  149 

forces  of  gravity  ca*  be  regarded  as  parallel  at 
each  point.  If  an  observer  is  stationed  at  0,  fig. 
149,  and  0  A  is  one  mile,  the  subtense  of  curva- 
ture (AB  or  DE)  is  eight  inches.  But  00  and  BC 
are  lines  perpendicular  to  the  points  0  and  B,  and 
are  therefore  plumb  lines  (60),  and  hence  the  surface  E  OB  is  a  spheri- 
cal surface.  In  other  words,  we  reach  the  more  general  principle  :— 

That  the  resultant  of  all  the  forces  acting  at  any  point  on  the  surface 
of  a  liquid  mass,  when  in  equilibrium,  must  be  normal  to  the  surface  at 
that  point. 

It  follows  from  this  again  :-— 


160  THE    THREE    STATES    OP    MATTER. 

2.  That  every  liquid  mass,  when  in  equilibrium,  can  be  considered  as 
made  up  of  an  infinite  number  of  very  thin  layers,  sustaining  at  all 
points  the  same  pressure,  and,  at  each  point  of  surface,  normal  to  all  the 
forces  there  acting. 

200.  Equilibrium  of  liquids  when  freed  from  the  influence  of 
gravity. — It  follows,  as  a  consequence  of  the  last  principle,  if  a  mass 
of  liquid  is  freed  from  the  influence  of  gravity,  and  abandoned  undis- 
turbed to  its  own  molecular  attractions,  that  it  will  assume  a  spherical 
figure ;  since  then  the  sphere  is  the  only  form  which  can  satisfy  the 
conditions  of  equilibrium.     This  theory  is  most  beautifully  demon- 
strated by  a  celebrated  experiment  called — 

The  experiment  of  Plateau,  who  conceived  that  the  influence  of 
gravity  might  be  avoided  by  suspending  a  mass  of  oil  in  alcohol, 
diluted  to  exactly  the  density  of  the  oil.  This  conception  is  perfectly 
realized  by  experiment.  By  care  and  certain  precautions  to  secure 
clearness  in  the  liquids,  a  considerable  sphere  of  oil  may  be  suspended 
in  any  part  of  the  alcoholic  mixture,  and  by  a  wire  arranged  to  rotate 
as  an  axis,  and  about  which  the  sphere  of  oil  readily  arranges  itself, 
the  oblate  figure  of  the  earth,  the  appearance  of  satellites,  or  even  the 
rings  of  Saturn,  may  be  imitated  in  a  most  instructive  and  striking 
manner. 

The  spherical  form  of  drops  of  rain  or  dew,  and  the  globular  drops 
of  mercury,  are  referable  to  the  conditions  of  fluid  equilibrium. 

201.  Equilibrium  of  a  liquid  in  communicating  vessels. — If 
two  or  more  vessels  communicate  with  each  other,  the  liquids  in  both 
or  all  the  vessels  stand  at  the  same  level.   This  law  rests  upon  the  fact, 
that  the  pressure  of  liquids  at  equal  depths,  150 

is  equal  in  all  directions.  If  the  fluid  stands 
at  a  higher  level  in  one  vessel  than  the  other, 
the  particles  of  the  former  exert  a  greater 
lateral  pressure  on  the  channel  of  communi- 
cation than  the  other  can  ;  these  particles  are, 
therefore,  continually  pushed  upwards,  until 
they  exert  an  equal  and  opposite  pressure, 
which  obtains  when  the  columns  are  at  an 
equal  height.  The  effect  is  the  same,  what- 
ever may  be  the  size  and  number  of  the  ves- 
sels. Fig.  150  represents  a  number  of  vessels 
of  different  shapes  and  capacities,  connected  with  a  common  reservoir ; 
if  we  pour  water  into  one  of  them,  it  will  rise  to  the  same  height  in 
the  other  vessels. 


OF    FLUIDS. 


161 


151 


202.  Equilibrium  of  liquids  of  different  densities  in  commu- 
nicating vessels.— When  two  liquids  of  different  densities  are  placed 
in  communicating  vessels,  their  surfaces 
will  not  rest  at  the  same  point  or  level; 
for  in  communicating  vessels,  the  heights 
of  the  liquid  columns  are  in  the  inverse 
ratio  of  the  specific  gravities  of  the  liquids. 

If  mercury  is  first  poured  into  the  lower 
part  of  the  apparatus,  fig.  151,  and  the 
tube  AB  is  then  filled  with  water,  this 
liquid  will  exert  a  pressure  on  the  mercury, 
causing  it  to  be  depressed  in  A  B,  and  to  rise 
in  the  other  tube.  Measuring  the  height 
of  the  columns  of  mercury,  C  D,  and  water, 
AB,  which  are  in  equilibrium,  they  will 
be  found  to  be  as  1  to  13-59.  These  num- 
bers represent  the  densities  of  water  and  mercury. 

Demonstration. — Let  S  represent  the  surface  of  the  mercury  at  B,  and  H 
be  the  height  of  the  column  of  water,  B  A,  and  Sp.  Gr.  the  specific  gravity  of 
water;  then,  by  g  198,  the  pressure  on  the  surface  is  P  =  S  H  (Sp.  Gr.)  for  the 
column  of  water,  and  for  the  mercury,  C  D,  it  is  P'  —  S'  H'  (Sp.  Gr.)'  But 
by  $  189  equilibrium  can  obtain  only  when  the  pressures  exerted  on  B  and  C 
are  proportional  to  the  area  of  those  surfaces,  or  where  P  :  P'  =  S :  S'.  Sub- 
stituting the  value  of  P  and  P',  it  follows  that 

H(Sp.  Gr.)  =  H1  (Sp.  Or.)' 

H:H'  =  (Sp.  Gr.)'  :  (Sp.  Gr.) 

In  other  words,  the  columns  are  in  equilibrium  when  their  heights  are 
inversely  as  their  specific  gravities,  which  was  to  be  proved. 

203.  The  spirit  level.— Since  by  §  199  the  surface  of  a  liquid  at 
rest  is  always  horizontal,  we  have  thereby  a  ready  means  for  determin- 
ing the  horizontal  line  by  use  of  the  spirit  level.  This  instrument  is  a 
glass  tube,  A  B,  fig.  152,  very  slightly  curved  upwards,  nearly  filled 
with  alcohol,  hermetically  152 

sealed  and  sheathed  in 
brass,  C  D.  The  small 
bubble  of  air,  M,  always 
rises  to  occupy  the  high- 
est point  of  the  apparatus. 
The  base  is  carefully  ad- 
justed, so  that  only  when 
the  instrument  is  placed  horizontally,  does  the  bubble  remain  in  the 
lentre,  at  a  fixed  mark. 


162  THE   THREE   STATES    OP    MATTER. 

204.  Artesian  wells. — All  springs  and  fountains  are  examples 
of  the  laws  of  equilibrium  of  liquids  in  communicating  vessels. 
Among  similar  phenomena,  artesian  wells  are  the  most  remarka- 
ble examples.  These  are  wells  (named  artesian  from  the  ancient 
province  of  Artois  in  France,  where  they  were  early  made,  although 
known  long  before  in  China),  bored  into  the  earth's  crust,  often  to  a 
great  depth.  The  crust  of  the  earth  consists  often  of  various  beds  or 
strata,  some  pervious  to  water  like  sandstones,  and  others,  like  clay, 
impervious. 

Fig.  153  presents  an  imaginary  section  of  a  portion  of  the  earth's  crust, 
containing  two  impervious  strata,  A  B,  CD,  and  one  pervious  stratum, 
KK.  Let  these  strata  reach  the  surface  in  elevated  land,  and  we 

153 


have  thus  a  basin  into  which  the  meteoric  waters  filter  and  from  which 
they  cannot  escape,  being  confined  by  the  impervious  strata  already 
named ;  now  an  artesian  boring  in  the  valley  H,  will  reach  the  impri- 
soned water  after  passing  A  B,  and  the  water  will  be  thrown  up  in  a 
jet,  the  height  of  which  will  depend  on  the  elevation  of  the  edges  of 
the  basin,  which  may  come  to  the  surface  in  lofty  hills  hundreds  of 
miles  away  from  the  well. 

A  well  of  this  kind  was  sunk  at  Louisville,  Ky.,  in  1857-8,  to  the  great  depth 
of  2086  feet  (Dupont's  well),  which  delivers,  through  a  bore  of  13  inches,  over 
three  hundred  thousand  gallons  of  sulphuretted  mineral  water  in  24  hours,  at 
170  feet  above  the  surface,  with  a  constant  temperature  of  76J°  F.  (824°  at  the 
bottom).  (Am.  Journ.  Sci.  [2]  xxvii.  174.)  Belcher's  well  in  St.  Louis  is  2199 
feet  deep,  and  yields  also  sulphuretted  water ;  while  the  famous  Grenelle  well 
in  Paris  is  1806  feet  deep,  and  yields  daily  600,000  gallons  of  soft  water,  warm 
enough  to  answer  the  purposes  of  the  great  slaughter-houses  surrounding  it. 
Artesian  wells  have  lately  been  successfully  bored  in  the  African  desert  on  the 
great  caravan  route. 

IV.     BUOYANCY  OP  LIQUIDS. 

205.  Theorem  of  Archimedes. — Solids  immersed  in  liquids  art 
buoyed  up  by  a  force  equal  to  the  weight  of  the  liquid  displaced. 


OF   FLUIDS. 


163 


This  very  important  principle  was  discovered  by  Archimedes,  about 
230  years  B.  c.,  and  is  called  after  him,  the  Principle  of  Archimedes. 
Its  correctness  is  proved  by  means  of  the  hydrostatic  balance,  from 
one  of  the  arms  of  which  (fig.  154)  is  hung  a  hollow  cylinder,  01 
bucket,  A,  having  a  cylindrical  mass  of  copper,  B,  exactly  fitting  into 
it,  and  suspended  from  it  by  means  of  a  hook.  Having  exactly  coun- 
terpoised the  beam  by  weights  on  the  other  arm  of  the  balance,  fill  up 
the  glass  vessel  with  water,  until  the  cylinder  B  is  wholly  immersed. 
The  cylinder  will  then  appear  to  have  lost  weight,  the  other  arm  going 
down.  If  the  bucket,  A,  is  now  exactly  filled  with  water,  the  equili- 
brium will  be  restored ;  proving  that  the  weight  lost  by  the  immersed 
body  is  equal  to  its  own  bulk  of  water. 

The  same  is  true  of  any  liquid  whatever.  It  is  also  true,  however, 
that  the  weight  lost  in  this  case  by  the  cylinder  must,  as  a  necessary 
result  of  the  law  of  action  and  reaction,  be  gained  by  the  water  in 
the  vase. 

This  fact  is  illustrated  by  arranging  the  apparatus  as  seen  in  fig.  155. 
After  fiaet  balancing  the  vase  of  water,  the  cylinder  B  is  suspended  in 
154  it  from  a  separate  support  C.     The  vase  then 

appears  to  have  gained  in  weight,  and  it  will 
be  found  requisite  in  order  to  restore  the  equi- 
librium  to   remove  therefrom  enough  water 
exactly  to  fill  the  cup  A. 
155 


The  theorem  of  Archimedes  is  a  necessary  consequence  of  the  me 


164  THE   THREE    STATES    OP    MATTER. 

chanical  condition  and  laws  of  equilibrium  of  liquids,  and  of  the 
impenetrability  of  matter.  The  whole  immersed  body  is  buoyed  up 
by  a  force  equal  to  the  resultant  of  all  the  forces  normal  to  each  point 
of  its  surface,  that  is  by  a  force  equal  to  the  weight  of  the  liquid  which 
it  displaces. 

206.  Another  demonstration  of  Archimedes'  principle.— Con- 
ceive a  cube  A  B,  fig.  156,  of  water  for  example,  say  one  cubic  inch  or 
a  cubic  centimetre  in  bulk,  isolated  and  156 

sustained  in  its  position  by  the  pressure  of 
the  surrounding  particles — such  being  the 
condition  of  equilibrium  existing  among 
the  particles  of  liquids  at  rest  (199). 
Hence  it  is  evident  that  the  weight  of  the 
ideal  cube  A  B  is  sustained  in  its  position 
of  equilibrium  by  a  buoyant  force  exactly 
equal  to  its  own  weight.  If  A  B  is  now 
solidified  by  any  cause  which  does  not 
change  its  volume,  it  is  evident  that  the 
conditions  of  its  equilibrium  also  remain 
unchanged.  We  may  therefore  replace  it 
by  any  other  substance  of  whatever  weight, 
having  the  same  dimensions,  and  the  new  solid  will  still  be  buoyed  up 
by  a  force  equal  to  the  weight  of  the  ideal  cube  of  water,  or  of  any 
other  liquid  in  which  it  is  immersed. 

The  form  of  the  body  is  evidently  immaterial,  and  therefore  it  fol- 
lows, as  before,  that  a  body  plunged  in  a  liquid  is  sustained  by  a  power 
equal  to  the  weight  of  the  liquid  displaced. 

Floating  bodies. — Accepting  the  Theorem  of  Archimedes,  it  follows, 
that  if  the  immersed  solid  be  of  the  same  weight  as  the  displaced  fluid, 
the  former  will  remain  at  rest  in  the  fluid,  in  any  position  in  which 
it  may  be  placed,  the  upward  pressure  exerted  upon  the  solid  being 
equal  to  its  own  weight. 

Since  the  specific  gravities  of  any  two  substances  are  to  each  other 
as  the  weights  of  equal  volumes  of  these  substances  (99),  it  follows  that 
any  homogeneous  solid  will  float  when  its  specific  gravity  is  less  than  that 
of  the  liquid,  and  that  it  will  sink  when  these  conditions  are  reversed. 

Hence,  iron  sinks  in  water,  but  floats  on  mercury ;  some  woods 
which  float  on  water  will  sink  in  oil  or  alcohol ;  while  oak,  which  floats 
on  salt  water,  will  sink  in  fresh  water.  But  if  the  iron  is  fashioned 
into  a  thin-walled  vessel,  and  the  dense  woods  into  hollow  boxes, 
they  will  then  float  on  the  same  liquids  in  which  they  before  sank, 
because  their  volumes  have  been  increased,  respectively,  without  in- 


OP   FLUIDS. 


165 


creasing  their  weight,  and  they  float  because  each  displaces  a  volume 
of  water  greater  in  weight  than  the  weight  of  the  floating  body. 

Examples  illustrating  this  principle  are  of  familiar  occurrence.   Iron  ships 

e.  g.,  the  Great  Eastern — float  as  buoyantly  as  ships  of  wood,  and  have  besides  a 
vast  capacity  for  floating  their  heavy  machinery,  coal,  and  cargo.  The  problem 
of  weighing  a  ship  and  cargo  resolves  itself  into  a  question  of  mensuration  of 
the  volume  of  water  displaced  by  her. 

Camels  are  tanks  of  iron  or  wood,  which  are  first  filled  with  water,  and  after 
being  secured  to  the  sides  of  loaded  vessels  the  water  is  pumped  out,  when  their 
buoyancy  aids  the  vessel  in  floating  over  a  bar,  or  in  shallow  water. 

floating  docks,  so  much  in  use  in  the  seaports  of  the  United  States,  are  similar 
contrivances  by  aid  of  which  the  heaviest  anl  largest  ships  are  safely  raised  en- 
tirely out  of  water  for  repairs.  The  elevating  force  is  solely  the  buoyancy  of  large 
sectional  tanks  previously  sunk  beneath  the  vessel,  and  then  pumped  out  by 
steam-engines. 

Cartesian  devil. — This  hydrostatic  toy,  known  also  as  the  ludeon,  exhibits  the 
principle  just  stated.  It  consists  of  a  small  glass  or 
enamel  figure,  fig.  157,  at  whose  head  is  fixed  a  bulb  of 
glass  having  a  small  opening,  0,  beneath.  It  is  filled 
with  water  to  such  an  extent,  that  when  placed  in  the 
cylinder  of  water  as  represented,  it  just  floats.  Over  the 
mouth  of  the  vessel  is  tightly  fixed  apiece  of  caoutchouc. 
Pressure  exerted  by  the  thumb  on  the  caoutchouc  will  be 
conveyed  through  the  water  to  the  air  contained  in  the 
bulb  0.  Sufficient  water  will  thus  enter  0  to  render  the 
specific  gravity  of  the  apparatus  heavier  than  that  of 
water,  when  it  sinks.  On  removing  the  pressure,  ex- 
pansion of  the  air  in  0  expels  the  water  which  was  pre- 
viously forced  into  it,  and  the  apparatus  rises.  By  a 
contrivance  similar  to  this,  the  beautiful  nautilus  shell 
rises,  to  float  upon  the  surface  of  the  sea,  or  sinks  again 
at  pleasure,  by  a  voluntary  contraction  or  expansion  of 
an  internal  cavity. 

Fishes  are  bodies  floating  in  a  state  of  equilibrium,  when  immersed  in  their 
own  element.  But  in  order  to  preserve  this  state  at  different  depths,  they  have 
an  air  bladder,  by  contracting  or  expanding  which,  their  bodies  acquire  the 
mean  density  of  the  water  in  which  they  are. 

207.  Equilibrium  of  floating  bodies. — In  order  that  a  floating 
body  may  be  in  equilibrium  it  is  necessary :  First,  That  the  weight  of 
the  fluid  displaced  should  be  equal  to  the  weight  of  the  floating  body: 
Second,  That  the  resultant  of  all  the  upward  pressures  of  the  liquid 
should  act  in  the  vertical  line,  passing  through  the  centre  of  gravity  of 
the  body. 

As  the  weight  of  a  body  may  be  considered  as  acting  at  a  single 
point  called  the  centre  of  gravity,  so  the  upward  pressure  of  a  liquid, 
acting  upon  a  body  immersed  in  it,  may  be  considered  as  acting  in  a 
single  point  which  will  be  the  centre  of  gravity  of  the  fluid  displaced. 
This  point  is  evidently  different  from  the  centre  of  gravity  of  the  body, 
17 


166 


THE    THREE    STATES    OF    MATTER. 


a 


and  may  therefore  appropriately  be  called  the  centre  of  buoyancy.  In 
a  homogeneous  solid  this  point  is  always  below  the  centre  of  gravity 
when  the  body  floats,  and  coincides  with  it  when  the  body  sinks.  Let 
abed,  fig.  158,  be  a  homogeneous  solid, 
G  will  represent  the  centre  of  gravity 
of  the  body,  and  P  the  centre  of  buoy- 
ancy, or  upward  pressure,  situated  at 
the  centre  of  gravity  of  the  liquid  dis- 
placed. 

When  the  floating  body  is  not  homo- 
geneous the  centre  of  gravity  may  be 
below  the  centre  of  buoyancy,  as  in  the 
case  of  a  ship  having  ballast  or  heavy 
cargo  stowed  in  the  hold. 

Let  the  floating  body  take  the  position  shown  in  fig.  159,  the  force 
of  gravity  will  act  at  G  in  the  direc- 
tion G  r,  but  the  upward  pressure  will 
act  from  a  new  centre  of  buoyancy, 
P',  at  the  centre  of  gravity  of  the 
displaced  fluid,  and  in  the  direction 
P'  q.  This  force  being  equal  to  the 
force  of  gravity  and  parallel  to  it,  but 
acting  in  an  opposite  direction,  the 
two  forces  form  a  couple  (48),  and 
tend  to  rotate  the  body  till  the  two 
forces  again  act  in  the  same  vertical 
line. 

When  the  centre  of  .gravity  and  centre  of  buoyancy  are  in  the  same 
vertical  line,  the  floating  body  will  be  in  equilibrium. 

This  equilibrium  may  be  neutral,  or  the  same  in  any  position  of  the 
floating  body  ;  unstable  when  by  any  movement  of  the  body  the  centre 
of  gravity  descends  : — or  stable  equilibrium  when  movement  of  the  body 
in  any  direction  causes  the  centre  of  gravity  to  ascend. 

Neutral  equilibrium. — A  sphere  of  uniform  density  floating  in  a 
liquid  is  an  example  of  neutral  equilibrium,  because,  whatever  position 
it  may  assume,  the  part  immersed  is  a  segment  of  a  sphere  of  the  same 
magnitude  and  form,  and  no  alteration  can  be  effected  in  the  relative 
positions  of  the  centre  of  gravity  and  the  centre  of  buoyancy. 

Unstable  equilibrium. — Let  abed,  fig.  160,  represent  a  rectangular 
prism  of  uniform  density,  floating  on  one  end,  the  centre  of  gravity 
being  at  G,  and  the  centre  of  buoyancy  or  upward  pressure  being  at  P. 

Although  G  and  P  are  in  the  same  vertical  line,  it  is  evident  that  the 


OF   FLUIDS.  1(57 

equilibrium  will  be  unstable,  because  when  the  body  moves  to  any  new 
position,  as  at  fig.  161,  the  centre  of  gravity  descends. 
160  161 


Stable  Equilibrium. — The  centre  of  buoyancy,  or  centre  of  upward 
pressure,  may  be  considered  as  the  centre  of  support  of  a  floating  body. 
When  this  centre  is  above  the  centre  of  gravity,  the  body  will  evidently 
be  in  a  position  of  stable  equilibrium.  It  will  also  be  in  a  position  of 
stable  equilibrium  when  the  centre  of  gravity  occupies  a  lower  position 
than  it  would  acquire  in  any  other  position  of  the  floating  body.  But 
in  such  cases  the  stability  of  the  equilibrium  of  the  floating  body  is  more 
readily  understood  by  reference  to  another  point  called  the  metacentre. 

208.  The  metacentre  of  a  floating  body  is  the  point  where  the 
vertical  passing  through  the  centre  of  buoyancy,  in  the  position  of 
equilibrium,  meets  the  vertical  drawn  through  the  new  centre  of  buoyancy, 
when  the  body  has  been  slightly  displaced  from,  this  position. 

By  reference  to  figs.  158  and  159  it  will  be  seen  that  G  r'  or  G  q  is  the 
vertical  which  passes  through  the  centre  of  buoyancy  in  the  position  of 
stable  equilibrium,  and  Px  q  the  vertical  passing  through  the  centre  of 
buoyancy  when  the  body  is  moved  a  little  from  the  position  of  equili- 
brium ;  hence,  q  is  the  metacentre  related  to  the  position  of  stable  equi- 
librium, and  in  this  case  it  is  above  the  centre  of  gravity. 

Referring  to  figs.  160  and  161,  we  see  that  the  metacentre  is  at  g^'fig. 
161,  or  at  a  point  below  the  centre  of  gravity. 

The  metacentre  may  also  be  found  by  taking  the  point  of  intersection  of  ver- 
ticals passing  through  the  centres  of  buoyancy  in  any  two  positions  near  each 
other. 

A  floating  body  will  be  in  stable  equilibrium  whenever  the  meta- 
centre is  above  the  centre  of  gravity,  and  the  degree  of  stability  will 
be  in  proportion  to  the  distance  of  the  metacentre  above  the  centre  of 
gravity.  This  depends  on  the  form  of  the  floating  body. 

When  the  centre  of  gravity  is  below  the  centre  of  buoyancy,  the  metacentre 


168 


THE    THREE    STATES    OF    MATTER. 


must  evidently  always  be  above  the  centre  of  gravity,  and  this  condition  is 
always  stable.  It  is  also  evident  that  the  stability  of  a  floating  body  increases 
with  the  breadth  of  the  part  submerged.  These  principles  are  of  great  import- 
ance in  the  construction  and  loading  of  ships.  The  metacentre  may  be  regarded 
as  a  sort  of  fulcrum  above  which  is  the  pressure  of  the  sails,  and  below  the 
weight  of  the  ship. 

Vessels  designed  for  transporting  passengers  and  light  cargo  require  heavy 
ballast  of  iron  or  stone  placed  near  the  keel,  to  preserve  the  equilibrium.  On 
the  other  hand,  vessels  loaded  with  iron  have  the  centre  of  gravity  so  low  as  to 
cause  injurious  strain  upon  the  ship,  unless  the  cargo  is  elevated  by  cross  piling 
or  other  supports  to  raise  the  centre  of  gravity  so  as  to  allow  the  ship  to  roll 
easily  in  a  heavy  sea.  The  equilibrium  of  small  boats  is  from  the  same  cause 
often  disturbed  by  the  unguarded  movements  of  the  passengers.  The  rolling 
of  a  vessel  in  a  storm  may  so  shift  the  position  of  the  cargo,  and  thus  remove 
the  centre  of  gravity,  that  the  vessel  may  be  thrown  upon  her  beam-ends,  and 
be  lost. 

V.     DETERMINATION  OF  SPECIFIC  GRAVITY. 

209.  The  problem  stated. — Methods. — We  have  already  consi- 
dered the  relations  of  density  and  specific  weight  to  mass  and  weight 
(96-99).    Most  of  the  methods  in  use  to  determine  specific  gravity 
depend  on  the  principles  of  hydrostatics  just  considered,  and  serve  as 
illustrations  of  them.     The  problem  is : — 

To  compare  the  weight  of  any  body  whose  specific  gravity  is  sought 
with  the  weiglit  of  an  equal  volume  of  water  taken 
as  unity.     The  specific  gravity  is  found  by  dividing 
the  first  weight  by  the  second. 

Methods. — This  operation  is  performed  first, 
by  the  hydrostatic  balance ;  second,  by  the  specific 
gravity  bottle;  third,  by  various  floating  instru- 
ments called  hydrometers  or  areometers. 

All  these  methods  resolve  themselves  into  special 
cases  of  the  Theorem  of  Archimedes,  §  205. 

210.  Specific   gravity  by  the  hydrostatic 
balance. — The  solid  (heavier  than  water)  is  sus- 
pended beneath  the  pan  of  a  balance  by  means 
of  a  fine  filament  of  raw  silk,  and  then  weighed, 
hanging  in  air.     It  is  then  immersed  in  water  as 
in  fig.  162,  and  the  weight  it  loses  determined. 
This  loss  is  equal  (according  to  the  principle  of 
Archimedes)  to  the  weight  of  a  volume  of  water 
of  the  same  bulk  as  the  immersed  body.     Sub- 
tracting the  weight  of  the   substance  in  water 
from  its  weight  in  air,  and  dividing  the  latter 

by  the  difference,  the  product  will  be  the  specific  gravity  required. 


OF    FLUIDS.  1G9 

Example. — A  piece  of  iron  weighed  in  air  460  grains,  in  water  401-16  gra. 
Then  460 — 401-16  =  53-84  grs.,  which  equals  the  weight  of  a  volume  of  water 
equal  to  the  iron,  and  460  -f-  58-84  =  7-8  =  specific  gravity  of  the  iron. 

To  make  the  case  general,  let  JFbe  the  weight  of  the  body,  and  W 
the  loss  of  weight  in  water,  then  by  the  definition 

(Sp.  Gr.)  =  —• 

The  result  thus  obtained  is  always  to  be  reduced  to  a  standard  tem- 
perature. 

For  solids  lighter  than  water. — If  the  body  whose  specific  gravity 
is  to  be  determined  is  lighter  than  water,  it  must  be  attached  to  some 
solid  (whose  weight  in  air  and  in  water  is  known)  sufficiently  dense  to 
sink  it  in  water.  The  compound  mass  is  weighed  first  in  air,  and  then 
in  water,  and  the  loss  determined,  the  weight  lost  by  weighing  the 
heavy  body  alone  in  water  being  known,  the  weight  of  the  light  body 
in  air,  divided  by  the  difference  between  these  losses,  gives  the  specific 
gravity. 

Example. — A  substance  weighed  in  air  200  grains,  attached  to  a  piece  of 
copper  it  weighed  in  air  2247  grs.,  in  water  1620  grs.,  suffering  a  loss  of  627  grs. 
The  copper  itself  loses,  when  weighed  in  water,  230  grs.,  627  —  230  =  397,  then 

W  163 

Sp.  Gr.  =—  =  200  -v-  397  =  -504. 

For  liquids. — The  hydrostatic  balance  also  applies  to 
liquids  as  well  as  to  solids — whether  the  liquids  are  denser 
or  lighter  than  water. 

For  this  purpose  a  small  glass  tube  is  prepared,  including 
enough  mercury  to  sink  it  in  any  liquid  not  heavier  than 
mercury.  It  is  hermetically  sealed,  the  end  bent  into  a  hook, 
and  the  whole  suspended  by  a  very  thin  platinum  wire  from 
the  pan  of  a  balance.  Fig.  163  shows  this  apparatus  of  full 
size. 

The  weight  of  the  volume  of  water  which  this  system  dis- 
places at  60°  F.  (or  at  4°  C.)  is  first  determined  by  the  mode 
described  for  solids.  This  is  a  constant  quantity,  and  may 
be  called  C.  If  the  tube  is  now  immersed  in  another  liquid, 
as  in  alcohol  for  example,  it  will  require  a  certain  weight  to 
restore  the  equilibrium  (the  weight  of  the  tube  and  mercury 
is  supposed  to  be  counterpoised  in  each  case  by  a  constant 
weight  prepared  for  the  purpose).  The  amount  of  this 
weight,  W  (required  to  restore  the  equilibrium),  is  the  weight  of  a 
volume  of  the  liquid  displaced  by  the  tube.  But  the  weight  of  the 
17* 


170 


THE   THREE    STATES   OF   MATTER. 


same  volume  of  water  is  known  ((7.)   Hence  the  specific  gravity  of  the 
liquid  is  ^-. 

Example.— A  glass  tube,  like  fig.  163,  lost  in  water  2-9910  grains  =  0,  in 

W 

alcohol  it  lost  2-4081  =  W.  —  =  -80511  =  Sp.  Or.  of  the  alcohol. 

211.  Specific  gravity  bottle. — For  liquids. — When  it  is  required 
to  determine  the  specific  gravity  of  a  liquid,  the  specific  gravity  bottle 
offers  the  easiest  and  most  simple  method.  Such  164 

a  bottle  is  shown  in  fig.  164.  It  is  closed  by  a 
ground  glass  stopper,  and  the  neck  is  drawn  out 
to  a  fine  tube  (the  upper  portion  of  which  serves 
for  a  funnel  in  filling  the  bottle),  upon  which,  at 
A,  is  traced  a  fine  line  to  which  the  bottle  is  to  be 
filled  at  each  experiment.  The  tare  of  the  bottle 
is  accurately  determined  and  noted  once  for  all. 
It  is  then  filled  to  A  with  pure  water  and  weighed 
again.  This  weight  less  the  tare  gives  its  capacity 
of  water  at  a  fixed  temperature.  To  determine 
the  specific  gravity  of  any  other  liquid,  the  bottle 
is  filled  with  it  and  weighed  as  before.  Deducting 
the  tare  of  the  bottle,  we  now  know  the  weight  of 
a  volume  of  the  liquid  equal  to  the  same  volume 
of  water.  Representing  these  two  weights  by  W 

W 
and  W,  we  have  (Sp.  Gr.)  —  •=.      In  all  cases, 

the  result  must  be  reduced  to  a  standard  tempera- 
ture as  described  in  the  Chapter  on  Heat. 

For  solids,  when  broken  in  small  fragments, 
we  may  also  use  the  specific  gravity  bottle.  In  this  case  the  weight 
of  the  bottle  when  empty,  and  also  when  filled  with  pure  water,  being 
known,  a  known  weight  of  the  solid  in  fragments  is 
introduced,  as  in  fig.  165.  Calling  the  weight  of  the 
bottle  and  water  =  Wa,  and  the  weight  of  the  solid  added 
W,  and  the  weight  of  the  bottle  solid  and  water  Wb,  it  is 
plain  that  the  weight  of  water  displaced  by  the  solid  is 
W  =  Wa  -f  W  —  Wb,  and  that  the  specific  gravity  of 
the  solid  is 

W 

^  P'     r''  ~~ =  Wa  +  W—  Wb' 

This  value  must  be  corrected  for  temperature  as  before. 
For  solids  soluble  in  water  we  must  employ  some  liquid 


OF    FLUIDS. 


172 


m  which  the  substance  is  insoluble,  as  alcohol,  oil  of  turpentine,  &c. 
The  specific  gravity  thus  determined  is  reduced  to  the  standard  of  water 
by  multiplying  it  by  the  known  density  of  the  liquid  employed ;  thus,  for 

Example. — A  substance  soluble  in  water  was  weighed  in  oil,  and  its  specific 
gravity,  compared  with  the  oil,  was  2-6,  the  specific  gravity  of  the  oil  was  -87; 
then  2-6  x  '87  =  2-262  the  specific  gravity  of  the  substance. 

212    Specific    gravities    by   hydrometers   or   areometers. — In 

this  mode  the  balance  is  replaced  by  floating  bodies  called  hydrometers 
or  areometers.  There  are  two  classes  of  these  instruments,  namely, 
first,  hydrometers  with  a  constant  volume ;  and,  second,  hydrometers  with 
a  constant  weight. 

^1.  Nicholson's  hydrometer  or  areometer  is  an  instrument  of  the 
first  class,  used  for  determining  the  specific  gravity  of  solids.  It  consists 
of  a  hollow  cylinder  of  metal  or  glass,  B,  fig.  1G6,  having  attached  at 
its  lower  end  a  cone,  C,  loaded  with  lead,  which  causes  the  apparatus 
to  assume  an  upright  position  when  placed  in  water.  166 

The  upper  part  of  the  cylinder  is  terminated  by  a 
slender  rod,  on  the  end  of  which  is  a  small  pan,  A, 
for  holding  weights.  The  whole  apparatus  must 
have  a  less  specific  gravity  than  water,  so  that  a 
certain  weight,  represented  by  C,  must  be  put  in  the 
pan  to  sink  the  areometer  to  the  water  mark,  0.  If 
we  wish  to  determine  the  specific  gravity  of  a  solid 
(whose  weight  must  be  less  than  C},  we  place  it  in 
the  pan  A,  and  add  weights  until  0  is  brought  to 
the  level  of  the  water.  The  weight  C,  minus  the 
weights  last  added,  will  be  the  weight  of  the  body 
in  air.  It  is  now  taken  from  A,  and  placed  in  C  ;  the 
additional  weight  now  required  to  sink  the  cylinder 
to  the  index,  0,  will  be  the  weight  lost  in  water. 
We  have  now  the  data  for  determining  the  specific  gravity  of  the  solid. 
For  example,  if  the  counterpoise  weighed  250  grs.,  and  a  mass  of 
lead  whose  specific  gravity  we  wish  to  ascertain,  requires,  when  placed 
in  A,  50  grs.  to  be  added  in  order  to  bring  the  hydrometer  to  the  point 
0,  then  (250 — 50)  200  is  the  weight  of  the  lead  in  air ;  placing  now 
the  lead  on  C,  we  find  that  it  requires  the  addition  of  17'47  grs.  on  A, 
in  order  to  counterbalance  the  instrument ;  consequently  the  specific 
gravity  of  the  lead  is  11'45.  T27°f  T  =  u'45-  If  the  substance  is  lighter 
than  water,  it  is  confined  under  a  perforated  cover  or  wire  cage  placed 
DD  0,  which  prevents  its  rising. 


172  THE    THREE    STATES    OF    MATTER. 

If  we  represent  these  successive  weights  by  C,  W,  and  W,  then  in 
any  case 

f rxr 

(8p.G,:)=-W7-. 

a.  Fahrenheit' a  ^hydrometer  is  the  same  instrument  (omitting  the  lower  pan) 
constructed  of  glass  and  designed  to  measure  the  specific  gravity  of  liquids. 
Knowing  (by  the  balance)  the  constant  weight  (C)  of  the  instrument,  and  also 
the  weight  (c)  required  to  sink  it  to  a  fixed  point  on  the  stem — the  sum  of  which 
weights  (by  210)  is  equal  to  the  weight  of  the  water  displaced.  We  have  only 
to  float  it  in  any  liquid  whose  specific  gravity  we  would  ascertain,  and  note  the 
weight,  W,  required  to  sink  it  to  the  fixed  point  on  the  stem.  The  weight  of 
the  liquid  displaced  is  then  C  -f-  W,  and  since  0  -\-  c  and  C  -f-  W  are  the 
weights  of  equal  volumes  of  water  and  of  the  liquid,  the  specific  gravity  of  the 
liquid  is  found  by  dividing  the  latter  by  the  former,  or  (Sp.  Gr.)  =  (C  -{-  W)  -^- 
(C-l-c.)  * 

l>.  Ilousseaii' a  hydrometer  is  a  form  of  this  instrument  adapted  to  determining 
the  specific  gravities  of  liquids  of  which  we  possess,  too  small  a  portion  to  float  a 
common  hydrometer.  For  this  end,  a  cup  of  glass  replaces  the  pan  A,  which  holds 
say  one  cubic  centimetre.  Thus  loaded,  the  instrument  sinks  to  a  point  marked 
20°  near  the  middle  of  the  stem.  The  stem  is  divided  between  this  point  and 
zero  into  twenty  equal  parts,  each  of  which  consequently  measures  one-twentieth 
of  a  gramme  or  0-05  gramme.  The  specific  gravity  of  a  liquid  is  then  found  by 
this  instrument  by  multiplying  0-05  by  the  number  of  the  division  to  which  it 
sinks  when  loaded  with  one  cubic  centimetre  of  the  liquid  used. 

2.  Gay  Lussac's  and  Beaume's  hydrometers  are  instruments 
having  a  constant  weight,  and  by  which  we  determine  the  specific 
gravity  of  a  liquid  by  measuring  the  volume  of  fluid  displaced  by  the 
floating  instrument — which  weight,  as  we  have  seen,  is  the  same  as  the 
weight  of  the  instrument  itself.  But  we  have  shown  (99),  that  for 
equal  absolute  weights  the  specific  weight  is  inversely  as  the  volume  or 
(Sp.  Gr.}  =  V/  -r-  V,  where  V  equals  the  volume  of  water  displaced  by 
the  instrument,  and  Fthe  volume  of  any  other  liquid  displaced  by  it. 
In  other  words,  we  can  find  the  specific  gravity  of  any  liquid  by  divid- 
ing the  volume  of  a  given  weight  of  water  by  the  volume  of  the  same 
weight  of  the  liquid  whose  specific  gravity  is  required. 

Instruments  of  this  class  are  very  common  and  in  constant  use  for 
determining  the  specific  gravity  of  alcohol,  acids,  alkaline  solutions, 
urine,  milk,  and  many  other  liquids.  Figs.  167  and  168  show  the  form 
of  Gay  Lussac's  densimeter,  as  it  is  often  called.  It  is  a  glass  tube  con- 
taining enough  mercury  in  the  lower  end  to  cause  the  tube  to  float  in 
pure  water  at  the  hundreth  division  of  a  scale  of  equal  parts  traced  or. 
paper  and  sealed  up  inside  the  tube.  If  it  displaces  100  measures  of 
water,  floated  in  sulphuric  acid  it  displaces  only  54  measures,  and 
therefore  the  specific  gravity  of  sulphuric  acid  is  100  -f-  54  =  1'85. 


OF    FLUIDS. 


173 


to  166 
Then 
168 


100 


For  fluids  lighter  than  water,  the  graduation  is  carried  up  say 
(as  we  know  of  no  liquid  of  a  less  specific  gravity  than  0'60). 
placed  in  pure  alcohol  it  rises  say  to  125  degrees,  or       jgy 
the  specific  gravity  of  alcohol  is  100  -*-  125  =  0'80. 

By  giving  the  instrument  the  form  shown  in 
fig.  168,  much  needless  length  is  saved  on  the 
stem,  since  the  ball  is  so  placed  as  to  be  always 
immersed,  and  its  buoyancy  is  equal  to  that  of  a 
much  greater  length  of  tube.  The  scales  are  also 
usually  divided  among  the  instruments — one  for 
liquids  lighter  than  water,  one  for  specific  gravities 
from  I*  to  1'33  (corresponding  to  100  to  75),  and 
another  reading  from  75  (corresponding  to  1'33)  at 
the  top  down  to  50  (corresponding  to  2'06)  near  its 
middle.  These  instruments  are  not  of  scientific  accu- 
racy, but  are  ready  modes  of  determining  off-hand 
the  approximate  specific  gravity  of  a  given  liquid. 

The  scales  of  Beaume"  (that  most  in  use),  as  well 
as  those  of  Cartier  and  Beck,  are  purely  arbitrary. 
Table  V.  at  the  end  this  volume  shows  the  corres- 
pondence of  their  degrees  to  real  specific  gravities. 

Table  VI.  gives  the  specific  gravity  of  some  of  the 
more  frequently  occurring  liquids  and  solids. 

§  2.    Hydraulics. 

I.     MOTION    OF    LIQUIDS. 

213.  Definition. — Hydraulics  (from  the   Greek  vdtap,  water,  and 
•j.oXo$,  a  pipe),  is  that  part  of  hydro-dynamics  which  treats  of  the  flow 
and  elevation  of  liquids,  especially  water,  and  the  construction  of  all 
kinds  of  instruments  and  machines  for  moving  them,  or  to  be  moved  by 
them.     Hero  of  Alexandria  (about  130  B.  c.)  appears  to  have  been 
the  earliest  author  on  this  subject. 

214.  Pressure  of  liquids  upon  the  containing  vessel. — A  vessel 
filled  with  water,  or  any  other  liquid,  and  closed,  is  subject  to  two  pres- 
sures acting  in  opposite  directions:  namely,  1.  The  atmospheric  pres- 
sure, acting  from  without  inwards  ;  and  2.  The  pressure  of  the  column 
of  contained  liquid  acting  against  the  walls.     If  a  vessel  so  situated  is 
pierced,  and  the  pressure  from  within  outwards  is  stronger  than  the 
external  pressure,  the  liquid  will  flow  out ;  but  if  the  external 

is  the  stronger,  the  liquid  will  not  escape. 


174 


THE    THREE    STATES    OF    MATTER. 


170 


Thif  statement  may  be  illustrated  by  filling  a  glass  vessel,  as  a  wine-glass, 
with  water,  placing  a  piece  of  paper  over  its  top,  and  supporting  the  paper  with 
the  hand,  at  the  same  time  inverting  the  glass ;  then  removing  the  hand  from 
the  paper  and  holding  the  glass  inverted,  the  fluid  will  not  escape,  the  external 
(atmospheric)  pressure  against  the  paper  being  greater  than  the  weight  of  the 
column  of  water  pressing  downwards. 

The  mass  of  liquid  escaping  from  an  orifice  in  a  vessel,  is  called  a 
vein. 

215.  Appearance  of  the  surface  during  a  dis-  169 
charge.— The  surface  of  a  liquid,  discharging  itself 

from  an  orifice  in  a  containing  vessel,  does  not  usually 
remain  horizontal. 

When  the  vein  issues  from  an  opening  in  the  bottom 
of  the  vessel,  and  the  level  of  the  liquid. is  near  the  ori- 
fice, a  funnel-shaped  depression  is  found  in  the  liquid, 
fig.  169.  If  the  liquid  has  a  rotatory  movement,  the 
funnel  is  formed  sooner  than  if  it  is  at  rest.  If  the 
orifice  is  at  the  side  of  the  vessel,  there  is  a  depression 
of  the  surface  upon  that  side,  above  the  orifice,  fig. 
173.  These  movements  depend  upon  the  form  of  the 
vessel,  the  height  of  the  liquid  in  it,  and  the  dimensions 
and  form  of  the  orifice. 

216.  Theoretical  and  actual  flow. — The  actual 
flow  from   an  orifice,  is  the  volume   of  liquid  which 

escapes  from  it  in  a  given  time.  The  theoretical  flow  is  a  volume 
equal  to  that  of  a  cylinder  which  has  for  its  base  the  orifice,  and  for  its 
height  the  velocity,  furnished  by  the  theorem  of  Torricelli.  That  is, 
the  theoretical  flow  is  the  product  of  the  area  of  the  orifice  multiplied 
by  the  theoretical  velocity. 

It  is,  however,  observed  that  the  vein  escaping  from  an  orifice,  con- 
tracts quite  rapidly,  so  that  its  diameter  is  soon  only  about  two-thirds 
of  the  diameter  of  the  orifice.  If  there  was  no  contraction  of  the  vein 
after  leaving  the  orifice,  and  its  velocity  was  the  theoretical  velocity, 
the  actual  flow  would  be  the  same  as  that  indicated  by  theory.  But  the 
section  of  the  vein  is  soon  much. less  than  at  the  orifice,  and  its  velocity 
is  not  so  great  as  the  theoretical  velocity,  so  that  the  actual  is  much 
less  than  the  theoretical  flow ;  and,  in  order  to  reduce  this  to  the  first, 
it  is  necessary  to  multiply  it  by  a  fraction  which  is  named  "  the  co-effi- 
cient of  contraction." 

From  comparative  experiments,  made  by  a  great  number  of  observers, 
the  actual  flow  has  beea  determined  to  be  only  about  two-thirds  of  the 
theoretical  flow. 


OF   FLUIDS. 


175 


Practically,  the  flow,  F,  in  a  unit  of  time,  is  calculated  by  the  formula  F  = 
»»  v  a,  where  m  is  a  constant,  representing  the  ratio  between  the  actual  and  theo- 
retical velocity  or  flow  ;  in  other  words,  between  the  area  of  the  orifice  and  the 
area  of  the  section  of  greatest  contraction  in  the  vein.  This  coefficient  of  con- 
traction, m  =  0-62;  and  thus  the  above  formula  becomes 

F  =  0-62. 


=  the  sectional  area  of  the  orifice. 

The  contraction  of  the  vein  is  most  noticeable  in  downward  flowing 
jets.     If  the  jet  is  thrown  upwards,  at  an  angle 
of  25°  to  45°,  the  vein  preserves  its  own  diameter  ; 
but  if  it  surpasses  45°,  its  section  increases. 

By  suspending  solid  particles  in  the  water,  the  cur- 
rents that  are  formed  by  an  escaping  vein  are  made 
visible.  The  solid  particles  direct  themselves,  in  curved 
lines,  towards  and  into  the  orifice,  as  a  centre  of  attrac- 
tion, fig.  171.  The  particles  in  immediate  contact  with 
the  orifice,  owing  to  friction,  not  moving  so  easily  as 
those  near  the  axis,  contraction  must  result;  we  can  see 
also,  that  gravity,  by  accelerating  the  velocity,  must  cause  continual  decrease 
in  the  section  of  the  jet. 

217.  Reaction  of  the  escaping  vein.  —  Barker's  mill.  —  When  a 
jet  of  liquid  escapes  from  an  orifice  in  a  containing  vessel,  the  pressure 
of  the  liquid  upon  the  walls  at  the  point  of  172 

escape  finding  no  counteracting  force,  the 
horizontal  component  of  the  column  is  not  de- 
stroyed as  when  the  opening  is  closed  ;  and  this 
force  reacts  to  thrust  the  vessel  in  a  direction 
opposite  to  that  of  the  escaping  vein. 

This  reaction  is  made  sensible  by  suspend- 
ing the  containing  vessel  on  a  free  vertical 
axis,  as  in  the  apparatus  known  as  Barker's 
Mill,  fig.  172.  The  orifices  of  escape  for  the  vein 
are  here  in  the  ends  of  a  horizontal  pipe  bent 
at  right  angles,  and  in  opposite  directions, 
formed  as  seen  at  AB,  where  the  arrow 
shows  the  point  of  reaction  of  the  escaping 
vein  upon  the  end-wall  of  the  tube. 

It  might  be  supposed,  as  was  assumed  by  Newton,  that  the  moving 
force  in  this  case  was  only  the  horizontal  component  of  a  force  equal 
to  a  column  of  liquid  whose  base  was  equal  to  the  area  of  the  orifice, 
and  whose  height  was  the  distance  of  its  centre  of  gravity  from  the 


176  THE   THREE    STATES    OF    MATTER. 

level.  But  the  effects  from  pressure  are  not  the  same  for  a  liquid  in 
motion  as  when  in  equilibrium  ;  and  D.  Bernoulli  has  demonstrated  — 

That  it  is,  in  this  case,  requisite  to  estimate  the  force  of  reaction  as 
double  the  height  of  the  liquid  above  the  centre  of  gravity  of  the  orifice. 

This  principle  is  applied  in  the  construction  of  reaction  water- 
wheels. 

218.  Plow.  —  The  volume  of  liquid  escaping  in  a  given  time  from  an 
orifice  is  called  its  flow.     This  depends  on  the  size  of  the  opening  and 
the  velocity  of  the  jet.     Assuming  the  motion  of  the  jet  to  be  uniform 
for  a  given  time,  say  one  second,  the  distance  passed  over  by  an  escap- 
ing molecule  in  this  time  is  called  its  velocity.     The  velocity  depends 
chiefly  on  the  height  of  the  liquid  above  the  centre  of  gravity  of  the 
orifice  ;  this  height  is  called  the  head  or  column. 

The  velocity  of  flow  is  modified  among  other  causes  also  by  the  friction  of  the 
liquid,  both  at  the  opening  and  against  the  walls.  When  the  aperture  is  made 
in  a  very  thin  wall  of  a  large  vessel,  so  as  to  reduce  as  much  as  possible  the 
causes  tending  to  modify  the  motion  of  the  escaping  fluid,  the  laws  of  the  escape 
are  comprised  in  the  following  theorem,  announced  by  Torricelli,  in  1643,  as  a 
consequence  of  the  law  of  falling  bodies  discovered  by  Galileo. 

219.  Theorem  of  Torricelli.  —  Liquid  molecules,  flowing  from  an 
orifice,  have  the  same  velocity  as  if  they  fell  freely  in  vacuo,from  a  height 
equal  to  the  vertical  distance  from  the  surface  of  the  liquid  to  the  centre 
of  gravity  of  the  orifice. 

If  .Ef  represents  the  height  of  the  head  above  the  centre  of  gravity 
of  the  orifice,  then  the  velocity  is  expressed  by  the  formula 


Deductions  from  the  Torricellian  Theorem.  —  1.  The  velocity 
depends  on  the  depth  of  the  orifice  from  the  surface,  and  is  independent 
of  the  density  of  the  liquid. 

Water  and  mercury  in  vacuo  would  fall  from  the  same  height  in  the 
same  time  ;  and  so  escaping  from  an  orifice  at  the  same  depth,  below 
the  surface,  would  pass  out  with  equal  velocity  ;  but  mercury  being  13'5 
times  as  heavy  as  water,  the  pressure  exerted  at  the  aperture  of  a  vessel 
filled  with  mercury,  will  be  13  '5  times  as  great  as  the  pressure  exerted 
at  the  aperture  of  a  vessel  filled  with  water. 

2.  The  velocity  of  flow  of  liquids  from  an  orifice  is  as  the  square  roots 
of  the  head. 

Thus,  stating  the  velocity  of  a  liquid  escaping  from  an  orifice  one  foot 
below  the  surface,  to  be  one;  from  a  similar  orifice,  four  feet  below  the 
surface,  it  will  be  two;  and  at  nine  feet,  three;  at  sixteen  feet,/owr  /  and 
soon. 


OF   FLUIDS. 


177 


Let  H  represent  the  height  of  the  liquid  above  the  orifice,  g  the  accelerating 
force  of  gravity,  and  v  the  velocity  of  discharge ;  we  shall  have  v  =  -i/^T 

220.  Demonstration  of  the  theorem  of  Torricelli.— The  theorem 
of  Torricelli  may  be  demonstrated  by  means  of  the  apparatus  shown 
at  fig.  173. 

A  cylindrical  vase,  a  c,  enlarged  into  a  reservoir  at  the  top,  is  filled  with  water. 
In  the  side  of  the  vase  are  orifices,  k,  I,  »<,  n,  o,  so  situated  that  m  is  at  the 
centre  of  a  c,  and  k  and  o  are  equidistant  173 

from  m,  as  are  also  I  and  n.  Let  x  repre- 
sent the  horizontal  range  of  a  spouting 
jet,  and  y  the  height  of  the  orifice  ahove 
the  horizontal  line  a  &,  let  H  be  the 
height  of  the  water  above  the  orifice, 
and  a  the  angle  of  elevation  of  the  direc- 
tion of  the  jet  as  it  issues  from  the  orifice  : 
then  by  the  laws  of  falling  bodies  (71), 
combined  with  the  laws  of  projectiles 
(103)  we  shall  have 

x  •=  vt  cos.  a,  and  y  =  ^gt* — vt  sin.  a. 
Eliminating  t  from  these  equations,  we 
obtain 


(M      y  = 


gx* 


20s 


— x  tang.  a. 


When  the  water  issues  horizontally  from 


gx 

-  —  —  , 
2v 


and 


the  orifice,  a  becomes  zero  and  y  = 


(2.) 


The  values  of  x  and  y  being  determined  by  observation  in  any  case,  the  value 
of  v,  or  the  velocity  with  which  the  jet  issues  from  the  orifice,  is  readily  calcu- 
lated by  formula  (2).  This  velocity  is  found  to  accord  very  nearly  with  the 
velocity  which  a  body  would  acquire  in  falling  freely  from  a  height  equal  to  the 
head  of  the  fluid  above  the  orifice. 

Bossuet  found  by  using  mercury  that  the  variation  from  this  value  of  v  was 
less  than  one  hundredth  part  of  the  velocity. 

There  is  a  remarkable  consequence  of  this  law  which  may  easily  be 
verified  by  experiment.  In  the  formula  for  the  value  of  x  replacing  v 
by  its  value 


(a).  The  value  of  x  is  the  greatest  possible  when  H=  y  =  $ac,  as  is 
shown  in  the  figure,  where  the  jet  issuing  from  the  centre  of  the  cylinder 
has  a  greater  range  than  any  jet  either  above  or  below  the  centre. 

(b).  Since  y  =  ac  —  H,  the  values  of  y  and  H  may  be  interchanged 
without  altering  the  value  of  x;  that  is,  two  jets  issuing  from  orifices  at 
equal  distances  above  and  below  m  meet  the  horizontal  line  ab  at  the 
18 


178  THE   THREE    STATES   OP   MATTER. 

same  point  as  is  shown  in  the  figure  where  the  jets  issuing  from  Jc  and 
o  have  the  same  range,  and  also  the  jets  I  and  n. 

The  value  of  x  and  y  being  determined  by  observation,  the  value  of  v,  or  the 
velocity  of  the  jet,  becomes  known  by  the  formula  (2). 

221.  The  inch  of  water  named  by  hydraulic  engineers  as  the  unit 
of  measurement  in  the  scale  of  water,  is  the  volume  of  water  which 
escapes  in  a  given  time,  say  one  minute,  through  an  orifice  of  one  inch 
diameter  whose  centre  is  one  and  one-twelfth  inches  below  a  constant 
surface. 

PRONY  has  harmonized  this  unit  with  the  French  metrical  system  by  employ- 
ing a  pipe  of  two  centimetres  internal  diameter  and  17  millimetres  long,  under  a 
head  of  two  centimetres.  He  preserves  the  term  inch  of  water,  restricting  it  to 
the  quantity  of  water  escaping  in  one  minute  from  such  an  opening,  equal  to 
13p333  litres,  or  11*766  quarts.  In  24  hours  this  orifice  will  furnish  20  cubic 
metres,  equal  to  4,402  gallons  English  measure. 

222.  Constitution  of  liquid  veins. — The  form  and  constitution 
of  liquid  veins  have  been  studied  by  a  great  number  of  experimenters. 
The  results  of  F.  Savart,  and  more  lately  of  G.  Magnus  (Poggendorff 
Annalen,  cvi.,  p.  1),  are  those  here  given. 

It  is  determined,  1.  That  if  a  liquid  vein  issues  quite  calmly  and 
vertically  downwards,  from  a  circular  orifice  in  a  plane  and  thin  hori- 
zontal wall,  no  movement  of  rotation  existing  in  the  mass  of  the  liquid, 
euch  a  stream  forms  a  continuous  perfectly  smooth  cylindrical  mass, 
the  diameter  of  which  diminishes  with  the  distance  from  the  orifice  to 
the  point  where  disintegration  commences.  From  this  point  the  vein 
assumes  a  turbid  appearance,  enlarges  in  diameter,  and  commences  to 
spirt  off  small  drops  laterally. 

2.  If  the  mass  of  liquid  is  in  rotation  in  the  vase,  or  any  cause  of 
vibration  exists,  as  from  the  sounding  of  a  musical  note,  then  the  vein 
is  separated  into  two  distinct  parts,  fig.  174.     The  portion  nearest  the 
orifice  is  calm  and  transparent,  like  a  rod  of  glass,  gradually  decreasing 
in  diameter.     The  second,  on  the  contrary,  is  constantly  agitated,  and 
takes  an  irregular  form,  in  which  are  distributed,  at  regular  distances, 
elongated    swellings,    called   "  ventral    segments,"   whose    maximum 
diameter  is  greater  than  that  of  the  orifice :  while  the  position  of  the 
first  swelling  is  always  much  nearer  the  orifice  than  the  point  where 
the  jet  without  swellings  commences  to  become  turbid. 

Magnus  found  that  the  best  means  to  produce  these  "  ventral  segments"  were 
a  large  tuning  fork  sounding  C  below  the  line — and  the  monotonous  hum  of  the 
magnetic  hammer  or  break-piece  used  in  electro-magnetic  apparatus. 

3.  The   swellings   consist  of  separate  isolated  masses  of  water,  as 
shown  in  fig.  175.     However  regular  their  external  form  may  be,  they 
are  still  formed  of  separate  masses,  as  may  be  readily  distinguished  by ' 


OF    FLUIDS. 


179 


174 


175 


holding  a  piece  of  wire  in  the  hand  so  that  one  of  its  ends  penetrates 
a  little  way  into  the  jet.  A  uniform  pressure  is  felt  when  the  wire 
is  struck  by  the  smooth  part  of  the  stream,  but 
when  struck  by  a  swelling  a  strong  vibratory  and 
intermitting  motion  is  felt.  The  separate  masses 
of  water  forming  the  swelling,  clearly  communi- 
cate this  motion  to  the  air,  and  thus  disturb  the 
flame  of  a  gas  jet  brought  near  them,  which  the 
smooth  part  of  the  stream  does  not  do. 

Savart  found  that  the  swellings  are  formed  of 
disseminated  globules,  elongated  in  the  transverse 
direction  of  the  vein,  and  that  the  contractions  or 
knots  are  formed  of  globules,  elongated  in  the 
longitudinal  way,  fig.  175 :  also  that  the  limpid 
part  of  the  vein  is  formed  of  annular  swellings 
which  originate  very  near  the  orifice,  propagating 
themselves  at  unequal  intervals  to  the  troubled 
part,  where  they  separate,  of  the  same  form  at  the 
instant  of  their  separation,  but  changing  periodi- 
cally. 

4.  The    "  ventral    segments"    are    produced  by 
the   vibration  of  the   orifice   through   which    the 
water  flows,  and   they  change  with   the  strength 
of  the  note  producing   the  vibration,  as  well  as 
with  the  diameter  of  the  orifice. 

The  vein  itself  occasions  a  tone,  partly  be- 
cause its  single  separate  masses  of  water  set  the 
adjacent  air  in  motion,  but  especially  by  the 
impact  of  these  masses  upon  some  sonorous  or  elastic  substance.  Where 
the  orifice  is  made  of  caoutchouc,  and  this  is  carefully  insulated  by  woolen 
pads  from  the  bottom  of  the  vase,  not  even  the  loud  tone  of  a  heavy 
tuning  fork  on  a  sounding  box  (377)  sufficed  in  Magnus's  experiments  to 
cause  the  production  of  ventral  segments.  Without  such  precautions 
they  are  often  set  up  spontaneously  by  vibrations  communicated  from 
the  falling  stream  through  the  solid  parts  of  the  apparatus. 

To  observe  the  constitution  of  the  swellings,  Magnus  used  a  revolving  card 
perforated  by  a  narrow  radial  slit,  like  the  toy  known  as  the  anorthoscope, 
illuminating  the  stream  by  a  lamp,  but  the  details  of  his  results  exceed  our  space. 

5.  If  the  vein  flows  from  a  very  small  orifice  (less  than  a  millimetre), 
the  small  drops  into  which  the  stream  breaks  up  move  quite  irregularly. 
But  on  sounding  a  note  the  drops  arrange  themselves  in  groups  with 
great  regularity — a  certain  number  always  follow  each  other  imme- 


180  THE   THREE    STATES   OF    MATTER. 

diately — a  somewhat  greater  interval  succeeds,  and  then  the  former 
grouping  of  drops  occurs  again. 

So  in  a  stronger  stream,  under  the  power  of  a  harmonious  note,  the  swellings 
and  knots  assume  more  regularity,  and  usurp  the  transparent  part,  which  almost 
entirely  disappears — the  flow  of  the  liquid  from  the  orifice  remaining  the  same 
as  at  first. 

6.  The  constitution  of  veins  thrown  out  in  any  direction  is  essentially 
the  same ;  but  the  number  of  pulsations  is  diminished  in  proportion  as 
the  vein  is  projected  more  vertically  upwards. 

223.  Escape  of  liquids  through  short  tubes. — Short  tubes  (called 
adjutages]  are  often  placed  in  an  orifice  to  increase  the  flow.    They  are 
either  cylindrical  or  conical.    If  the  vein  pass  through  the  tube  without 
adhering  to  it,  the  flow  is  not  modified ;  if  the  vein  adhere  (the  liquid 
wetting  the  interior  walls),  the  contracted  part  is  dilated,  and  the  flow 
increased.    In  the  last  case,  and  with  a  cylindrical  adjutage,  its  length 
not  being  more  than  four  times  its  diameter,  the  flow  is  augmented 
about  one-third. 

Conical  adjutages  converging  towards  the  exterior  of  the  reservoir, 
increase  the  flow  still  more  than  the  preceding,  the  flow  and  velocity  of 
the  vein  varying  with  the  angle  of  convergence.  Conical  adjutages 
diverging  towards  the  exterior,  give  the  greatest  flow.  They  may  give 
a  flow  2 — 4  times  as  great  as  that  which  an  orifice  of  the  same  diameter 
in  a  thin  wall  furnishes,  and  1*46  times  greater  than  the  theoretical 
flow. 

Practically,  the  flow  during  a  second  from  cylindrical  adjutages  of  a  length 
three  and  a  quarter  times  the  diameter,  is  found  by  the  formula, 

F  =  0-82  8i/2gH  =  3-62  »|///;  «  being  the  area  of  the  tube  and  #the  head. 

224.  Escape  of  liquids  through  long  tubes. — When   a  liquid 
passes  through  a  long  straight  tube,  the  velocity  of  the  flow  soon  dimi- 
nishes greatly  owing  to  the  friction  between  the  liquid  particles  and 
the  walls.    Bends  or  curves  in  the  tube  increase  the  loss  in  velocity,  for 
the  same  reason.     The  discharge  thus  becomes  very  much  less  than  it 
would  be  from  an  orifice  in  a  thin  wall,  and  to  obviate  this  evil  the  tube 
is  generally  inclined  ;  the  liquid  then  passes  down  an  inclined  plane,  or 
it  is  forced  through  by  pressure,  applied  at  the  opposite  end. 

Formulae. — The  discharge,  D,  per  second  through  straight  tubes  of  uniform 
diameter  entirely  open  at  the  end  may  be  determined  by  the  formula, 


in  which  //  is  the  height  of  the  water  above  the  orifice  of  discharge,  d  the 


FLUIDS. 


181 


diameter,  and  I  the  length,  of  the  tube.  All  these  quantities  are  to  be  taken  in 
metres.  The  formula  gives  the  value  of  D  in  cubic  metres,  which  may  be  reduced 
to  "  inches  of  water"  (221)  by  multiplying  the  result  by  75.  This  formula  was 
deduced  from  the  experiments  of  Eytelwein.  When  the  tube  is  very  long,  we 
may  neglect  54d  as  very  small  in  comparison  with  I,  and  the  formula  to  deter- 
mine the  diameter  required  to  discharge  a  given  volume  of  liquid  is, 

d  =  0-298 


The  velocity  of  the  discharge  is  given  by  the  formula, 


For  long  tubes  the  term  54c?  may  be  neglected,  and  modifying  the  coefficient 
to  correspond  with  the  results  obtained  by  Prony  with  tubes  2280  metres  long. 


v  =  26-79 


225.  Jets  of  water. — As  the  velocity  of  a  liquid  escaping  from  an 
orifice  is  the  same  as  that  which  a  body  acquires  falling  from  a  height 
equal  to  the  distance  from  the  surface  of  the  liquid  to  the  orifice,  a  jet 
of  water  spouting  upwards,  should  rise  to 

the  level  of  the  liquid  in  the  reservoir.  But 
this  never  quite  takes  place,  fig.  176,  be- 
cause of — 1st,  the  friction  in  the  conducting 
tubes  destroying  the  velocity — 2d,  the  re- 
sistance of  the  air — 3d,  the  returning  water 
falling  upon  that  which  is  rising.  The 
height  of  the  jet  is  increased  by  having  the 
orifices  very  small,  in  comparison  with  the 
conducting  tube ;  piercing  them  in  a  very 
thin  wall,  and  inclining  the  jet  a  little,  thus 
avoiding  the  effect  of  the  returning  water. 

It  has  been  determined  that  the  differences  between  the  height  of  vertical  jets 
and  that  of  the  reservoirs  are  approximately  as  the  squares  of  the  height  of  the 
jets.  Experiment  has  assigned  the  number  0-01  as  the  coefficient,  and  the  for- 
mula which  gives  the  height,  h,  of  a  jet  under  a  head  represented  by  H,.ia 
H  —  h  =  0-01A2  : — the  unit  of  measure  being  the  French  metre. 

If  air  is  mingled  in  the  water,  the  mixture  being  lighter  than  water,  the  jet 
can  be  made  to  rise  higher  than  its  source. 

226.  Pressure  exerted  by  liquids  in  motion. — When  a  liquid  is 
in  motion,  either  in  a  conduit  tube  or  an  adjutage,  the  pressure  it  exerts 

18* 


182 


THE    THREE    STATES    OF    MATTER. 


on  the  walls  is  not  the  same  as  it  is  in  equilibrium,  and  generally  it  is 
less,  as  the  velocity  of  flow  is  greater. 

If  the  effective  velocity  is  177 

equal  to  theory,  the  interior 
pressure  upon  the  walls  of 
the  adjutage  will  be  equal  to 
the  statical  pressure  in  a 
state  of  equilibrium.  As  the 
effective  velocity  increases, 
the  interior  pressure  upon 
the  walls  of  the  adjutage 
becomes  less  than  the  pres- 
sure in  a  state  of  equilibrium,  and  it  may  even  become  less  than  the 
external  atmospheric  pressure,  but  it  can  never  become  null. 

This  principle  may  be  demonstrated  by  the  apparatus  shown  in  fig. 
177,  where  a  bent  tube,  m  n,  is  inserted  into  a  cylindrical  adjutage,  and 
when  the  lower  end  is  placed  in  a  vessel  of  water,  as  shown  in  the 
figure,  the  fluid  will  mount  up  in  the  tube  to  a  certain  point  n. 

If  the  tube  m  n  is  not  too  long,  the  water  will  mount  up  and  enter 
the  adjutage,  and  flow  out  with  the  jet.  But  the  fact  that  the  water 
will  not  mount  over  in  the  tube  m  n,  unless  it  is  very  short,  proves  that 
the  external  atmospheric  pressure  is  always  opposed  by  a  certain 
amount  of  internal  pressure.  It  may  also  be  shown  that  the  interior 
pressure  never  becomes  null,  but  that  there  is  merely  a  diminution  of 
pressure,  by  placing  the  apparatus  in  a  vacuum,  when  the  water  will 
flow  out  in  the  direction  m  n. 

227.  Velocity  of  rivers  and  streams. — The  velocity  of  streams 
varies  very  much.  The  slower  class  of  rivers  have  a  velocity  of  less 
than  three  feet  per  second,  and  the  more  rapid  as  much  as  six  feet  per 
second,  which  gives  respectively  about  two  and  four  miles  per  hour. 

The  velocities  vary  in  different  parts  178 

of    the   same    transverse    section   of    a 
stream,  for  the  air  upon  the  surface  of 
the  water,  as  well  also  as  the  solid  bottom 
of  the  stream,  has  a  certain  effect  in  re- 
tarding   the    current.     The   velocity   is 
found  to  be  greatest  in  the  middle,  where  the  water  is  deepest,  fig.  178,  some- 
where in  m,  below  the  surface;  then  it  decreases  with  the  depth,  towards  tho 
sides,  being  least  at  a  and  b. 

Stream  measurers. — To  measure  the  velocity  of  streams,  various 
means  are  employed.  The  most  simple  is  a  glass  bottle  filled  with 
water,  sunk  just  below  the  level  of  the  current,  and  provided  at  the 
cork  with  a  small  flag,  that  stands  above  the  surface. 


OF    FLUIDS. 


183 


A  wheel  may  also  be  used,  furnished  with  float-boards,  placed  in  the  stream 
and  immersed,  so  that  the  whole  surface  of  the  boards  is  covered  with  water. 
The  friction  in  this  case  is  very  small,  so  that  the  wheel  revolves  with  very 
nearly  the  velocity  of  the  stream.  By  observing  the  number  of  revolutions  of 
the  wheel  in  a  given  time,  the  rapidity  of  the  current  is  measured. 

To  ascertain  the  velocity  at  different  depths,  the  simplest  instrument  is  Pictot'a 
tube.  It  consists  of  a  tube  bent  nearly  at  right  angles,  terminated  by  a  funnel- 
shaped  mouth  :  the  upper  part  of  the  tube,  above  water,  is  of  glass.  To  observe 
with  this  instrument,  it  is  sunk  with  its  funnel  up  stream  at  the  depth  where  its 
velocity  is  required.  If  the  water  was  still,  the  height  of  the  column  within  and 
without  the  tube  would  be  equal ;  but  as  it  is  in  motion,  the  water  will  rise  in  the 
tube  to  counterbalance  the  force  with  which  the  water  is  impelled  (the  impulse 
of  the  stream),  the  column  of  water  in  the  tube  rising  higher  as  the  velocity  of 
the  stream  is  greater. 

II.     WATER-POWER  AND  WATER-WHEELS. 

228.  Water-wheels. — The  motive  power  of  water  is  of  extensive 
practical  importance,  from  the  number  of  machines  driven  by  water- 
wheels. 

229.  The  overshot  wheel. — Fig.  179  is  used  when  the  supply  of 
water  is  moderate  and  variable.     The  water  is  delivered  at  the  top  of 
the   wheel,    which   may   move   with    the  179 

hands  of  a  watch,  as  in  the  figure,  or  the 

reverse.     It  is  furnished  with  buckets  of 

such  a  shape  as  to  retain  as  much  of  the 

water   as   possible,  until  they  reach  the 

lowest  practicable  point  on  the  wheel,  and 

none  after  that  point.     In  this  wheel  the 

effect  is  produced  both  by  impact,  and  by 

the  weight  of  the  water.     The  water  is 

received  as  near  the  summit  as  possible,  and  the  buckets  are  so  shaped 

as  to  retain  the  water  to  the  lowest  practicable  point  in  its  descent, 

corresponding  to  about  five  on  the 

face  of  the  watch. 

230.  The  undershot  wheel.— 
Fig.  180  receives  its  impulse  at  the 
bottom  ;   it  is  furnished  with  float- 
boards  instead  of  buckets.     If  they 
are  placed  at  right  angles  to  the  rim 
of  the  wheel,  they  may  turn  either 
way.     When  the  wheel  is  required 
to   turn   only  in  one  direction,  the 
float-boards    are    placed   as   in   the 

figure,  so  as  to  represent  an  acute  angle  towards  the  current :  the  wate 
acts  then  partly  by  its  weight. 


184  THE    THREE    STATES    OF    MATTER. 

The  breast-wheel. — Fig.  181  is  moved  both  by  the  weight  and 
momentum  of  the  water.  It  is  furnished  with  buckets,  formed  to 
retain  the  water  as  long  as  possible.  The  breast-wheel  is  the  form 
most  generally  adopted,  as  it  allows  of  a  larger  diameter  for  a  given 
fall  than  the  overshot-wheel,  with  more  economy  of  power  than  the 
undershot-wheel. 

A  more  distinct  idea  of  these  different 
water-wheels  may,  perhaps,  be  gained 
by  illustration  from  the  face  of  a  watch. 
In  the  breast-wheel,  the  water  may  be 
received  (according  to  the  desired  mo-—/ 
tion  of  the  wheel)  between  eight  and 
eleven  o'clock,  or  between  one  and  four 
o'clock.  According  as  the  water  is  re- 
ceived above  half-past  nine  or  below 
half-past  three  on  the  watch,  the  wheel: 
is  called  a  high  or  low  breast-wheel. 

231.  Boyden's  American  Turbine. — The  turbine  is  a  horizontal 
water-wheel,  revolving  entirely  submerged,  and  is,  of  all  forms  of 
water-wheel,  the  most  energetic  and  economical  of  power.  This 
machine  was  first  constructed  in  an  efficient  form  by  M.  Fourneyron  in 
1827  as  the  result  of  experiments  commenced  in  1823  ;  but  the  honor 
of  perfecting  the  turbine  and  establishing  the  mathematical  principles 
by  which  it  may  be  adapted  to  every  variety  of  water-power,  whether 
with  high  or  low  fall  of  water,  in  both  small  and  large  streams,  is  due 
to  U.  A.  Boyden,  Esq.,  of  Massachusetts,  under  whose  direction  tur- 
bines have  been  extensively  introduced  in  the  cotton  manufactories  of 
Lowell  and  elsewhere.  Two  of  the  turbipes  constructed  under  the 
superintendence  of  Mr.  Boyden  have  been  found  to  give  a  useful  effect 
to  eighty-eight  per  cent,  of  the  power  of  the  water  employed. 

The  water  enters  the  centre  of  the  wheel,  descending  in  its  vertical 
axis,  and  is  delivered  through  a  great  number  of  curved  guides  so 
arranged  that  the  water  enters  the  buckets  in  directions  nearly  tangent 
to  the  circumference  of  the  wheel.  The  water  is  received  by  the  curved 
buckets  in  the  direction  of  greatest  efficiency,  and  having  expended  its 
force,  it  escapes  from  the  wheel  in  a  direction  corresponding  very  nearly 
with  the  radii. 

The  upper  part  of  fig.  182  shows  a  horizontal  section  of  the  turbine,  and  a 
perpendicular  section  is  shown  in  the  lower  part  of  the  same  figure.  Fig.  183 
shows  ^a,  section  of  the  turbine  with  the  iron  sluice  and  other  attachments  as 
they  stand  in  the  wheel-pit.  The  letters  refer  to  the  same  parts  in  both  figures. 
K  K  is  a  stationary  disc  of  cas'  iron  supported  by  the  disc  tube  M  M  made  fast 
to  the  upper  curb  at  P.  The  curved  guides,  g  g  g  g,  made  of  plate  iron,  are 


OF    FLUIDS. 


185 


secured  to  the  disc  K,  and  to  the  rim  L  L  above,  in  such  a  manner  as  to  give 
the  least  possible  obstruction  to  the  water  as  it  flows  through  the  guides  into 
the  revolving  wheel.  The  arrrows  show  the  course  of  the  water  through  the 
iron  sluice  E,  and  on  the  disc  through  the  guides  into  the  wheel.  The  wheel 
itself  consists  of  a  central  plate  of  cast  iron,  and  of  two  crowns  cccc,  of  the 
same  material,  between  which  are  the  curved  buckets  bbbb.  The  lower  crown 
is  firmly  secured  to  the  central  plate.  The  buckets  are  let  into  curved  grooves 
in  the  crowns,  and  have  tenons,  passing  through  mortices  in  the  crowns,  riveted 
above  and  below. 

182 


The  vertical  shaft,  dd,  is  made  of  cast  iron,  and  is  accurately  turned  in  every 
part.  The  entire  weight  of  the  wheel  is  supported  by  a  series  of  collars  attached 
to  the  shaft  and  moving  in  the  suspension  box  e.  The  box  e  is  hung  upon  gim- 
bals at  h  (like  a  mariner's  compass),  supported  by  framework  resting  in  the 
masonry  of  the  wheel-pit.  The  lower  end  of  the  shaft  is  steadied  by  a  pin  pass- 
ing into  the  step  i,  which  is  adjusted  by  a  screw.  R R  is  a  cylindrical  gate  which 
drops  down  between  the  guides  and  the  movable  part  of  the  wheel,  to  regulate 
the  flow  of  water  according  to  the  amount  of  power  required.  Attached  to  the 
gate  are  the  brackets  SS,  connected  with  the  rackwork  and  endless  screw  shown 
at  W,  by  which  the  gate  is  raised  or  lowered.  A  self-regulating  adjustment  of 
the  gate  is  secured  by  a  governor  not  sh  own  in  the  figure.  Ordinary  gearing. 


186 


THE   THREE   STATES   OF   MATTER. 
183 


OF   FLUIDS.  187 

attached  to  the  upper  part  of  the  shaft,  communicates  the  power  of  the  wheel  to 
the  machinery  to  be  driven.  The  curved  iron  sluice  E  rests  upon  beams  N't 
secured  in  the  masonry  of  the  wheel-pit  and  by  stancheons  NN. 

Turbines  may  be  divided  into  high  and  low  pressure  machines.  High 
pressure  turbines  are  adapted  to  hilly  countries  and  deep  mines  where 
high  falls  of  water  may  be  commanded ;  in  these  cases  the  height  of 
the  column  of  water  will  compensate  for  the  srnallness  of  its  volume, 
reservoirs  being  provided  to  keep  up  a  constant  supply. 

The  low  pressure  turbines  produce  great  effect  with  a  head  of  water 
of  only  nine  inches,  and  are  suitable  for  situations  in  which  a  large 
volume  of  water  flows  with  a  small  fall. 

The  results  of  an  investigation  by  Arago,  Prony,  and  others,  who  were 
appointed  by  the  French  Academy  of  Sciences  to  report  upon  turbines, 
are  as  follows  : — 

(1).  That  these  wheels  are  applicable  equally  to  great  and  small  falls 
of  water. 

(2).  That  they  transmit  a  useful  effect  equal  to  from  70  to  78  per 
cent,  of  the  total  moving  force  of  the  water  employed  (88  per  cent,  has 
been  secured  by  Boyden's  wheel). 

(3).  That  they  will  work  at  very  different  velocities  above  or  below 
that  corresponding  to  the  maximum  effect,  without  the  useful  effect 
varying  materially  from  that  maximum. 

(4).  That  they  will  work  from  one  to  two  yards  deep  under  water, 
without  the  proportion  which  the  useful  effect  bears  to  the  total  force 
being  sensibly  diminished. 

(5).  In  consequence  of  the  last-mentioned  property,  they  utilize  at  all 
times  the  greatest  possible  proportion  of  power,  as  they  may  be  placed 
below  the  lowest  levels  to  which  the  water  surface  sinks. 

The  mathematical  formulae  for  adapting  turbines  to  every  variety  of  water- 
power,  and  much  other  valuable  information,  will  be  found  in  a  treatise  on  the 
Hydraulic  Experiments  at  Lowell,  by  Mr.  J.  B.  Francis,  from  whose  work  the 
above  condensed  description  has  been  principally  obtained. 

*MOLECULAR  FORCES  ACTING  BETWEEN  PARTICLES  OF  UNLIKE 

KINDS. 

I.     CAPILLARITY. 

232.  Observation.— Definition.— The  complete  discussion  of  the 
action  of  Molecular  Forces  between  particles  of  unlike  kinds  belongs 
appropriately  to  Chemical  Physics.  We  have  already  noticed  some  of 
the  phenomena  of  adhesion  properly  referable  to  this  section  (147 
and  following).  It  now  remains  to  consider  briefly  those  special  cases 
of  this  general  subject  which  affect  the  laws  of  fluid  equilibrium.  We 
refer  especially  to  the  Phenomena  of  Capillarity  and  Endosmose. 


188 


THE   THREE    STATES    OF    MATTER, 


The  laws  of  fluid  equilibrium  which  we  have  already  considered 
apply  only  to  vessels  of  considerable  diameter,  in  which  the  effects  of 
adhesion  between  liquids  and  solids  (148)  may  be  safely  neglected. 

In  very  narrow  vessels,  and  particularly  in  tubes  of  small  bore,  the 
effects  of  this  kind  of  molecular  attraction  become  very  sensible.  Such 
tubes  are  called  capillary  tubes,  from  capillus  a  hair,  in  allusion  to  the 
hair-like  fineness  of  their  bore.  The  effects  of  such  tubes  on  liquids 
are  distinguished  by  the  general  term  capillarity. 

233.  General  facts  in  capillarity. — If  tubes  of  small  bore,  open 
at  both  ends,  are  placed  vertically  in  water,  the  liquid  is  seen  to  mount 
both  in  the  tubes  and  on  the  outside,  fig.  184,  rising  higher  within  as 
the  tubes  are  smaller.  If  the  bore  is  over  half  an  inch  in  diameter, 
this  effect  is  not  very  sensible.  The  experiment  becomes  more  satis- 
factory if  made  in  communicating  vessels  (202),  of  which  one  branch 
is  much  narrower  than  the  other,  as  in  fig.  185.  Two  slips  of  glass 
plunged  in  water,  and  brought  near  each  other,  also  exhibit  the  effect 
of  capillarity.  In  narrow  communicating  vessels,  then,  the  laws  of 
equality  of  level  do  not  hold  good. 

If  the  experiment  is  tried  with  mercury  (which  does  not  wet  the 
glass)  there  is  a  depression  of  the  surface  of  the  liquid  both  within 
and  without  the  tube,  fig.  186,  and  this  becomes  greater  as  the  tubes 
are  smaller,  as  seen  in  the  two  branches  of  the  communicating  vessels, 
fig.  187.  In  a  greased  tube  water  is  similarly  depressed. 

185  184  186  187 


These  phenomena  are  independent  of  atmospheric  pressure— taking 
place  equally  in  a  vacuum  or  in  compressed  air.  They  are  also  inde- 
pendent of  the  thickness  of  the  walls  of  the  tube  (148),  but  they  vary 
with  the  material  of  the  tube,  and  with  the  nature  of  the  liquid. 

Thus,  in  tubes  of  the  same  internal  diameter,  placed  in  liquids 
capable  of  wetting  the  surface  of  the  glass,  the  elevation  is  different  for 
each  liquid.  In  tubes  of  0*0472  inch  diameter  of  bore,  water  rises  0*905 


OP   FLUIDS  189 

inches  (or  about  4  inches  in  tubes  of  T^  inch  bore),  essence  of  turpen- 
tine 0-385,  pure  alcohol  0'278,  whale  oil  about  the  same,  while  ether 
rises  still  less.  In  some  liquids  the  elevation  is  scarcely  sensible,  while, 
as  we  have  seen  in  mercury  and  other  liquids  not  wetting  the  surface 
of  the  tube,  there  is  a  depression. 

Form  of  the  surface.— These  changes  of  level  are  accompanied  by 
a  change  of  form  in  the  surface  of  the  liquid  in  the  capillary  column. 
It  is  concave  if  there  is  elevation — plane  if  there  is  no  change  of  level, 
and  convex  if  there  is  depression.  The  first  case  is  called  the  concave 
meniscus,  and  the  last  the  convex  meniscus. 

The  cause  of  these  phenomena  is  to  be  sought  in  the  mutual  action 
of  molecular  forces  (146)  and  of  gravity. 

A  needle  covered  with  grease,  gently  placed  upon  the  water,  floats,  because, 
not  being  moistened  by  the  liquid,  there  is  produced  a  depression  in  which  it  is 
supported.  Thus,  many  insects  walk  and  skim  on  the  surface  of  water  without 
plunging  in.  Oil  and  other  burning-fluids  in  lamps,  and  the  melted  tallow  and 
wax  of  candles,  are  supplied  to  their  flames  by  means  of  the  capillarity  of  their 
wicks ;  so  there  is  an  absorption  of  liquids  in  wood,  in  sponge,  in  cloth,  and  in 
all  bodies  that  possess  sensible  pores. 

234.  Cause  of  the  curve  of  liquid  surfaces  by  the  contact 
of  solids. — The  form  of  the  surface  of  a  liquid  in  contact  with  a 
solid,  depends  upon  the  relation  which  exists  between  the  attraction  of 
the  solid  for  the  liquid,  and  the  liquid  particles  for  -each  other. 

Let  A  B,  fig.  188,  represent  a  fluid  surface,  and  D  E  the  surface  of  a  solid 
immersed  vertically  in  the  fluid.  Any  liquid  particle,  as  A,  is  submitted  to  the 
action  of  three  forces,  viz. :  1st.  Gravity,  which,  as  it 
acts  equally  upon  all  the  particles  of  the  fluid,  may  be 
omitted  from  the  present  discussion.  2d.  The  cohesive 
attraction  of  the  fluid  acting  through  the  quadrant 
B  A  E,  and  having  its  resultant  in  A  P.  3d.  The  adhe- 
sive attraction  of  the  solid  for  the  particle  A.  This 
latter  force  may  be  considered  as  divided  into  two 
parts;  the  attraction  of  that  part  of  the  solid  above 
the  surface  of  the  fluid,  whose  resultant  will  be  A  Q ; 
and  the  attraction  of  that  part  of  the  solid  below  the 
surface  of  the  fluid,  which  will  have  a  resultant  in  A  Q'.  Let  B  P  E  be  drawn  at 
the  limit  of  sensible  cohesive  attraction  of  the  fluid  for  the  particle  A,  and  let 
A  P,  or  P,  represent  the  intensity  of  the  resultant  of  all  the  cohesive  attraction 
»f  the  liquid  for  the  particle  A ;  also  let  mno  have  the  same  relation  to  the 
adhesive  attraction  of  the  solid,  and  Q  and  Q'  will  represent  the  intensity  of  this 
force  above  and  below  the  surface  of  the  liquid. 

Completing  the  parallelogram  AQCQ',  A  C  =  2  Q  cos.  45°  will  represent  the 
resultant  of  all  the  attraction  of  the  solid  for  the  particle  A.  On  A  C  and  A  P, 
construct  the  parallelogram  A  P  R  C,  and  A  R  will  be  the  resultant  of  A  P 
and  A  C. 

19 


190 


PHYSICS   OF   SOLIDS   AND   FLUIDS. 


The  direction  of  the  resultant  A  B  will  be  determined  by  the  value  of 
2  Q  cos.  45°  —  P  cos.  45°,  or  2  Q  —  P.  There  will  evidently  be  three  cases : 

2  Q  —  P  >  0,     2  Q-+P  =  Q,     and  2  Q  —  P  <  0. 

In  the  first  case  the  resultant  will  lie  in  the  angle  C  A  E,  and  the  fluid  will 
wet  the  solid.  In  the  second  case  the  resultant  will  lie  in  A  E,  in  the  plane 
which  separates  the  solid  and  the  fluid.  In  the  third  case  the  resultant  will  lie 
in  the  angle  B  A  E,  and  the  fluid  will  not  wet  the  solid.  In  this  case  there  is 
no  necessity  to  suppose  any  repulsion  between  the  solid  and  the  fluid,  but  only 
that  the  cohesive  attraction  of  the  fluid  is  more  than  twice  as  great  as  the  attrac- 
tion of  the  solid  for  the  fluid. 

As  the  surface  of  a  liquid  is  always  perpendicular  to  the  direction  of  the  forces 
which  solicit  its  molecules  (199)  in  the  first  case,  the  surface  of  the  fluid  at  A 
will  be  tangent  to  the  plane  M  N,  fig.  189,  which  is  perpendicular  to  the  general 
resultant  A  B.  At  A',  where  the  attraction  is  more  feeble,  the  resultant  A'  B' 
will  be  more  nearly  perpendicular,  and  at  a  point  A",  where  the  sensible  attrac- 
tion is  zero,  the  resultant  A"  B"  will  be  vertical,  and  the  curve  A  A'  A"  will 
become  tangent  to  a  horizontal  plane. 

189  190 


A.  C 


In  the  case  of  a  small  tube,  T,  the  concave  surface  of  the  fluid  will  be  sensi- 
bly spherical.  When  2*Q  —  P  =  0,  the  resultant  A  B  lies  in  the  line  A  E,  and 
the  surface  of  the  liquid  in  contact  with  the  solid  is  horizontal,  because  the 
attractive  force  of  the  solid  and  fluid  combined  is  the  same  as  if  the  surface  of 
the  fluid  was  indefinitely  extended. 

When  2  Q  —  P  is  less  than  zero,  or  negative,  the  resultant  A  B  will  be  found 
in  the  angle  B  A  E,  and  the  surface  will  be  tangent  to  the  plane  M  N  at  the 
point  A ;  it  will  therefore  be  convex,  as  shown  at  A  A",  fig.  190.  In  a  capillary 
tube,  U,  the  surface  will  be  convex  and  sensibly  spherical. 

235.  Experimental  illustrations. — Capillary  phenomena  are  easily 
explained,  when  we  know  that  under  the  double  influence  of  the  attrac- 
tion of  a  solid  and  a  liquid,  the  surface  of  the  liquid  may  be  either 
concave,  plane,  or  convex,  as  the  relative  intensities  of  these  forces 
vary ;  we  can  also  see,  that  the  ascent  or  depression  of  the  liquid  in 
capillary  tubes  is  a  direct  consequence  of  the  terminal  form  of  the 
liquid.  This  explanation  is  easily  verified  by  experiment. 

o.  Take  a  bent  tube,  similar  to  fig.  185,  but  let  the  capillary  branch  be 
shorter  than  the  other,  and  pour  water,  drop  by  drop>  into  the  larger  branch, 
the  liquid,  as  it  rises  to  the  top  of  the  tube,  in  the  short  capillary  branch  will 


OP  FLUIDS.        .<  191 

present  successively  a  concave,  then  a  plane,  and  at  last  a  convex  surface.  Afl 
the  water  stands  in  a  convex  form  above  the  end  of  the  tube,  the  concave  sur- 
face in  the  larger  branch  will  rise  above  it,  showing  that  the  rise  of  the  liquid 
above  the  level  due  to  hydrostatic  pressure  depends  upon  the  form  of  the  surface. 

b.  Let  a  capillary  tube,  with  a  small  sphere  blown  in  it,  as  shown  in  fig.  191, 
be  soldered  into  the  bottom  of  a  small  glass  vessel  or  tube,  into  which  mercury 
is  slowly  dropped.    As  the  mercury  rises  into  the  sphere, 

it  will  take,  at  A,  the  form  of  a  very  convex  button.  As 
it  rises  to  B  B  and  C  C,  the  convexity  of  the  surface  will 
gradually  diminish,  although  it  will  make  a  constant 
angle  (about  45°)  with  the  walls  of  the  glass  sphere/ as 
shown  by  the  dotted  lines.  When  it  arrives  at  D  D, 
where  the  surface  of  the  sphere  is  inclined  45°,  the 
surface  of  the  mercury  will  be  horizontal,  and  still 
higher  it  will  be  concave.  These  successive  stages  of 
curvature  are  seen  in  filling  a  mercurial  thermometer. 

This  experiment,  depending  upon  the  constant  angle 
made  by  the  surface  of  the  mercury  with  the  walls  of  the 
tube,  enables  us  to  show  that  the  level  of  the  mercury  in 
the  capillary  tube  is  higher  or  lower  than  in  the  vessel 
with  which  it  communicates,  according  as  the  surface  is 
concave  or  convex. 

The  level  at  which  a  liquid  may  be  maintained  in  a  capillary  tube 
depends  on  the  diameter  of  the  canal  at  the  upper  level  of  the  liquid. 

c.  An  impressive  verification  of  this  fact  is  obtained  by  soldering  a  capillary 
tube  to  the  top  of  a  glass  vase  or  low  air-bell,  like  a  cupping-glass  or  beaker. 
If  the  diameter  of  the  capillary  tube  is  not  more  than  the  one-hundredth  of  an 
inch,  a  column  of  water  of  the  diameter  of  the  vase  will  be  sustained  by  the 
capillary  force  at  the  height  of  nearly  four  inches — the  height  of  the  column 
requisite  to  restore  equilibrium  "being  independent  of  the  diameter  of  the  vase. 

The  same  apparatus  being  reversed  and  plunged  in  a  bath  of  mercury  will 
evince  a  corresponding  depression  of  the  level  of  the  mercury  in  the  capillary 
tube,  the  vase  remaining  void  of  mercury. 

It  is  evident  from  these  experiments  that  capillarity  is  a  very 
energetic  force,  and  when  we  remember  that  the  capillary  canafe  in 
vegetables  are  usually  smaller  than  the  one-hundredth  of  an  inch,  and 
those  in  the  animal  body  are  very  much  smaller,  it  is  easy  to  under- 
stand the  ascensional  force  of  sap  in  plants,  and  the  functions  of  the 
capillaries  in  animals. 

d.  By  this  power  it  is  that  the  soil  in  dry  seasons  receives  moisture  from  below 
to  supply  the  waste  of  evaporation, — and  conversely  that  the  benefits  of  rain 
descend  to  the  lower  strata.     Hence  in  dry  climates  the  surface  soil  is  covered 
with  saline  effloresenccs  left  by  the  evaporation  of  water  holding  salts  in  solution. 

e.  Rocks  are  split  by  the  swelling  of  wooden  plugs  driven  forcibly  in  tho 
dry  state  into  holes  drilled  for  the  purpose,  and  afterwards  wet  with  water. 

236.  Influence  of  the   curve  on  capillary  phenomena. — The 

ascent  or  depression  of  liquids  in  capillary  spaces,  is  owing  to  the 


192 


THE    THREE    STATES    OF    MATTER. 


form  of  the  surfaces.  Let  abed,  fig.  192,  represent  a  concave 
meniscus,  the  particles  of  which  are  sustained  in  equilibrium  by  the 
forces  before  mentioned ;  these  particles  do  not  exercise  any  pressure 
on  those  below  them,  and  therefore  at  c  b  there  is  a  line  above  whicb 
the  particles  of  fluid  are  sustained  by  upward  attraction,  and  bekrw 
which  it  is  sustained  by  equal  external  pressure  of  the  column  op. 
192  193 


The  sensible  attraction  of  the  walls  of  the  tube  does  not  extend  so 
far  as  the  perpendicular  height,  d  c,  of  the  curve.  It  is  only  a  small 
portion  of  the  wall  of  the  tube  just  above  the  extremity,  d,  of  the  curve 
that  supports  the  fluid.  The  action  of  every  part  below  d,  while  it 
tends  to  elevate  the  fluid  below,  also  tends  to  depress  the  portion  of 
fluid  above  it,  and  these  two  influences  neutralize  each  other.  The 
particles  of  fluid  about  d,  and  within  the  limit  of  sensible  attraction, 
are  drawn  upward  by  the  attraction  of  the  tube,  and  these  particles, 
by  their  cohesive  attraction,  support  those  below,  until  the  weight  of 
the  capillary  column  becomes  equal  to  the  adhesive  attraction  of  the 
solid  for  the  particles  within  the  limit  of  attraction  about  the  point  d. 

In  determining  the  height  of  liquids  in  capillary  tubes,  the  height  of 
the  column  supported  by  capillary  attraction-  must  be  added  to  the 
elevation  produced  by  external  pressure. 

When,  as  in  fig.  193,  the  meniscus  is  convex,  the  equilibrium  still 
exists,  for  the  liquid  molecules  being  attracted  obliquely  inwards  and 
downwards,  the  downward  pressure  is  greater  than  on  the  exterior  of 
the  tube,  and  therefore  the  surface  of  the  liquid  within  the  tube 
descends  until  the  pressure  on  the  base,  mn,  is  the  same  as  on  any 
exterior  point,  g,  of  the  same  layer. 

237.  Law  of  the  elevation  and  depression  of  liquids  in  capil- 
lary tubes. — It  has  been  demonstrated  by  Laplace,  that  the  attraction 
of  the  meniscus  is  equal  to  a  constant  coefficient,  depending  on  the 
nature  of  the  liquid  and  that  of  the  tube.  In  a  cylindrical  tube  with 
a  circular  base,  experience  has  demonstrated,  that  the  concave  surface 
is  sensibly  a  hemisphere,  with  a  radius  equal  to  half  the  diameter  of 
the  tube.  The  attraction  of  the  meniscus  is,  therefore,  in  inverse  ratio 


OF   FLUIDS. 


193 


with  the  radius,  or  the  diameter  of  the  tube,  and  in  consequence,  the 
liquid  column  will  be  raised  by  this  force  to  a  height  which  varies 
according  to  its  intensity.  The  length  of  the  liquid  column  contained 
in  the  tube  is  a  little  less  than  calculation  would  indicate,  according 
to  the  above  rule,  because  of  the  weight  of  the  meniscus,  but  this  error 
is  very  small,  less  as  the  capillarity  of  the  tube  is  less,  the  influence 
of  the  weight  of  the  meniscus  decreasing  rapidly  as  the  diameter  of  the 
bore  diminishes.  The  height  of  the  liquid  in  the  tube  is,  therefore, 
never  absolutely  in  inverse  ratio  to  the  diameter,  but  the  law  is  nearly 
exact  when  we  add  to  the  height  one-sixth  of  the  diameter  of  the  tube, 
which  is  the  correction  required  for  the  weight  of  the  meniscus. 

Corrections  for  this  error  being  thus  made,  the  law  would  be  correct, 
had  the  meniscus  an  accurately  spherical  surface,  but  this  obtains 
only  when  the  diameter  is  very  small  (2  or  3  m.  m.,  '07874,  or 
•11811  inches)  the  surface  in  general  ceases  to  be  truly  spherical,  and 
the  ascent  or  depression  depends  on  the  curve  of  the  surface,  which 
varies  much  more  rapidly  than  the  diameter  of  the  tube. 

238.  Depression  of  mercury  in  capillary  tubes. — The  rapidity 
vvith  which  capillarity  diminishes,  in  tubes  of  great  diameter,  is  seen  in 
the  following  table : — 

TABLE  OF  DEPRESSIONS  OF  MERCURY  IN  CAPILLARY  TUBES. 


Diameter  of 
tube. 

Depressions  in 
m.  m.  according 
*>    to  Laplace. 

According  to 
Young. 

According  to 
Jacoby. 

According  to 
Cavendish. 

20-  m.  m. 

0-038 

0-031 

0-031 

15-       " 

0-137 

0-111 

0-118 

0-131 

ID- 

0-445 

0-402 

0-406 

0-406 

S' 

0-712 

0-669 

0-673 

0-820 

6- 

1-171 

1-139 

1-134 

1-377 

5- 

1-534 

1-510 

1-513 

1-735 

4- 

2-068 

2-063 

2-066 

2-187 

3- 

2-918 

2-986 

2-988 

3-054 

2-5 

3-566 

'•v 

2- 

4-454 

4-887 

4-888 

4-472 

The  numbers  contained  in  the  first  column  have  been  calculated  by 
M.  Bouvard,  according  to  the  formula  of  Laplace ;  those  of  the  last 
two  columns  have  been  obtained  directly  by  experiment. 

239.  Ascent  of  liquids  in  capillary  tubes.— For  all  liquids,  the 
ascent  or  depression  in  capillary  tubes,  decreases  according  to  analo- 
gous laws.  If  the  tubes  are  very  small,  the  heights  augmented  with 
one-sixth  of  their  diameter,  are  inversely  as  the  diameters.  If  the 
tubes  are  very  large,  we  may  ascertain  very  accurately  the  heights  to 
19* 


194  THE   THREE   STATES   OF   MATTER. 

which  liquids  would  rise  by  very  complicated  calculations,  or  we  may 
obtain,  approximately,  their  capillary  effects,  in  supposing  them  pro- 
portional to  the  depression  mercury  undergoes  in  tubes  of  the  same 
diameter.  For  the  same  tube,  and  for  the  same  liquid,  the  capillarity 
depends  much  on  the  temperature,  decreasing  more  rapidly  than  the 
density. 

According  to  Gay  Lussac,  the  elevation  of  water  in  a  capillary 
.tube  of  1  m.  m.,  (-03937  in.)  is  30  m.  m.,  (-11811  in.)  and  different 
liquids  elevate  themselves,  in  the  same  tubes,  to  heights,  which  are  in 
the  following  relation  : — 

Water, 100- 

Saturated  solution  of  chloride  of  ammonium,       .     102'7 
"  "  sulphate  of  potash,     .        .      957 

"  "  "  copper,      .         .       84' 

Nitric  acid, 75- 

Hydrochloric  acid,        ......      70' 1 

Alcohol, 40-8 

Oil  of  lavender,    .        .        .  .        .        .      37'5 

240.  Laws  of  the  equilibrium  of  liquids  between  parallel  or 
inclined  laminae. — Phenomena  analogous  to  those  presented  in  capil- 
lary tubes,  may  be  observed  when  two  laminae,  plunged  in  a  liquid, 
are  brought  near  to  each  other.  If  the  laminae  are  made  wet,  the 
liquid  elevated  between  them,  is  terminated  by  a  cylindrical  surface  ; 
if  not  moistened,  the  liquid  is  depressed,  and  is  terminated  by  a  convex 
surface  ;  and  it  is  observed  that : — 

1st.  A  liquid  is  regularly  elevated  or  depressed  between  two  lamina, 
inversely  as  the  interval  which  separates  them. 

2d.  That  the  height  of  the  194 

ascension  or  depression  for  a 
given  interval,  is  half  that 
which  would  take  place  in  a 
tube  having  a  diameter  equal 
to  that  of  the  interval. 

When  we  plunge  two  in- 
clined laminae  (with  their 
line  of  contact  in  a  vertical 
position)  in  a  liquid  which 
wets  them,  a  concave  surface 
may  be  observed  between  them,  fig.  194,  the  liquid  rising  toward  the 
upper  point  of  their  line  of  contact.  The  surface  of  the  liquid  takes 
the  form  of  the  curve  known  in  geometry,  under  the  name  of  the 
equilateral  hyperbola  ;  this  curve  is  produced  by  capillarity. 


OF   FLUIDS. 


105 


241.  Movement  of  drops  of  liquid  in  conical  tubes  or  between 
laminae. — When  a  drop  of  liquid  is  contained  in  a  conical  tube,  or 
between  two  laminae  having  their  lines  of  contact  horizontal,  the  liquid, 
if  it  wets  the  tube  or  laminae,  is  terminated  by  195 

two  concave  surfaces,  and  the  liquid  is  drawn 

towards  the  smaller  end  of  the  tube,  or  towards  m 

the  angle  of  the  laminae,  i.  e.  in  the  direction 

from  m  to  m7,  fig.  195,  because  the  liquid  being 

terminated  by  concave  surfaces,  the  pressure  from  without  inwards 

decreases  as  the  radius  of  the  concave  surface  diminishes,  so  that  the 

resultant  pressure  is  directed  from  m  towards  196 

m'.    If  the  liquid  is  mercury,  or  any  fluid  that 

does  not  wet  the  surrounding  body,  the  two 

surfaces  will  be'convex,  and  the  pressure  from 

without  inwards  will  be  greater  in  proportion  as 

the  radius  of  curvature  becomes  less,  hence  the  resultant  pressure  will 

be  from  m  towards  m',  fig.  196,  and  the  drop  will  be  driven  towards  the 

larger  end  of  the  tube,  or  towards  the  more  open  parts  of  the  laminae. 

242.  Attraction  and  repulsion  of  light  floating  bodies. — The 
attraction  and  repulsion  which  we  observe  between  light  bodies  floating 
on  the  surface  of  liquids,  is  due  to  capillarity.    Two  floating  bodies  are 
drawn  near  to  each  other  either  when  both  are,  or  both  are  not  moistened, 
and  repelled  if  the  liquid  wets  only  one  of  them. 

Let  a  and  6,  fig.  197,  be  two  floating  bodies 
whose  surfaces  are  wet  by  the  liquid.  Between 
the  bodies  a  small  mass  of  fluid  is  elevated  by 
capillary  attraction,  of  which  the  point  m  is 
higher  than  the  level  of  a  b,  the  highest  points 
of  the  exterior  curves. 

The  weight  of  the  column  m  tends  to  draw 
the  two  bodies  together,  acting  like  a  loaded 
cord  suspended  between  the  two  bodies.  The 
mutual  cohesion  of  the  molecules  of  the  liquid 
surface,  m,  causes  it  to  serve  as  a  cord,  and 
the  adhesion  of  the  liquid  to  the  floating  bodies 
at  the  highest  points,  serves  as  the  attachments 
of  the  extremities.  When  the  two  bodies  are 
not  wet  by  the  liquid,  the  liquid  is  depressed 
between  the  bodies,  and  the  external  pressure 
upon  the  two  bodies  drives  them  together,  as 
shown  in  the  middle  section  of  the  figure. 

When  one  body  is  wet  by  the  liquid,  and  the  other  is  not,  the  result  of  capil- 
lary attraction  is  to  cause  the  two  bodies  mutually  to  repel  each  other. 

If  the  body  which  is  wet  is  removed  beyond  the  influence  of  the  other  body, 
the  concave  meniscus  will  rise  on  both  sides  of  the  body  to  the  dotted  line  o,  in 
the  lower  part  of  the  figure.  In  the  same  manner,  if  the  body  not  wet  were 
alone,  the  meniscus  of  depression  would  extend  on  both  sides  to  the  dotted  line,  r. 


196  THE    THREE    STATES    OF    MATTER. 

If  now  we  suppose  the  two  bodies  brought  so  near  each  other  that  the  concave 
meniscus  of  fluid  attached  to  one  body  will  come  in  contact  with  the  convex 
depression  of  the  other,  the  surface  of  the  liquid  will  take  a  form,  n  k,  interme- 
diate between  the  two  curves  which  would  have  been  formed  when  the  bodies 
were  entirely  separated  j  that  is,  the  more  elevated  point  n  will  be  below  o,  and 
the  point  of  greatest  depression  at  k  will  be  above  the  point  r.  The  body  wet 
will  therefore  be  drawn  outward  by  the  weight  of  that  part  of  the  external 
meniscus  which  is  more  elevated  than  the  internal,  as  represented  by  the  distance 
o  n  •  and  the  body  not  wet  will  be  driven  away  from  the  first  by  the  excess  of 
hydrostatic  presssure  due  to  the  difference  of  level,  k  r,  on  the  two  sides  of  the 
second  body. 

Escape  of  Liquids  from  Capillary  Tubes. 

243.  Plow  of  liquids  from   capillary  tubes. — Fluids   escaping 
from  capillary  tubes  are  subject  to  the  following  laws : — 

1.  For  the  same  tube  the  flow  is  proportioned  to  the  pressure. 

2.  With  tubes  having  an  equal  pressure  and  length,  the  flow  is  pro- 
portional to  the  4th  power  of  their  diameters. 

3.  For  the  same  pressure  and  the  same  diameter,  the  flow  is  in  inverse 
ratio  to  their  length. 

4.  The  flow  increases  vfith  the  temperature. 

The  inequalities  in  the  flow  of  different  liquids  under  the  same  cir- 
cumstances does  not  seem  to  depend  on  their  viscosity  or  their  density ; 
for  alcohol  flows  slower,  and  oil  of  turpentine,  or  sugar  solution,  faster 
than  water.  So  also  nitrate  of  potash  solution  flows  faster,  and  serum 
flows  less  swiftly,  than  pure  water ;  alcohol  added  to  serum  retards  its 
movement,  while  if  nitrate  of  potash  solution  be  added  to  the  mixture, 
the  serum  recovers  its  usual  velocity. 

These  experiments  made  with  glass  tubes,  were  repeated  on  the  bodies  of  ani- 
mals recently  killed,  by  injecting  the  various  fluids  into  the  principal  arteries. 
The  results  were  found  to  accord,  tending  to  prove  that  the  circulation  of  blood 
and  other  fluids  in  the  arteries  and  veins  of  living  bodies,  is  subject  to  the  same 
laws  as  the  flow  of  liquids  in  capillary  tubes  of  glass. 

II.     OSMOSE  OR  OSMOTIC  FORCE. 

244.  Osmose,  Exosmose,  Endosmose. — Osmose  is  the  transmis- 
sion of  liquids  into  each  other  through  the  pores  of  an  interposed 
medium  which  ordinarily  offers  more  resistance  to  the  passage  of  one 
of  the  liquids  than  of  the  other. 

When  a  membranous  sac,  or  a  vessel  filled  with  a  fluid,  and  closed 
by  a  membrane,  is  plunged  into  another  liquid  capable  of  mixing  with 
the  first,  two  currents  are  established  through  the  membranous  partition. 
The  current  from  within  outwards  is  called  exosmose  (from  e£a>  out- 
wards, and  a)irp.oq  impulsion),  and  the  current  from  without  inwards  is 
called  endosmose  (from  evdov  inwards,  and  wff/j.os). 


OF   FLUIDS. 


197 


198 


The  more  general  term  osmose  has  been  substituted  by  Graham  for 
the  two  correlative  terms  just  denned,  as  being  a  better  expression  of 
all  the  phenomena  concerned. 

The  phenomena  of  osmose  are  closely  allied  to  those  of  capillarity.  They 
have  been  very  accurately  studied,  particularly  by  Dutrochet,  who  brought 
forward  his  researches  in  1827,  and  more  recently  by  Prof.  Graham. 

245.  Endosmometer.— The  existence  and  rapidity  of  these  currents 
is  ascertained  by  the  endosmometer,  an  instrument  which  may  be  thus 
constructed.    To  a  membranous  pouch  or  bladder  is  fitted,  hermetically, 
a  glass  tube  as  in  fig.  198. 

The  jar  or  bladder,  and  part  of  the  tube,  is  filled  with  a  dense  liquid, 
as  a  strong  solution  of  gum  or  sugar,  and 
placed  in  a  tall  cylindrical  jar,  which  is 
then  filled  with  distilled  water,  until  it 
stands  exactly  at  the  level  of  the  fluid  in 
the  tube.  For  very  exact  experiments, 
this  level  is  constantly  maintained  by  the 
addition  to,  or  the  removal  of  the  water 
in  the  outer  jar.  After  a  time,  gum  will 
be  found  in  the  outer  vessel,  a  current 
from  without,  inwards,  also  taking  place. 

If  we  wish  to  determine  more  accurately  the 
actual  as  well  as  the  comparative  flow  of  dif- 
ferent liquids,  we  may  use  an  apparatus  con- 
structed as  follows  : — Over  the  open  mouth  of 
a  bell  jar,  of  a  few  ounces  capacity,  is  placed 
a  plate  of  perforated  zinc,  to  support  firmly  a 
piece  of  fresh  ox-bladder,  which  is  securely 
tied  over  it.  To  the  upper  aperture  is  attached 
a  graduated  tube,  open  at  both  ends,  the  capa- 
city of  whose  interior  bears  a  certain  definite 
relation,  as  j^th,  to  that  of  the  lower  open- 
ing of  the  bell  jar ;  so  that  a  rise  or  fall  in  the 
tube  as  of  100  m.  m.  (3-937  in.)  indicates  the  en- 
trance or  removal  of  a  stratum  of  liquid,  1  m.  m. 
(0-03937  in.)  thickness  over  the  whole  surface. 

246.  Necessary  conditions. — According  to  M.  Dutrochet,  in  order 
successfully  to  produce  the  phenomena  of  endosmose,  it  is  necessary : — 

1st.  That  the  liquids  be  susceptible  of  mixing. 

2d.   That  they  are  of  different  densities. 

3d.  That  the  membrane  or  wall  (septum]  which  separates  them  is  per- 
meable to  one  or  both  liquids. 

Materials  for  septum. — All  thin  animal  and  vegetable  membranes, 
thin  plates  of  burnt  clay,  slate,  marble,  pipe-clay,  &c.,  produce  endos- 


198  THE    THREE    STATES    OF    MATTER. 

motic  effects  in  a  more  or  less  notable  degree.  Of  inorganic  materials, 
those  which  contain  most  silicic  acid  are  less  permeable.  A  chemical 
action  on  the  materials  of  the  septum,  invariably  takes  place  (except- 
ing with  alcohol  and  cane-sugar  solutions),  whether  it  is  formed  of 
bladder  or  of  earthenware.  Where  the  partition  is  not  susceptible  of 
being  acted  upon,  the  endosmotic  action  is  very  slight. 

247.  Direction  of  the    current. — The  endosmotic  current  is  in 
general  directed  towards  the  more  dense  liquid,  but  alcohol  and  ether 
are  exceptions ;  they  acting  as  denser  liquids,  although  lighter  than 
water ;  so  also  as  acids  are  more  or  less  diluted,  there  is  endosmose 
towards  the  acid  or  towards  the  water.     The  excess  in  the  quantity  of 
the  liquid  which  passes  into  the  endosmometer,  is  proportional  to  the  sur- 
face of  the  membrane,  and  to  the  different  heights  to  which  the  liquids 
mount  in  capillary  spaces,  the  elevation  taking  place  from  that  side  of 
the  liquid  which  has  least  capillary  action. 

248.  Organic   solutions. — Neutral    organic   substances,    such    as 
gum-arabic,  urea,  and  gelatine,  produce  but  little  endosmotic  action. 
Of  all   vegetable   substances,   sugar   solution ;    and   albumen   among 
animal  bodies;    are  those   which,    with    equal   density,    possess   the 
greatest  power  of  endosmose.     The  figures  attached  to  the  following 
substances,  indicate  the  proportional  height  to  which  the  liquids  rose 
when  the  endosmometer,  being  filled  successively  with  solutions  of 
them,  of  the  same  density,  was  placed  in  pure  water :  gelatine  3,  guin 
5,  sugar  11,  albumen  12. 

249.  Inorganic  solutions. — Neutral  salts  do  not  possess  any  pecu- 
liar power  of  endosmose,  but  diffuse  themselves  with  nearly  the  same 
rapidity  as  if  no  porous  partition  was  used.   Alkaline  solutions  greatly 
accelerate  endosmose.     This  may  be  observed,  even  in  solutions  which 
contain  but  1  part  of  the  alkaline  salt  in  1000  of  water.     In  mode- 
rately dilute  solutions  (containing  not  more  than  2  per  cent,  of  the  salt) 
the  action  is  most  rapid. 

The  soluble  salts  in  the  soil  are  taken  up  by  the  rootlets  of  plants  by 
the  combined  action  of  capillarity  and  endosmose ;  the  salts  entering 
the  plant  more  rapidly  than  the  water  which  holds  them  in  solution. 

250.  Endosmose  of  gases. — There  is  endosmose  between  gases,  as 
between  liquids ;  if  we  connect  two  vessels  containing  different  gases, 
having  a  dry  membrane  between  them,  the  gases  will  gradually  mix, 
equal  currents  being  established  in  both  ;  but  if  the  membrane  is  moist, 
unequal  currents  (that  is,  endosmose)  are  formed.    Thus,  a  soap  bubble 
placed  in  a  jar  of  carbonic  acid,  will,  in  a  little  time,  burst,  owing  to 
the  increase  of  volume  caused  by  endosmose. 

251.  Theories  of  endosmose.— Many  theories  have  been  proposed  to 


OP   FLUIDS.  199 

account  for  these  phenomena :  such  as  that  endosmose  was  due  to  an  unequal 
viscosity  of  the  two  liquids ;  to  currents  of  electricity  passing  in  the  direction 
of  the  endosmose;  to  the  unequal  permeability  of  the  membrane  for  the  two 
liquids,  or,  that  the  phenomenon  was  due  to  capillary  action,  joined  to  the  affi- 
nity of  the  two  liquids.  Very  probably  endosmose  depends  on  the  same  forcei 
that  produce  capillarity,  but  obviously  they  are  not  the  only  forces  which  exert 
influence,  for  we  find  that  heat,  which  always  diminishes  capillarity,  augments 
the  strength  of  the  endosmose. 


Problems  on  Hydrodynamics. 
Elasticity  of  Liquids. 

93.  A  cubic  foot  of  water  at  the  freezing  point  is  submitted  to  a  pressure  of  20 
atmospheres.     How  great  is  the  condensation  ?  and  what  is  the  specific  gravity 
of  the  condensed  liquid  ? 

94.  What  is  the  specific  gravity  of  sea  water  at  the  depth  of  three  miles, 
reckoning  the  specific  gravity  at  the  surface  1-026,  and  the  compressibility 
0-0000436,  and  allowing  a  column  of  fresh  water  33  feet  high  to  equal  the 
pressure  of  one  atmosphere  ? 

95.  How  much  would  the  volume  of  a  cubic  foot  of  alcohol,  at  45°  Fahrenheit, 
be  diminished  by  a  pressure  of  four  atmospheres  ? 

Hydrostatic  Pressure. 

96.  In  the  hydrostatic  press,  given  the  diameters  of  the  two  cylinders  A  and 
B,  and  the  force  applied  to  the  pump  P :  determine  the  pressure  produced. 

97.  In  the  hydrostatic  press,  suppose  the  diameter  of  the  smaller  cylinder  to 
be  1  inch,  and  the  diameter  of  the  larger  cylinder  to  be  15  inches,  the  length  of 
the  pump-handle  to  be  3  feet  from  the  fulcrum,  and  the  distance  of  the  piston  2 
inches  from  the  fulcrum,  the  lever  being  one  of  the  second  order :  what  is  the 
relation  of  the  pressure  exerted  to  the  power  employed  ? 

98.  A  cubical  vessel  is  filled  with  fluid :  compare  the  pressures  upon  the  sides 
and  bottom. 

99.  A  slender  rod  is  immersed  vertically  in  a  fluid :  divide  it  into  three  por- 
tions which  shall  be  equally  pressed. 

100.  Compare  the  pressures  on  two  equal  isosceles  triangles  just  immersed  in 
the  same  fluid,  one  with  its  base  upwards,  the  other  with  the  base  downwards. 

101.  A  cylindrical  vessel  is  filled  with  a  heavy  fluid:  what  proportion  does  \ 
the  pressure  on  the  cylindrical  surface  bear  to  the  entire  weight  of  the  fluid  ? 

102.  If  the  tube,  T,  of  the  water-bellows,  fig.  144,  is  10  feet  high,  and  the 
surface  of  the  bellows,  B  C,  is  18  inches  in  diameter,  what  weight  will  be  sus- 
tained when  the  tube  is  filled  with  water  ?  and  what  when  the  tube  is  filled  with 
mercury  ? 

103.  The  sides  of  a  hollow  pyramid  are  isosceles  triangles,  the   base   is   a 
rectangle  having  sides  a  and  6.   and  the  height  of  the  pyramid  is  c.     If  the 
pyramid  be  placed  with  its  base  on  a  horizontal  plane,  and  filled  with  water, 
how  does  the  whole  amount  of  pressure  on  the  four  sides  compare  with  the 
pressure  upon  the  bottom  ? 

104.  A  hemispherical  vessel,  6  inches  in  diameter,  without  a  bottom,  stands 
on  a  horizontal  plane.    When  just  filled  with  water,  the  liquid  begins  to  run  out 
at  the  bottom.     Determine  the  weight  of  the  vessel. 


200  THE    THREE    STATES    OF    MATTER. 

105.  What  height  must  a  column  of  mercury  have  to  balance  a  column  of 
water  25  feet  high  in  a  communicating  vessel  ? 

106.  If  a  vessel  of  water  communicates  with  a  vessel  of  ether,  standing  at  a 
height  of  20  inches,  at  what  elevation  will  the  water  stand  ? 

Buoyancy  of  Liquids. 

107.  A  man  exerting  all  his  force  can  raise  a  weight  of  300  Ibs. :  what  would 
be  the  weight  of  a  stone  (Sp.  Gr.  =  2-5)  which  he  could  just  raise  under  water  ? 

108.  If  a  given  piece  of  silver  be  balanced  by  its  weight  of  iron  in  air,  what 
addition  must  be  made  to  the  iron  so  that  the  iron  and  silver  may  be  in  equili- 
brium when  immersed  in  water  ? 

109.  How  much  will  12  ounces  of  gold  weigh  when  immersed  in  alcohol  (Sp. 
Gr.  =  0-798)  ? 

110.  If  an  alloy  of  gold  and  silver,  weighing  22  ounces  in  air,.loses  1£  ounces 
when  weighed  in  water,  how  much  of  the  alloy  is  gold,  and  how  much  silver  ? 

111.  To  avoid  imposition  in  the  purchase  of  lead  (due  to  the  fraudulent  intro- 
duction of  pigs  of  iron  encased  in  lead),  the  Russian  government  are  in  the 
habit  of  weighing  the  lead  offered  for  sale  with  weights  of  lead,  on  a  balance  so 
arranged  that  both  pans  can  be  immersed  in  water  after  they  are  brought  to 
equilibrium.     If  the  equilibrium  remains  undisturbed,  the  lead  is  pure.    Other- 
wise its  degree  of  adulteration  can  be  calculated.     Suppose,  by  the  above  test, 
that  1500  Ibs.  of  commercial  lead  is  found  to  be  adulterated  to  such  a  degree  as 
to  require  the  addition  of  10    Ibs.  of  lead  weights  under  water  to  produce  equi- 
librium, what  is  the  amount  of  iron  encased  in  the  commercial  lead  (Sp.  Gr.  of 
lead  =  11-45 ;  of  cast  iron  =  7-64)  ? 

Floating  Bodies. 

112.  Supposing  the  specific  gravity  of  a  man,  of  water,  and  of  cork,  to  be 
1*12,  1,  and  0-24  respectively,  what  quantity  of  cork  must  be  attached  to  a  man 
weighing  150  Ibs.,  that  he  may  just  float  in  water  ? 

113.  A  cylinder,  whose  length  is  greater  than  its  diameter,  having  a  specific 
gravity  of  0*63,  floats  in  water,  what  portion  of  the  diameter  of  the  cylinder  is 
immersed  ? 

114.  What  is  the  bulk  of  a  hollow  vessel  of  copper,  weighing  5  Ibs.,  which 
just  floats  in  water  ? 

115.  How  much  bulk  must  a  hollow  vessel  of  iron  occupy,  weighing  one  ton, 
that  it  may  float  with  only  one-half  its  bulk  immersed  in  water  ? 

116.  A  ship  entering  a  river  from  the  ocean  sinks  2  inches,  and  after  dis- 
charging 12,000  Ibs.  of  cargo  rises  one  inch;  what  is  the  weight  of  the  ship  and 
cargo,  reckoning  the  specific  gravity  of  sea  water  1-026  ? 

117.  A  life-boat  contains  100  cubic  yards  of  wood  (Sp.  Gr.  =  0-8),  and  50 
cubic  yards  of  air  (Sp.  Gr.  =  0-0012).     When  filled  with  fresh  water,  what 
weight  of  iron  ballast  (Sp.  Gr.  =  7-645)  must  be  thrown  into  it  before  it  will 
sink? 

118.  A  parallelepiped  of  ice  whose  dimensions  are  15-75  yards,  20-45  yards, 
and  10-5  yards,  is  floating  in  sea  water  on  its  broadest  face ;  the  specific  gravity 
of  sea  water  is  1-026,  and  that  of  ice  0-93.    Required  the  height  of  the  ice  above 
the  surface  of  the  water. 

119.  When  two  persons,  A  and  B,  descend  together  to  the  bottom  of  a  lake  in 
a  cylindrical  diving-bell,  it  is  observed  that  the  water  stands  1  inch  lower  within 
the  bell  than  when  A  descends  alone;  the  pressure  of  the  atmosphere  is  equal 
to  a  column  of  water  33  feet  high,  the  diameter  of  the  bell  is  4  feet,  and  the  sur- 


OP   FLUIDS.  201 

rs  -«  of  the  water  within  it,  at  the  bottom  of  the  lake,  is  20  feet  below  the  surface 
ol   the  lake ;  find  the  volume  of  B. 

120.  A  piece  of  flint  glass  weighs  in  air  4320  grains,  and  in  water  it  weighs 
3! $5  grains  :  what  is  its  specific  gravity? 

121.  Determine  the  specific  gravity  of  granulated  tin  from  the  following  data: 
"Weight  of  bottle  filled  with  water  at  60°  F.,  .    44-378  grammes. 

"        "   tin, 9-431         " 

"         "   bottle  tin  and  water,       ....     52-515         " 

122.  The  same  specific  gravity  bottle  used  in  the  last  example  is  supplied  with 
7*432  grammes  of  powdered  glass.     The  weight  of  bottle  water  and  powdered 
glass  is  49-859  grammes,  what  is  the  specific  gravity  of  the  powdered  glass  ? 

123.  A  body  weighs  14  Ibs.  in  air,  and  9  Ibs.  in  water ;  another  body  weighs 
81  Ibs.  in  air,  and  7  Ibs.  in  water :  what  are  their  respective  specific  gravities, 
and  how  do  they  compare  with  each  other  ? 

124.  The  counterpoise  of  a  Nicholson's  hydrometer  requisite  to  sink  it  to 
zero  weighs  25  grammes ;   with  a  piece  of  brass  on  the  upper  pan  it  requires 
8-171  grammes  to  sink  it  to  zero,  and  10-241  grammes  when  the  same  piece  of 
brass  is  on  the  lower  pan :  what  is  the  specific  gravity  of  the  brass  ? 

125.  A  Fahrenheit's  hydrometer  weighs  700  grains — to  sink  it  in  water  300 
grains    are   requisite  (volume  of  water  =  to  volume  of  hydrometer  =  1000 
grains),  placed  in  alcohol  132  grains  are  required  to  bring  it  to  zero  (832  grains 
=  volume  of  alcohol  =  volume  of  hydrometer).     What  is  the  specific  gravity 
of  the  alcohol  ? 

Motion  of  Liquids. 

126.  What  volume  of  water  will  flow  from  an  orifice  2|  inches  in  diameter,  in 
7  seconds,  if  the  centre  of  the  orifice  is  10  feet  below  the  surface  of  the  fluid  ? 

127.  A  vessel  20  feet  deep  is  raised  5  feet  above  a  plane :  how  far  will  a  jet 
reach  issuing  5  feet  from  the  bottom  ? 

128.  A  jet  of  water  issuing  from  a  vessel,  3  feet  below  the  surface,  and  an 
equal  distance  above  the  horizontal  plane  on  which  it  falls,  is  seen  to  have  a 
horizontal  range  of  2-3  feet;  how  does  the  velocity  of  discharge  compare  with 
the  theoretical  velocity  ? 

129.  A  jet  of  water  issues  from  a  cylindrical  adjutage  2  inches  in  diameter, 
6i  inches  long,  with  a  head  of  10  feet.     What  amount  of  water  is  discharged 
per  hour  ? 

130.  What  quantity  of  water  will  be  discharged  per  day  through  a  tube  one 
inch  in  diameter  and  19  feet  long,  under  the  pressure  of  21  feet  head  ? 

131.  If  a  fire-engine  discharges  16-8  cubic  feet  of  water  through  a  f  inch 
pipe  in  one  minute,  how  high  will  the  water  be  projected,  the  pipe  being  directed 
vertically  ? 

Capillarity. 

132.  What  will  be  the  difference  of  level  in  a  glass  tube  ^  inch  diameter, 
bent  in  the  form  of  the  letter  U,  when  one  branch  is  filled  with  mercury  and  the 
other  branch  with  alcohol  ? 

133.  A  block  of  marble  10  feet  long  and  2  feet  thick  (the  tenacity  of  marble 
being  9000  Ibs.  to  the  square  inch),  is  burst  asunder  by  the  capillary  attraction 
of  a  series  of  wooden  plugs.     The  series  of -plugs  being  8  inches  apart,  1  inch 
in  diameter,  and    5    inches   long,  the   plugs   are   driven    dry,  and   afterwards 
allowed  to  absorb  water  by  capillarity.     What  height  would  be  required  for  a 
series  of  columns  of  water,  acting  upon  the  orifices  where  the  plugs  are  inserted, 
to  produce  a  similar  rupture  of  the  marble  ? 

20 


202  THE  THREE   STATES   OF   MATTER. 


CHAPTER  IV. 

OF  ELASTIC  FLUIDS,  OR  GASES. 
Pneumatics. 

I.    DISTINGUISHING   PROPERTIES   OF   GASES. 

252.  Definitions. — Pneumatics  —  Gases,  vapors, — tension. — 

Pneumatics  (from  /Zveu/jta,  a  spirit  or  breath,)  is  a  subdivision  of  the 
general  subject  of  Hydrodynamics  (186),  and  is  devoted  to  the  consid- 
eration of  the  properties  of  elastic  fluids. 

Gases  are  elastic  fluids,  aeriform,  transparent,  and  usually  colorless 
and  invisible.  The  blue  color  of  the  air  is  due  to  watery  vapor  in  the 
atmosphere.  In  gases,  the  molecular  force  of  repulsion  (146)  prevails 
over  the  force  of  attraction — and  in  the  permanent  gases  this  force  has 
never  been  overcome. 

Vapors  differ  from  gases  chiefly  in  that  they  are  produced  by  the 
action  of  heat  upon  liquids — as  steam  is  produced  from  water ;  and  by 
their  returning  again  to  the  liquid  state  at  ordinary  temperatures  by 
the  loss  of  heat. 

Tension  is  an  expression  for  the  tendency  of  a  gas  to  expand ;  the 
degree  of  expansive  force  in  each  gas  being  specific  and  varied  by  tem- 
perature, and  mechanical  means. 

Oases,  simple  or  compound. — Of  the  thirty-four  gaseous  bodies  known  in 
chemistry,  four  only  are  simple  or  elementary,  viz.  :  oxygen,  nitrogen,  hydrogen, 
and  chlorine.  The  three  first.named  of  these  gases,  together  with  the  compound 
gases,  oxyd  of  carbon  (CO)  and  the  binoxyd  of  nitrogen  (N  02),  are  the  only 
aeriform  bodies  which  have  thus  far  resisted  the  united  effects  of  cold  and  pres- 
sure, and  permanently  retained  their  gaseous  state.  Hence  they  are  called 
permanent  or  incoercible  gases. 

All  other  gases,  whether  simple  or  compound,  have,  by  the  means  named, 
been  coerced  into  the  liquid  or  solid  state,  and  are  hence  called  non-permanent 
or  coercible  gases. 

253.  Expansion  of  gases.— Expansion  is  the  most  characteristic 
property  of  gases.     This  molecular  force,  for  all  that  appears,  would 
separate  the  particles  of  a  gas  indefinitely  through  all  space,  were  there 
no  counteracting  causes. 

Under  normal  conditions,  the  atmosphere  is  in  a  state  of  equilibrium 
between  the  earth's  attraction  and  its  own  expansive  force.  If  we 


OF   GASES.  203 

disturb  this  condition  of  equilibrium,  we  see  evidence  of  the  exercise 
of  the  power  of  expansion.     In  fig.  199 

199,  a  moist  bladder,  partly  filled  with 
air,  is  subjected  to  a  partial  vacuum 
under  the  air-bell.  As  the  pressure 
in  the  bell  is  diminished  by  working 
the  air-pump,  the  portion  of  confined 
air  expands,  and*  distends  the  flaccid 
bladder  until  it  fills  the  jar.  As  soon 
as  the  equilibrium  of  pressure  is  re- 
stored by  opening  a  communication 
with  the  external  air,  it  contracts 
again  to  its  original  dimensions. 

It  appears,  therefore,  that  gases,  like 
liquids,  are  in  a  state  of  equilibrium, 
the  only  difference  in  the  conditions 
of  equilibrium  being  that,  in  liquids, 
this  state  results  from  the  opposite 
effects  of  the  two  molecular  forces;  while  in  gases,  the  repulsive  force 
is  held  in  control  by  gravity,  or  some  extraneous  force. 

254.  Mechanical  condition  of  gases. — Perfect  freedom  of  motion 
among  their  particles,  as  a  consequence  of  equilibrium,  brings  gases 
under  the  general  definition  of  fluids.     Being  also  elastic,  ponderable, 
and  impenetrable  (14),  it  follows  that  all  the  characteristic  properties 
of  liquids  already  discussed,  apply  also  to  gases.     Atmospheric  air  is 
the  type  of  permanent  gases.     For  its  chemical  constitution,  reference 
is  made  to  chemistry. 

II.     PROPERTIES    COMMON    TO    BOTH    LIQUIDS    AND   GASES. 

255.  Gases  transmit  pressure  equally  in  all  directions. — The 
theorem  of  Pascal,  already  demonstrated  with  respect  to  liquids  (189), 
is  also  true  of  gases. 

Suppose  the  vessel,  fig.  200,  to  be  filled  with  20° 

air  in  the  usual  state  of  tension.  By  its  elas- 
ticity it  exerts  afi  equal  pressure  in  all  direc- 
tions ;  and  by  the  reasoning  in  \  189,  the 
pressure  it  exerts  on  the  pistons  a,  b,  c,  d,  is 
in  proportion  to  their  areas.  '  The  same  is 
true  of  any  part  of  the  inner  surface  of  the 
vessel,  or  of  any  section  of  its  interior. 

If  the  air  within  and  without  the  vessel  has  the  same  tension,  then 
the  pistons  have  no  tendency  to  move,  the  inner  and  outer  pressures 


204  THE   THREE   STATES   OF   MATTER. 

exactly  balancing  each  other.  Any  pressure  applied  upon  either  of 
the  pistons  develops  an  increase  of  elastic  force  in  the  gaseous  contents 
of  the  vessel,  proportioned  to  the  amount  of  compression.  This  pres- 
sure reacts  on  every  portion  of  the  inner  surface  of  the  vessel,  and  moves 
each  of  the  other  pistons  outwards  with  a  force  proportioned  to  its  area. 

The  chief  difference  between  the  transmission  of  pressure  in  gases  and  liquids 
is,  that  in  gases,  owing  to  their  elasticity,  the  effects  of  pressure  are  not  felt  at 
long  distances,  so  instantaneously  as  in  liquids.  * 

The  distribution  of  illuminating  gas  in  cities  through  many  miles  of  pipes, 
illustrates  both  the  law  and  the  exception. 

The  reaction  due  to  elasticity  prevents,  as  is  well  known,  the  driving  of  a 
blast  of  air  in  an  effective  manner  through  small  and  tortuous  passages. 

The  laws  and  illustrations  regarding  the  pressure  and  equilibrium  of  liquids, 
contained  in  §§  191,  192,  193,  and  199,  are  also  true  of  gases;  and  it  is  there- 
fore needless  to  repeat  them  in  this  connection. 

256.  The  atmosphere. — Its  general  phenomena. — A  vast  aerial 
ocean  rests  upon  the  surface  of  the  earth,  penetrates  even  its  solid 
crust,  and  is  dissolved,  to  a  certain  extent,  in  its  waters.  It  is  composed 
of  the  two  incoercible  gases,  nitrogen  and  oxygen,  in  the  proportion  of 
nearly  four  parts  of  the  first,  to  one  part  of  the  second,  by  measure. 
It  is  held  in  its  place  by  the  force  of  gravitation,  which,  counteracting 
the  molecular  force  of  repulsion,  brings  it  to  equilibrium  at  about  forty- 
five  miles  above  the  earth.  This  height  of  the  atmosphere  has  been 
determined  chiefly  from  the  phenomena  of  refraction,  as  observed  in 
its  effect  on  the  rising  and  setting  of  the  heavenly  bodies. 

It  is  the  opinion  of  Bunsen  and  others  that  the  atmosphere  extends  to  a  dis- 
tance of  about  200  miles,  although  its  density,  above  45  miles,  is  too  small  to 
refract  light  to  such  a  degree  as  to  enable  us  to  observe  it.  Many  pneumatic 
experiments  are  thought  also  to  indicate  an  altitude  of  the  atmosphere  exceeding 
45  miles. 

The  atmosphere  partakes  of  the  motion  of  the  earth,  but  its  state  of 
rest,  with  respect  to  bodies  on  the  earth's  surface,  is  disturbed  by  winds 
and  currents,  caused  by  agencies  to  be  considered  hereafter. 

Like  the  ocean,  the  upper  surface  of  the  atmosphere  must,  theoretically, 
have  a  definite  surface,  since  each  particle  is  influenced  by  gravity  in 
a  similai  manner,  and  the  resultant  direction  of  thes^p  actions  at  any 
point  must  be  a  radius  of  the  earth  (199). 

It  follows  from  §  191,  that  each  molecule  of  air  exerts,  at  a  given 
level,  the  pressure  due  to  the  weight  of  a  continuous  line  of  molecules, 
extending  vertically  from  the  point  chosen  to  the  outer  limits  of  the 
atmosphere.  Therefore  its  upward  pressure  (192),  its  pressure  on  the 
sides  of  any  vessel  (193),  and  its  buoyancy  (205),  are  the  same,  and 
governed  'by  the  same  laws  as  those  already  enunciated  for  liquids ; 


OF   GASES. 


205 


provided  always  that  there  is  a  communication,  however  small,  between 
the  outer  air  and  the  interior  of  any  given  vessel. 

257.  Atmospheric  pressure. — The  great  weight,  and  consequent 
pressure  of  the  atmosphere  upon  bodies  near  the  surface  of  the  earth, 
was  unsuspected  by  mankind  in  general,  until  Torricelli,  in  1643,  first 
announced  it. 

As  it  is  exerted,  in  obedience  to  the  laws  of  fluid  equilibrium  (199), 
alike  above,  below,  and  on  the  sides  of  all  bodies,  a  man  of  usual  size 
moves  about  unconscious  that  he  sustains  a  constant  load  of  over  30,000 
pounds,  or  more  than  fifteen  tons.  If  this  pressure  is  partially  re- 
moved from  one  surface  of  a  body,  its  existence  then  becomes  very 
manifest. 

201  202 


In  fig.  201,  the  upper  end  of  an  air-jar  is  hermetically  sealed  by  a  bladder 
skin  tied  on  when  wet  and  dried.  Its  lower  edge  rests  upon  the  well-ground 
plate  of  an  air-pump.  As  the  air  in  the  jar  is  gradually  exhausted  by  working 
the  pump,  the  surface  of  the  bladder  becomes  more  and  more  depressed,  until, 
linally,  the  membrane  bursts,  with  a  sharp  report,  owing  to  the  pressure  of  the 
atmosphere  resting  upon  it. 

This  experiment  demonstrates  the  downward  pressure  of  the  atmosphere  only. 

Its  upward  pressure  is  illustrated  by  the  apparatus  seen  in  fig.  202. 

A  glass  jar  having  an  open  bottom,  and  sustained  on  a  tripod,  is  covered  by 
an  impervious  caoutchouc  bag.  When  a  partial  vacuum  is  produced  in  the  jar 
through  the  upper  opening,  the  yielding  bag  rises  and  carries  with  it  the 
weight  which  is  hung  below.  This  heavy  mass  is  sustained  in  mid  air  as  on  an 
elastic  spring  by  the  upward  pressure. 

The  upward  pressure  of  the  air  may  also  be  illustrated  by  a  familiar  experi- 
ment with  a  tumbler.  Fill  a  tumbler  with  water,  and  lay  over  it  a  piece  of 
paper, — hold  the  paper  in  its  place  by  laying  upon  it  a  board  or  the  palm  of  the 
hand,— turn  the  tumbler  bottom  upwards,  and  remove  the  hand  or  board,  the 
20* 


206 


THE    THREE    STATES    OF    MATTER. 


upward  pressure  of  the  atmosphere  will  then  retain  the  paper  in  its  place,  closing 
the  tumbler,  and  preventing  the  discharge  of  the  water. 

The  pressure  of  the  air  from  all  sides  is  shown  by  the  well-known 
Magdeburg  hemispheres.  203 

This  apparatus  is  composed  of  two  hollow  hemi- 
spheres of  brass,  fig.  203,  whose  accurately  fitting 
edges  are  well  greased.  One  of  the  hemispheres  is 
furnished  with  a  stop-cock,  by  which  connection 
is  made  with  an  air-pump.  Placing  this  apparatus 
upon  the  air-pump,  and  exhausting  the  air,  it  will 
be  found  that  the  hemispheres  can  no  longer  be 
separated,  no  matter  in  what  position  they  may  be 
held  j  proving  that  the  atmospheric  pressure  which 
alone  keeps  the  hemispheres  together,  is  exerted  in 
all  directions.  Rings  adapted  to  each  hemisphere, 
enable  two  persons  to  test  their  strength  against 
the  atmospheric  pressure.  Otto  V.  Guerick,  who 
invented  them,  employed  a  pair  which  held  all  the 
power  of  a  strong  team  of  horses. 

These  illustrations,  easily  multiplied  by  the  ingenuity  of  the  teacher,  give  evi- 
dence of  the  fact  of  atmospheric  pressure  in  all  directions,  but  do  not  indicate  its 
amount. 

258.  Buoyancy  of  air. — Bodies  weighed 
in  air  are  sustained  or  buoyed  up  by  a  force 
equal  to  the  weight  of  the  volume  of  air  dis- 
placed, in  accordance  with  the  Archimedean 
principle  (205). 

This  law  is  well  illustrated  by  the  appa- 
ratus seen  in  fig.  204.  A  hollow  globe  of 
brass  is  counterpoised  on  one  arm  of  a  balance 
by  a  brass  weiglri  at  the  other  end.  Placed 
on  the  plate  of  an  air-pump,  and  covered  by  n 
a  bell-glass,  the  air  may  be  removed  from  N; 
contact  with  the  two  masses  previously  in 
equilibrium ;  and,  in  proportion  as  the  vacuum 
is  produced,  the  globe  begins  to  preponderate  by  a  force  as  much 
greater  than  the  action  of  gravity  upon  the  counterpoise  as  the  weight 
of  its  own  volume  of  air  is  greater  than  that  of  the  counterpoise. 

The  brass  and  platinum  weights  used  in  delicate  determinations  of 
weight  are  standards  only  when  in  vacuum.  Let  us  then  represent  the 
various  values  as  follows  : — 

W  =  weight  of  the  body  in  air  as  estimated  by  standard  weights,  and  also 
the  weight  of  the  standard  weights  themselves  in  a  vacuum. 
7'  =.  volume  of  the  standard  weights  in  cubic  inches. 
V  =  volume  of  the  body  in  cubic  inches. 

w  =  weight  of  one  cubic  inch  of  air  at  the  time  of  the  weighing. 
W  =  weight  of  the  body  in  a  vacuum — which  we  wish  to  find. 


OF   GASES.  207 

We  can  now  easily  deduce  the  following  values : — 

Pto  =  buoyancy  of  air  on  the  weights. 

Vw  =  buoyancy  of  air  on  the  body. 

W —  Vw  =  actual  weight  of  standard  weights  in  air. 

W —  Vw  =  actual  weight  of  body  in  air. 

Since  these  weights  just  balance  each  other,  we  have, 

W—  Vw  =  W—  Vw,     or  W=W'-\-v>(V—  V). 

The  correction  w  (V—V),  which  must  be  made  to  the  weight  determined  by 
the  balance  in  air  in  order  to  obtain  the  weight  in  a  vacuum,  is  evidently  addi- 
tive when  the  volume  of  the  body  is  greater  than  the  weights,  and  subtractive 
when  these  conditions  are  reversed.  When  the  volumes  are  equal,  the  correction 
becomes  zero,  and  the  balance  yields  the  same  results  in  air  as  in  a  vacuum.* 

If  a  vessel,  whose  capacity  is  100  cubic  inches,  is  exhausted  of  air 
and  weighed,  fig.  205,  and  after  filling  it  with  dry  air  at  the  ordinary 
temperature  and  pressure,  it  is  weighed  again,  it  will  205 

be  found  that  its  weight  is  31*074  grains  more  than  at. 
first;  that  is,  100  cubic  inches  of  air  weigh  31*074 
grains.  Air  is  the  standard  of  comparison  in  density 
for  all  gases  and  vapors. 

259.  Impenetrability  of  air. — Air  is  impenetrable. 
This  may  be  shown  by  inverting  a  hollow  vessel,  as  a 
tumbler,    upon   the   surface   of  water;   when   pressed 
downward  the  water  will  not  rise  and  fill  the  tumbler, 
because  of  the  impenetrability  of  the  air.     The  diving- 
bell  depends  on  this  quality  of  air :  it  consists  of  a  large 
bell-shaped  vessel,  sunk  by  means  of  weights  into  the 

sea,  with  its  mouth  downwards.  Notwithstanding  the  open  mouth, 
and  enormous  pressure  of  the  sea,  the  water  is  excluded  from  the  bell, 
because  of  the  air  contained  within. 

260.  Inertia  of  air. — Wind  is  only  air  in  motion.     If  the  air  had 
no  inertia,  it  would  require  no  force  to  impart  motion  to  it,  nor  could 
it  acquire  momentum.    We  know  that  the  force  encountered  by  a  body 
moving  through  the  air  (that  is,  displacing  the  air),  is  in  proportion  to 
the  surface  exposed,  and  the  velocity  with  which  it  is  moving  (143). 

The  sailing  of  ships,  the  direction  of  balloons,  the  wind-mill,  and  the 
frightful  ravages  of  the  tornado,  are  all  familiar  examples  of  the  power 
of  moving  air,  and  consequently  proofs  of  its  inertia. 

III.     BAROMETERS  AND  BALLOONS. 

261.  Torricellian  vacuum.— Measure    of   atmospheric    pres- 
sure.— The  amount  of  pressure  exerted  by  the  atmosphere  was  first 
determined  by  Torricelli,  a  disciple  of  Galileo,  in  1643. 

*  Cooke's  Chem.  Physics,  p.  269. 


208 


THE   THREE    STATES    OF    MATTEK. 


If  a  glass  tube,  aB,  fig.  206,  about  32  inches  in  length,  is  filled  with 
mercury,  and  then  inverted  in  a  vessel  of  the  same  fluid,  the  liquid 
column  will  fall  some  distance,  and  after  several  oscillations  will  come 
to  rest  at  n,  a  height  at  the  level  of  the  sea,  of  about  thirty  inches 
above  the  level,  cfc,  of  the  mercury  in  the  vessel.  206 

The  space  n  B,  above  the  mercury,  is  the  most 
complete  vacuum  attainable  by  mechanical  means, 
and  is  called  the  Torricellian  vacuum.  If,  after 
having  closed  the  mouth  of  the  tube,  we  lift  it  out 
of  the  dish,  we  shall  find  that  the  weight  of  the 
column  of  mercury  pressing  against  the  finger  is 
very  considerable.  When  we  place  the  tube  in  the 
vessel  of  mercury,  we  have  this  same  force  exerted, 
the  column  of  mercury  tending  to  flow  out  of  the 
tube,  and  another  force,  the  weight  and  pressure 
of  the  atmosphere,  tending  to  push  the  mercury  up 
in  the  tube.  The  length  of  the  mercurial  column, 
it  is  evident,  is  in  proportion  to  the  atmospheric 
pressure,  which  under  ordinary  circumstances,  is 
equivalent  to  a  column  of  mercury  thirty  inches  in 
height. 

We  may  now  easily  estimate  the  pressure  on  any  given 
surface,  as,  for  example,  a  square  inch.  If  we  should 
take  a  tube  whoso  base  is  a  square  inch,  and  repeat  the 
above  experiment,  the  column  a  n  would,  as  before,  be 
sustained  at  a  'height  of  thirty  inches ;  but  the  weight 
of  a  column  of  mercury  thirty  inches  in  height  and  one 
inch  square,  is  very  nearly  fifteen  Ibs. ;  therefore  the 
atmospheric  pressure  on  a  square  inch  is  fifteen  Ibs. 
(accurately  14-7225  Ibs). 

If  the  tube  were  filled  with  a  liquid  lighter  than  mercury,  a  proportionally 
longer  column  would  be  sustained  by  the  pressure  of  the  atmosphere  :  the  length 
of  the  column  being  inversely  as  the  densities  of  the  two  fluids.  If  water,  which 
is  about  13*5  times  lighter  than  mercury,  was  used,  the  column  of  water  sustained 
would  be  13'5  times  as  long  as  the  mercurial  column,  or  about  thirty-four  feet. 

262.  Pascal's  experiments. — The  experiment  of  Torricelli  excited 
the  greatest  sensation  throughout  the  scientific  world,  and  the  explana- 
tion he,  gave  of  it  was  generally  rejected. 

Pascal,  who  flourished  at  that  time,  perceived  its  truth,  and  proposed  to  sub- 
ject the  experiment  to  a  test  which  must  put  an  end  to  all  further  dispute.  "  If," 
said  Pascal,  "  it  be  really  the  weight  of  the  atmosphere  under  which  we  live, 
that  supports  the  column  of  mercury  in  Torricelli's  tube,  we  shall  find  by  trans- 
porting this  tube  to  a  loftier  point  in  the  atmosphere,  that  in  proportion  as  we 
leave  below  more  and  more  of  the  air,  there  will  be  a  less  column  of  mercury 
sustained  in  the  tube."  Pascal  therefore  carried  a  Torricellian  tube  to  the  top  of 
a  lofty  mountain,  called  the  Puy-de-Dorne,  in  Auvergne  (central  France).  It 


OP   GASES. 


209 


207 


was  found  that  the  column  gradually  diminished  in  height  a3  the  elevation  to 
which  the  instrument  was  carried  increased.  He  repeated  this  experiment  at 
llouen  (France),  in  1646,  with  a  tube  of  water,  and  found  that  the  column  was 
sustained  at  a  height  of  about  thirty-four  feet,  or  13-59  times  greater  than  the 
height  of  the  column  of  mercury. 

263.  Construction  of  barometers.  —  Barometer  is  the  name  given 
to  Torricelli's  tube.  This  instrument  has  different  forms,  according  to 
the  use  for  which  it  is  designed.  There  are,  however,  certain  conditions  to 
be  fulfilled  in  the  construction  of  barometers,  whatever  may  be  their  form. 

1st.  It  is  necessary  that  the  mercury  be  perfectly  pure  and  free  from 
oxyd,  otherwise  it  adheres  to  the  glass;  again,  by  impurities,  its 
density  is  changed,  and  the  height  of  the  column  in  the  barometer  is 
greater  or  less  than  it  should  be. 

2d.  It  is  necessary  that  there  be  a  perfect  vacuum  above  the  surface 
of  the  mercury  in  the  tube  ;  for  if  there  be  a  little  air,  or  vapor,  as  of 
water,  the  elasticity  of  these  will  continually  depress  the  mercurial 
column,  preventing  its  rising  to  the  true  height. 

To  obtain  a  perfect  vacuum,  a  small  portion  of  pure  mercury  is  boiled  in  th» 
barometer  tube,  and  when  cooled,  another  portion 
of  mercury  is  added,  and  again  boiled,  and  so  on,^ 
until  the  tube  is  full;  by.  this  means  the  air  and 
moisture  which  adhered  to  the  walls  of  the  tube  are 
driven  out  completely.  The  boiling  must  not  be  too 
long  continued,  otherwise  a  portion  of  oxyd  will 
be  formed,  which  will  dissolve  in  the  mercury  and 
alter  its  density.  The  tube  being  filled,  we  invert 
it  in  a  vessel  of  pure  mercury.  In  order  to  determine 
whether  there  is  not  some  air  or  moisture  in  the 
tube,  we  incline  the  tube  quickly  ;  if  the  mercury 
gives  a  dry  metallic  sound  when  striking  the  sum- 
mit of  the  tube,  it  is  a  proof  of  their  absence,  while, 
if  they  be  present,  the  sound  is  deadened. 

2(54.  Apparatus  illustrating  the  princi- 
ple of  the  barometer.  —  By  means  of  the  air- 
pump,  and  the  apparatus  fig.  207,  the  princi- 
ple of  the  barometer  is  beautifully  shown. 

The  apparatus  consists  of  a  large  bell-glass,  R, 
with  two  syphon  barometer  tubes  attached.  One  of 
them,  B,  has  its  cistern  within  the  bell.  The  other 
barometer,  whose  cistern  is  without  the  bell,  com- 
municates with  its  interior  by  the  curved  tube  1  1'. 
When  this  apparatus  is  placed  on  the  air-pump,  and 

exhausted  of  air,  the  mercury  in  B  falls  in  proportion  to  the  vacuum  produced, 
and  rises  in  the  tube  C  I,  in  the  same  proportion.  In  B  we  see  the  effect  of  dimin- 
ished pressure,  as  on  a  mountain  or  in  a  balloon  ;  in  C  the  pressure  of  the  external 
air  causes  the  mercury  in  it  to  rise,  forming  a  gauge  of  the  exhaustion.  When 
the  air  is  allowed  to  enter,  the  mercury  in  the  tubes  resumes  its  former  position. 


210 


THE    THREE    STATES    OF    MATTER. 


265.  Height  of  the  barometric  column  at  different  elevations. 
— The  following  table  gives  a  comparative  view  of  the  height  of  mer- 
cury in  the  barometer  at  different  elevations  above  the  sea. 

At  the  level  of  the  sea,  the  mercury  stands  at         30          inches. 

5,000  feet  above     "  "  "  24-773       " 

10,000     "     [height  of  Mt.  JEtna,]  "  20-459       " 

15,000     "     [height  of  Mt.  Blanc,]  "  16'896       " 

3  miles  16-361       " 

6     "     [above  the  top  of  the  loftiest  mountain,]    8'923       " 

9     "  4-866       " 

15     "  1-448      " 

266.  Cistern  barometer. — The  cistern  barometer  is 
the  most  simple  form  of  this  useful  instrument.     It  con- 
sists of  a  Torricelli's  tube  of  glass,  filled  with  mercury 
and  plunged  into  a  vessel  containing  the  same  metal; 
this  vessel  or  cistern  is  of  various  forms. 

That  it  may  be  transported  easily,  the  cistern  is  divided  into 
two  compartments,  m,  n,  fig.  208 ;  the  upper  division  is  cemented 
to  the  tube,  communicating  with  the  atmosphere  by  the  small 
hole  a.  The  two  compartments  are  united  by  the  narrow  neck 
into  which  the  lower  part  of  the  barometer  tube  enters,  fitting 
closely,  although  not  touching  the  walls ;  leaving  only  so  small 
a  space,  that  capillarity  will  not  allow  the  mercury  to  escape 
from  the  lower  compartment  when  we  incline  the  barometer.  So 
that  in  whatever  position  we  place  it,  no  air  can  enter  the  lower 
end  of  the  tube. 

This  barometer  is  always  fixed  on  a  wooden  support,  at  the 
upper  part  of  which  is  a  graduated  scale,  whose  zero  is  the  level 
of  the  mercury  in  the  cistern.  The  sliding  scale  i  indicates  the 
level  of  the  mercury  in  the  tube.  There  is  attached  209 

to  barometers  also  a  slider,  moving  by  the  hand 
upon  which  is  a  vernier,  by  means  of  which  we 
can  distinguish  very  small  variations.  But  the 
level  of  the  mercury  in  the  cistern  varies  as  the 
column  of  mercury  in  the  tube  ascends  or  de- 
scends, for  then  a  certain  quantity  of  mercury 
passes  from  the  cistern  into  the  tube,  or  the  re- 
verse, so  that  the  zero  (the  level)  changing  the 
graduation  on  the  scale,  does  not  indicate  the 
true  height  of  the  barometer. 

Fortin's  barometer.— This  error  is 
avoided  in  the  barometer  of  Fortin,  fig. 
211,  by  means  of  a  cistern  of  peculiar  con- 
struction, shown  in  fig.  209. 

The  lower  part  is  of  deer-skin,  and  is  elevated  or  depressed  by  means  of  the 


OF    GASES. 


211 


screw,  C,  pressing  the  plate  D  B.  At  the  upper  wall  of  the  cistern  is  fixed  a 
small  ivory  needle,  A,  whose  point  corresponds  exactly  to  the  zero  of  the  scale, 
graduated  on  the  case.  At  each  observation  with  this  instrument,  care  is  taken 
to  make  the  level  of  the  mercury  in  the  cistern,  correspond  with  212 

this  point,  which  is  accomplished  by  turning  the  screw  up  or 
down. 

Vernier. — To  secure  great  accuracy  in  measuring        211 
the  height  of  the  mercurial  column,  the  barometer  is 
furnished  with  a  vernier,  B  C,  fig.  210.    Ten  divisions 
on  the  vernier  correspond  with  nine  divisions  of  the 
graduated    scale.     The   vernier    is  210 

moved  by  a  rack  and  pinion  until  its 
lower  extremity  corresponds  very 
accurately  with  the  surface  of  the 
mercury  in  the  barometer  tube.  In 
the  figure  the  mercurial  column  is 
seen  to  stand  a  little  above  the  divi- 
sion marked  760.  Counting  upward 
we  see  that  the  seventh  division  of 
the  vernier  is  exactly  opposite  one 
of  the  divisions  on  the  graduated 
scale.  This  gives  the  small  portion 
of  the  column  above  760  equal  to 
seven-tenths  of  a  division  of  the 
scale,  and  the  height  of  the  column 
is  read  760-7. 

This  form  of  barometer  has  been 
adopted  by  the  Smithsonian  Insti- 
tution, and  is  made  by  Mr.  Green, 
of  N.  Y. 

267.  The  syphon  baro 
meter,  invented  by  Gay  Lus- 
sac,  consists  of  two  tubes,  fig. 
212,  of  the  same  internal  dimen- 
sions, united  by  a  very  capil- 
lary neck,  both  closed  at  their 
upper  extremities,  the  air  enter- 
ing the  cistern  through  a  small 
hole  at  C.  The  large  tubes  being 
of  the  same  interior  diameter, 
the  capillary  action  is  mutually  destroyed.  The  capillary  tube  is  made 
small,  so  that  when  we  turn  the  instrument  over,  it  remains  full, 
because  of  its  capillarity.  For  measuring  the  height  of  the  mercury, 
there  are  two  scales,  E  and  D,  graduated  in  different  directions,  having 
their  common  zero  at  0,  on  a  line  intermediate  between  the  two  mer- 
curial surfaces ;  so  that  by  adding  the  indications  of  these  two  scales, 
we  have  the  difference  in  the  level  of  the  mercury  in  the  two  tubes. 


212 


THE   THREE   STATES   OF   MATTER. 


But  a  quick  movement,  transportation  in  a  carriage  or  on  horseback,  may 
divide  the  mercurial  column  in  the  capillary  tube,  and  thus  allow  the  air  to  pass 
into  the  long  arm,  whereby  the  accuracy  of  the  instrument  would  be  destroyed. 

In  order  to  obviate  this  inconvenience,  M.  Bunten  215 

has  modified  the  instrument  as  represented  in  fig.  213. 
The  long  arm  A  drawn  out  to  a  point,  enters  into  and 
is  soldered  to  a  larger  tube,  K,  which  is  attached  to 
the  capillary  tube.     With  this  arrangement,   should 
bubbles  of  air   even  pass  through  the  capillary  tube, 
they  cannot  enter  the  long  arm,  but  are         214 
retained  in  the  top  of  K.     These  bubbles 
of  air  have  no  influence  on  the  observa- 
tions, and  may  be  driven   out  by  simply 
heating  the  tube. 

268.  "Wheel     barometer.— The 
wheel   barometer   is   an   instrument 
of  no  scientific  value,  but  has  a  cer- 
tain popular  interest  as  it  purports 
to  declare  the  state  of  the  weather. 
The  apparatus  consists,  figs.  214  and 
215,  of  a  dial  plate  attached       213 

to  a  syphon  barometer  hav- 
ing a  small  cylindrical  cis- 
tern, upon  whose  surface 
rests  a  float;  this  is  at- 
tached to  a  silk  string, 
which  winds  around  a  pul- 
ley, 0,  and  is  terminated 
by  the  counterpoise  P  ;  the 
axis  of  the  pulley  carries 
a  needle,  which  rests  upon 
the  face  of  the  dial  plate. 
When  the  pressure  of  the  atmosphere  changes,  the  column  rises  or  falls 
in  the  tube  accordingly,  and  carries  along  with  it  the  float.  The  pulley 
turns  and  moves  the  needle  to  the  words  rain — fair — changeable,  &c., 
which  are  designed  to  correspond  to  certain  heights  of  the  mercurial 
column. 

269.  Causes  of  error. — In  order  to  obtain  the  true  height  of  the 
mercury  in  a  barometer,  we  must,  after  making  the  observation,  deter- 
mine by  calculation  the  error  caused  by  capillarity,  and  by  the  variations 
of  density,  caused  by  changes  of  temperature. 

Correction  for  capillarity. — When  the  barometer  tube  is  of  capil- 
lary diameter,  the  surface  of  the  mercury  in  it  becomes  convex  (233) 
and  the  depression  is  greater  by  as  much  as  the  tube  is  more  capillary. 


OF    GASES. 


213 


For  correcting  this  error,  it  is  necessary  to  know  the  diameter  of  the 
tube,  and  then  by  means  of  the  table  (238),  ascertain  the  depression, 
whici  must  always  be  added  to  the  observed  height. 

Correction  for  temperature. — In  all  mercurial  barometers,  we 
must  have  regard  to  the  temperature,  for  as  heat  expands  mercury,  it 
diminishes  its  density,  and  in  consequence,  under  the  same  atmospheric 
pressure  the  mercury  would  rise  as  much  higher  as  the  temperature  wa  < 
more  elevated.  Consequently  barometric  observations  cannot  be  com- 
pared, unless  they  were  taken  at  the  same  temperature,  or  are  brought 
by  calculation  to  the  same  standard. 

As  it  is  entirely  arbitrary  what  temperature  shall  be  chosen;  that  of  melting 
ice  has  generally  been  taken.  A  table  showing  the  expansion  and  contraction 
of  mercury  at  different  temperatures  may  be  found  in  the  chapter  upon  heat. 
The  metallic  and  aneroid  barometers  have  already  been  described  (163,  164). 

270.  Variations  of  the  barometric  height. — When  we  observe  a 
barometer  during  many  days,  we  notice  that  not  only  does  its  height 
vary  from  day  to  day,  but  also  in  the  same  day.  The  amount  of  these 
variations  increases  from  the  equator  towards  the  poles.  The  greatest 
variations  (excepting  extraordinary  cases)  are  6  m.  m.  ('2362  in.)  at 
the  equator;  30  m.  m.  (1*181  in.)  at  the  tropic  of  cancer;  40  m.  m. 
(1-5748  in.)  in  France,  and  60  m.  m.  (2'3622  in.)  25°  from  the  pole^. 
The  greatest  variations  take  place  in  winter. 

The  mean  diurnal  height  is  the  average  of  twenty-four  successive  observations 
taken  from  hour  to  hour.  M.  Ramond  has  found  the  height  of  the  barometer  at 
noon  to  be  the  mean  of  the  day.  The  216 

mean  monthly  height  is  the  average  of  the 
thirty  mean  daily  heights  of  a  month. 
The  mean  annual  height  is  the  average  of 
the  three  hundred  and  sixty-five  mean 
daily  heights  of  a  year. 

At  the  equator  the  mean  annual  height 
is  758  m.  m.  (29-842  in.)  It  increases, 
passing  from  the  equator,  and  attains  its 
maximum  of  763  m.  m.  (30-04  in.)  between 
the  latitudes  of  30°  and  40°;  it  decreases 
in  more  elevated  latitudes.  The  mean 
monthly  height  is  greater  in  winter  than  in 
summer,  because  of  the  cooling,  and  conse- 
quent increased  density  of  the  atmosphere. 

The  scale,  fig.  216,  shows  the  barometric 
variations  of  the  different  months.  Equal 
distances,  taken  on  the  lower  horizontal  j.  f.  m.  a.  m.  j.  j.  a.  ».  o.  n.  d. 
line,  j — d,  represent  the  duration  of  the  different  months,  and  the  curved  lines  s> 
the  commencement  of  each  interval,  the  mean  barometric  heights  correspondin 
to  the  successive  months.  We  have  then  curves,  whose  inflexions  make  known 
the  variations  of  the  mean  from  one  month  to  another.  The  four  curves  repre- 
21 


V 


II 


214  THE    THREE    STATES    OF    MATTER. 

sent  the  monthly  means  as  observed  at  Calcutta,  C,  at  Havana,  H;  Paris,  P, 
and  at  St.  Petersburg,  S.  P.  The  differences  of  the  curves  represent,  with 
great  distinctness,  the  differences  of  the  mean  barometric  heights.  Calcutta 
and  Havana,  on  the  same  latitude,  have,  it  will  be  seen,  very  different  monthly 
means. 

Variations  observed  in  Barometers  are  of  two  kinds. 

1st.  Accidental  variations,  which  do  not  offer  any  regularity  in  their 
movements,  and  which  depend  on  seasons,  the  direction  of  the  wind, 
and  geographical  position. 

2d.  Diurnal  variations. — It  was  about  the  year  1722,  that  the  hourly 
variations  of  the  barometer  were  proved  to  take  place  in  a  regular 
manner.  From  that  time,  many  observers  have  labored  to  determine 
the  extent  and  the  periods  for  the  different  parts  of  the  earth.  Alex. 
Von  Humboldt,  with  others,  has  demonstrated  by  a  long  series  of  very 
accurate  observations  at  the  equator,  that  the  maximum  of  height  cor- 
responds to  9  o'clock  in  the  morning ;  the  barometer  then  falls  to  its 
minimum  at  four,  or  half  past  four  o'clock  in  the  afternoon;  it  then 
rises,  attaining  a  second  maximum  about  ten  o'clock  at  night.  These 
movements  are  so  regular,  they  almost  serve  to  mark  the  hours  like  a 
clock,  but  they  are  very  small.  M.  Humboldt  found  that  the  distance 
between  the  highest  point  in  the  morning,  and  the  lowest  point  in  the 
afternoon,  was  but  two  m.  m.  In  the  temperate  zones,  these  diurnal 
variations  also  take  place,  but  are  very  difficult  to  ascertain,  because 
of  the  accidental  variations,  so  that  it  requires  extended  and  very  accu- 
rate observations  in  order  to  determine  them.  The  hours  of  the  maxi- 
mum and  minimum  of  the  diurnal  variations,  appear  to  be  nearly  the 
same  in  all  climates,  varying  a  little  with  the  season.  Thus,  in  winter 
(in  France),  the  maximum  is  at  nine  o'clock  in  the  morning,  the  mini- 
mum at  three  o'clock  in  the  afternoon,  and  the  second  maximum  at 
nine  o'clock  in  the  evening.  In  summer,  the  maximum  takes  place 
before  eight  o'clock  in  the  morning,  the  minimum  at  four  o'clock  in 
the  afternoon,  and  the  second  maximum  at  eight  o'clock  at  night.  In 
spring  and  in  autumn,  the  critical  hours  are  intermediate. 

271.  Relation  between  barometric  changes  and  the  weather. 
— Those  variations  of  the  barometer  which  are  not  periodic,  are  gene- 
rally supposed  to  be  indications  of  changes  in  the  weather.  For  it  has 
been  noticed  that  those  days  in  which  the  column  of  mercury  was 
2972  inches  in  height,  there  was  very  changeable  weather ;  that  in  a 
majority  of  those  days  when  the  mercury  rose  above  this  point,  there 
was  fine  weather  ;  when  it  fell  below  this  point,  stormy  weather,  snow, 
or  rain,  prevailed.  It  is  from  these  coincidences  between  the  height 
of  the  barometer  and  the  state  of  the  weather,  that  there  is  marked  on 


OF   GASES.  215 

the  scale  or  dial  plate  of  barometers,  at  certain  heights,  the  words 
stormy,  rain  or  snow,  variable,  fine  weather,  &c.,  and  it  is  supposed 
that  when  the  mercury  stands  at  the  height  indicated  respectively  by 
these  words,  we  should  have  corresponding  weather.  Now,  although 
this  may  be  true  to  a  certain  extent,  yet  a  little  reflection  will  show  the 
fallacy  of  such  indications.  The  height  of  the  mercurial  column  varies 
with  the  position  of  the  barometer,  and  consequently  two  barometers, 
in  different  places,  not  upon  the  same  level,  would  indicate  different 
coming  changes.  The  changes  of  weather  are  indicated  in  the  barome- 
ter, not  by  the  actual  height  of  the  mercurial  column,  but  by  its 
changes  of  height. 

Rules  by  which  coming  changes  are  indicated. — The  follow- 
ing rules  may,  to  some  extent,  be  relied  upon,  but,  for  reasons  already 
stated,  must  be  taken  with  a  considerable  degree  of  allowance. 

1.  The  sudden  fall  of  the  mercury  is  usually  followed  by  high  winds 
and  storms. 

2.  The  rising  of  the  mercury  indicates  generally  the  approach  of 
fair  weather  ;  the  falling  of  it  shows  the  approach  of  foul  weather. 

3.  In  sultry  weather,   the  falling  of  the  mercury  indicates  coming 
thunder.     In  winter,  the  rise  of  the  mercury  indicates  frost.     In  frosty 
weather,  its  fall  indicates  thaw,  and  its  rise  indicates  snow. 

4.  Whatever  change  of  weather  follows   a  sudden  change   in   the 
barometer,  may  be  expected  to  last  but  a  short  time. 

5.  When  the  barometer  alters  slowly,  a  long  continuation  of  foul 
weather  will  succeed  if  the  column  falls,  or  of  fair  weather  if  the 
column  rises. 

6.  A  fluctuating  and  unsettled  state  in  the  mercurial  column,  indi- 
cates changeable  weather. 

272.  Measure  of  heights  by  the  barometer. — Since  the  level  of 
the  mercury  in  the  barometer  falls,  as  we  ascend  above  the  earth,  we 
see  that  it  is  possible  to  determine  by  barometric  observations,  the  ele- 
vation of  a  mountain,  or  of  any  other  place  above  or  below  the  level 
of  the  sea.  ff  the  atmosphere  had  a  uniform  density,  we  could  ascer- 
tain, by  a  very  simple  calculation,  the  height  to  which  the  barometer 
was  raised,  from  the  amount  of  the  fall  of  the  mercurial  column ;  for, 
mercury  being  10,466  times  heavier  than  air,  a  fall  of  one  m.  m. 
(•03937  in.)  of  the  barometric  column,  would  indicate  that  the  column 
of  air  had  diminished  10,466  m.  m.  (412-054  in.),  and  therefore  the 
height  measured  would  be  10,466  m.  m.  But  as  the  atmospheric 
pressure  diminishes  very  rapidly  as  we  ascend,  such  calculations  are 
of  no  value  except  for  small  elevations,  and  it  is  necessary  to  deter- 


216  THE    THREE    STATES    OF    MATTER. 

mine  the  rate  of  diminution  in  density  of  the  air,  in  proportion,  as  it  is 
further  removed  from  the  earth.  Tables  have  also  been  constructed  by 
which  we  can  easily  calculate  the  level  between  any  two  places,  when 
we  know  the  height  of  the  barometer,  and  the  temperature  of  the 
atmosphere.* 

The  altitude  of  any  place  above  the  level  of  the  sea  may  also  be  cal- 
culated by  the  following  formula,  given  by  Prof.  Guyot,  in  the  tables 
referred  to  below : — 

If  we  call 

h  =  the  observed  height  of  the  barometer,    I 

T  =  the  temperature  of  the  barometer,          L  at  the  lower  station. 

t  =  the  temperature  of  the  air,  j 

hf  =  the  observed  height  of  the  barometer,  ) 

T'  =  the  temperature  of  the  barometer,        I  at  the  upper  station. 

t'  =  the  temperature  of  the  air,  J 

If  we  make,  further, 

Z  =  the  difference  of  level  between  the  two  barometers ,- 

L  =  the  mean  latitude  between  the  two  stations ; 

H  =  the  height  of  the  barometer  at  the  upper  station  reduced  to  the  tempera- 
ture of  the  barometer  at  the  lower  station ;  or, 

H  =  h'  -{  1  +  0-00008967  (T  —  T)  \  j 

The  expansion  of  the  mercurial  column,  measured  by  a  brass  scale,  for  1° 
Fahrenheit  =  0-00008967; 

The  increase  of  gravity  from  the  equator  to  the  poles  =  0-00520048,  or 
0-00260  to  the  45th  degree  of  latitude  ; 

The  earth's  mean  radius  =  20-886,860  English  feet; 

Then  Laplace's  formula,  reduced  to  English  measures,  reads  as  follows  : — 


h 

Z  =  log.  -  X  60158-6  Eng.  feet, 
H 


1  -|-  0.00260  cos.  2  L 


z  -f  52252  h        \ 

1  T    20886860      *~  10443430 j 


2,  in  this  formula,  is  the  approximate  value  of  Z,  as  given  by  that  part  of  the 
formula  preceding  the  parenthesis  in  which  z  is  introduced. 

Heights  may  be  calculated  by  the  above  formula,  but  the  calculation  is  much 
facilitated  by  the  use  of  the  Smithsonian  Tables. 

273.  Balloons. — Bodies  in  air  (like  solids  plunged  in  liquids)  lose 
a  part  of  their  weight,  equal  to  the  weight  of  the  air  displaced.  From 
this  it  follows,  that  if  a  body  weighs  less  than  an  equal  volume  of  air 
it  will  rise  in  the  atmosphere  until  it  meets  with  air  of  its  own  density: 
hence,  heated  air,  smoke,  &c.,  rise,  because  they  are  less  dense  than 
cold  air. 

Dr.  Black,  of  Edinburgh,  announced  in   1767,  that  alight  vessel  filled  with 

*  Guyot's  Meteorological  and  Physical  Tables,  Smithsonian  Collections. 


OF    GASES. 


217 


hydrogen  gas,  would  rise  in  the  air ;  and  Cavallo,  in  1782,  communicated  to  the 
Royal  Society  in  London  the  fact,  that  soap-bubbles,  filled  with  hydrogen,  would 
ascend  in  the  atmosphere.  The  brothers  Montgolfler,  in  1782,  first  constructed 
balloons.  These  consisted  of  globes  of  cloth,  lined  with  paper.  The  one  that 
they  first  exhibited  publicly,  was  a  globe  about  thirty  feet  in  diameter,  open  at 
the  lower  part,  below  which  was  placed  a  fire.  This,  expanding  the  air  within 
the  globe,  diminished  its  density,  and  the  balloon  rose  to  a  height  of  nearly  a 
mile.  Hot-air  balloons  are,  therefore  (in  allusion  to  their  inventors),  usually 
called  Montgolfiers.  Balloons  filled  with  hydrogen  were  first  introduced  by  Mr. 
Charles,  professor  of  physics  in  Paris,  in  1782 ;  and  in  November  of  the  same 
year,  Pilatre  de  Rosier  made  the  first  aerial  voyage,  in  a  balloon  filled  with  hot 
air.  The  ascension  took  place  from  Boulogne.  Soon  after,  Messrs.  Charles  a.nd 
Robert,  in  the  garden  of  the  Tuilleries,  repeated  the  same  experiment  in  a  bal- 
loon filled  with  hydrogen  gas.  At  this  epoch,  aerial  voyages  multiplied.  In 
January,  1784,  seven  persons  rose  from  Lyons,  three  from  Milan,  &c.  •  and  soon, 
so  familiarized  were  the  public  with  this  method  of  navigating,  that  it  was  not 
uncommon  for  people  to  ascend  in  a  balloon  which  was  restrained  from  going 
too  far  by  means  of  a  cord  ;  when  the  adventurers  had  attained  a  certain  height, 
the  balloon  was  drawn  down  by  means  of  the  cord,  and  other  voyagers  took 
their  place. 

Gay  Lussac,  September  16,  1804,  made  an  ascent  remarkable  for  the  fact? 
with  which  it  enriched  science,  and  for  the  height  which  was  attained,  namely 
7016  metres,  or  about  23,019  feet.  In  those  elevated  regions.  Gay  Lussac  found 
respiration  and  the  circulation  of  the  blood  much  accelerated,  because  of  the 
rarefaction  of  the  atmosphere ;  his  heu?t  making  120  pulsations  in  a  minute, 
while  66  was  its  normal  rate.  He  also  collected  there  specimens  of  air  for 
chemical  analysis,  and  determined  the  cold  of  space. 

Construction    and    fill-  217 

ing  of  balloons. — Generally 
the  balloon  is  pear-shaped. 
It  is  made  of  a  material  imper- 
vious to  hydrogen  gas,  often 
of  strips  of  taffeta  sewed  to- 
gether, and  covered  with  a 
varnish,  composed  of  linseed 
oil  and  caoutchouc,  dissolved 
in  essence  of  turpentine,  or 
of  a  tissue  formed  of  a  layer 
of  caoutchouc  interposed  be- 
tween two  layers  of  taffeta, 
and  called  mackintosh. 

To  fill  the  balloon,  A,  fig.  21  7, 
an  aperture  at  its  lower  end  is  placed  in  communication,  by  means  of  a  tube. 
T,  with  vessels,  ti,  generating  hydrogen  (from  the  action  of  dilute  sulphuric 
acid  on  iron).  When  the  balloon  is  sufficiently  filled,  the  aperture  is  closed. 
Suspended  by  means  of  a  net-work  of  ropes  covering  the  whole  apparatus,  is  a 
boat  formed  of  wicker-work,  for  the  reception  of  the  aeronauts,  fig.  218.  At  the 
upper  part  of  the  balloon  is  a  valve,  which  the  manager  may  open  or  shut  at 


218 


THE    THREE    STATES    OF    MATTER. 


by  means  of  ;i  cord.    As  illuminating  gas  can  usually  be  procured  more 
easily  than  hydrogen,  it  is  frequently  used  by  aeronauts ;  but  being  at  least  seven 
times  more  dense  than  pure  hydrogen,  the  balloon  requires  to  be  of  a  correspond- 
ingly larger  size,  in  order  to  obtain  the  same  ascensional  force. 
218  219 


The  balloon  must  not  be  completely  filled,  for  the  atmospheric  pres- 
sure diminishing  upwards,  the  gas  in  the  interior  will  expand  in  a  like 
ratio,  and  tend  to  burst  the  balloon.  A  number  of  fatal  accidents  have 
taken  place  from  this  cause. 

When  the  aeronaut  wishes  to  descend,  he  pulls  the  cord  which  opens 
the  valve  in  the  upper  part  of  the  balloon,  and  thus  the  hydrogen 
escapes,  and  the  balloon  comes  down.  If  he  wishes  to  ascend,  he 
throws  out  bags  of  sand  which  he  has  taken  up  with  him,  and  the  bal- 
loon, becoming  thus  lighter,  rises  to  a  correspondingly  greater  height. 

Parachute. — Aeronauts  often  abandon  their  balloons,  and  descend 
in  a,  parachute.  This  apparatus  is  composed  of  strong  cloth,  and  when 
extended,  has  the  appearance  of  an  umbrella,  fig.  219,  with  this  differ- 
ence, that  the  whale-bones  are  replaced  by  cords,  sustaining  a  small 
boat,  in  which  the  aeronaut  places  himself.  There  is  a  small  chimney, 
or  hole,  in  the  top  of  the  parachute,  in  order  to  allow  the  air,  which 
would  accumulate,  to  escape  regularly,  otherwise  it  would  escape  fitfully 
by  the  sides,  throwing  the  apparatus  violently  around,  to  the  imminent 
peril  of  its  occupants. 

IV.     COMPRESSIBILITY  OF  GASES. 

274.  Mariotte's  law. — Boyle  and  Mariotte  discovered  the  law  of 
fche  compression  of  gases,  which  is  as  follows : — 


OF    GASES. 


219 


At  the  same  temperature,  the  volume  occupied  by  the  same  bulk  of  air, 
is  in  inverse  ratio  to  the  pressure  which  it  supports.  From  which  it 
follows,  that  the  density  and  tension  of  a  gas  are  proportional  to  the 
pressure. 

Let  V  and  V  represent  the  volume  of  a  gas  at  different  pressures 
Pand  Px,  and  D  and  D/  the  different  densities.  Then 


V  :   P  =  P*  •  P,     whence 


=  V  ~  and 


220 


!PL 

V 

Px  /)' 

D  :  D'  —  P:  P',     whence  D'  =  D—  and  P/  =  P  — . 

Experimental  verification  of  Mariotte's  Law. 

In  order  to  verify  this  law,  the  apparatus  called  Mariotte's  tube  ia 
employed.  To  an  upright  support  of  wood  is  attached  a  bent  tube,  fig. 
220,  whose  two  vertical  branches  are  unequal  in 
length.  The  longer  limb  is  open  at  the  top,  and  fur- 
nished with  a  scale  which  indi-  219 
cates  heights  ;  the  shorter  is  closed 
at  the  top,  and  is  divided  into 
parts  of  equal  capacity.  Mercury 
is  poured  into  the  tube  so  that  the 
level  of  the  liquid  in  the  two 
branches  is  found  on  the  same 
horizontal  line,  la.  The  air  in 
the  shorter  limb  then  occupies  a 
definite  volume,  indicated  by  the 
graduation.  If  more  mercury  is 
idded,  until  the  measured  volume 
of  air  is  reduced  one-half,  as  from 
ten  to  five,  occupying  only  the 
space  above  Zx,  and  we  now  mea- 
sure the  difference  of  level  between 
the  two  surfaces  of  mercury,  viz. : 
a'  h,  we  shall  find  that  it  is  the 
same  as  the  height  of  the  baro- 
metric column.  That  is,  the  pres- 
sure of  the  column  of  mercury  in 
the  Mariotte's  tube  is  equivalent 
to  one  atmosphere ;  adding  this 
pressure  to  that  which  the  atmo- 
sphere exerts  on  the  mercury,  we 
have  the  air  subjected  to  double  of  its  usual  pressure,  and  it  is,  conse- 


220  THE    THREE    STATES    OF    MATTER. 

quently,  reduced  in  volume  one-half.  If  we  subject  it  to  a  pressure  ot 
three  atmospheres  it  will  be  reduced  to  one-third ;  of  four  atmospheres, 
to  one-fourth  of  its  original  bulk,  &c.  By  this  law,  at  a  pressure  of  814 
atmospheres  air  would  become  as  dense  as  water. 

The  law  of  Mariotte  may  also  be  verified  for  pressures  less  than  one  atmo- 
sphere, by  using  a  barometer  tube,  about  two-thirds  filled  with  mercury,  and 
inverted  in  the  deep  cistern,  fig.  221,  filled  with  mercury.  Sinking  the  tube  to 
such  a  depth  that  the  level  of  the  mercury  within  and  without  is  the  same;  the 
contained  air  is  under  the  pressure  of  one  atmosphere,  and  occupies  a  known 
volume.  If  the  tube  is  now  raised  until  by  a  diminution  of  pressure  the  given 
volume  of  air  is  doubled,  it  will  be  found  that  the  length  of  the  mercurial  column 
in  the  tube  is  half  that  in  the  barometer  :  that  is,  the  air  under  a  pressure  of  one- 
half  an  atmosphere  has  doubled  its  volume.  The  volume  here,  as  in  the  other 
case,  is  in  inverse  ratio  to  the  pressure. 

275.  Experiments  of  Despretz. — Mariotte's   law  was   generally 
received  as  correct,  until  Despretz,  not  doubting  its  correctness,  so  iir 
as  air  was  concerned,  undertook  to  test  this  law  in  its  application  to 
other  gases.     For  this  purpose  he  filled  several  tubes  of  the     222 
same  height  with  different  gases,  and  inverted  them  in  a  vessel 

of  mercury,  placing  behind  them  a  graduated  scale,  as  shown 
in  fig.  222.  This  apparatus  was  then  introduced  into  a  glass 
cylinder  filled  with  water,  and  subjected  to  pressure  by  means 
of  a  forcing-pump. 

As  the  pressure  increased,  the  height  of  the  mercury  in  the 
different  tubes  varied,  as  shown  in  the  figure,  and  this  variation 
increased  with  the  pressure.  Carbonic  acid,  sulphuretted  hy- 
drogen, ammonia,  and  cyanogen  were  compressed  more,  and 
hydrogen  less,  than  common  air.  These  experiments,  in  which 
the  probability  of  error  is  extremely  small,  show  that  each  gas 
has  a  special  law  of  compressibility,  differing  more  or  less  from  the  law 
announced  by  Mariotte. 

A  series  of  very  accurate  experiments,  subsequently  conducted  by  Pouillet, 
by  a  different  method,  confirmed  the  results  of  Despretz,  who  had  announced 
the  unequal  compressibility  of  different  gases. 

276.  Experiments  of  Regnault.* — Mariotte's  law  has  been  subjected 
to  the  test  of  very  careful  and  repeated  experiments  by  Dulong,  Arago,  and 
others.    But  the  most  complete  and  reliable  experiments  are  those  conducted  by 
Regnault. 

Regnault  kept  the  column  of  gas  upon  which  he  was  experimenting  at  a  uni- 
form temperature  by  a  stream  of  cold  water  flowing  through  a  cylinder  which  sur- 
rounded  the  tube  of  condensed  air  or  other  gas.  The  utmost  precaution  was  taken 
to  remove  every  trace  of  moisture  from  the  gases  employed.  The  temperature 
and  atmospheric  pressure  were  carefully  noted  at  every  experiment,  and  due 


MSmoires  de  1'Acadgmie  des  Sciences,  Tom.  XXI.,  p.  329. 


OF    GASES. 


221 


allowance  made  for  their  changes.  The  temperatuie  of  the  column  of  mercury 
employed  to  measure  the  pressure  was  noted,  and  the  height  of  the  column  cor- 
rected accordingly.  Finally  the  condensation  of  the  mercurial  column  due  to 
its  own  weight  was  also  considered,  and  every  possible  precaution  was  observed 
to  secure  the  utmost  accuracy  in  the  experiments. 

Results  obtained  by  Regnault. 

The  following  table  gives  some  of  the  principal  results  obtained  by  Regnault. 

Let  P  represent  the  pressure,  when  any  gas  occupies  a  volume  V,  and  P'  the 
pressure  when  the  volume  of  the  same  gas  is  V.    If  Mariotte's  law  were  strictly 

PV 
correct,  we  should  have  PV  equal  to  P'V,  or  — - — f  ought  to  be  equal  to  unity. 


Air. 

Nitrogen. 

Carbonic  Acid. 

Hydrogen. 

p 

PV 

P               PV 

p 

PV 

P        \        PV 

P'V 

P'V 

P'V 

P'V 

m.  m. 

m.  m. 

m.m.      1 

m.  m.     i 

738-72 

1-001414 

753-46 

1-000088 

764-03    1-007597 

u                  (i 

4209-48 

1-002765 

4953-92 

1-002952 

3186-13    1-028698 

2211-18    0-998584 

8177-48 

1-003253 

8628-54 

1-004768 

9351-72 

1-045625 

2845-18    0-996121 

9336-41 

1-006366 

10981-42 

1-006456 

9619-97 

1-155865 

9176-50    0-992933 

PV 

We  here  see  that  in  the  four  gases  examined,  the  ratio  — — f  was  found  very 

nearly  equal  to  unity,  showing  that  though  Mariotte's  law  is  not  absolutely  true, 
it  is  sufficiently  accurate  for  most  purposes. 

In  the  case  of  air,  nitrogen,  and  carbonic  acid,  the  compressibility  augments 
more  rapfdly  than  the  increase  of  pressure,  while  in  the  case  of  hydrogen  the 
compressibility  diminishes.  It  has  also  been  ascertained  that  the  rate  of  com- 
pressibility for  any  gas  varies  with  the  temperature.  For  example,  carbonic 
acid  at  212°  F.  agrees  almost  exactly  with  Mariotte's  law. 

277.  General  conclusions  on  the  compressibility  of  gases. — 
From  a  careful  consideration  of  all  the  experiments  upon  the  conden- 
sation of  gases,  it  seems  reasonable  to  conclude  that : — 

1st.  There  is  some  temperature,  differing  for  different  gases,  at  which 
the  compressibility  of  gases  corresponds  with  Mariotte's  law.  That  at 
higher  temperatures  the  compressibility  diminishes,  and  at  lower  tem- 
peratures the  compressibility  increases. 

2d.  Almost  all  gases,  by  a  certain  amount  of  pressure,  are  liquefied, 
and  it  is  found  that  their  compressibility  increases  very  rapidly  near  the 
point  of  liquefaction. 

Although  these  conclusions  are  based  upon  the  analogies  of  science, 
and  apparently  indicated  by  experiments,  yet  further  observations  are 
required  for  their  confirmation. 


222 


THE    THREE    STATES    OF    MATTER. 


V  .    INSTRUMENTS  DEPENDING  ON  THE  PROPERTIES  OF  GASES. 

278.  Manometers. — Manometers  are  instruments  designed  to  mea- 
sure the  tension  of  gases  or  vapors  above  the  atmospheric         223 
pressure.     The  unit  of  measurement  which  has  been  chosen 

for  these  instruments  is  the  pressure  of  the  atmosphere, 
which,  at  the  level  of  the  sea,  is  (261)  equal  to  about  15  Ibs. 
to  the  square  inch,  and  therefore  a  pressure  of  two  or  of  three 
atmospheres  signifies  a  pressure  of  30  Ibs.  or  of  45  Ibs.  ~ 
Manometers  are  of  very  various  construction,  two  of  which 
will  be  mentioned,  namely  : — 

279.  1st.  Manometer  with  free  air. — This  consists  of 
a  glass  tube,  B  D,  fig.  223,  open  at  both  ends,  placed  in  a 
cistern  of  mercury,  to  which  it  is  cemented.     The  cistern  is 
connected  with  an  iron  tube  A  C.   By  this  tube  the  pressure 
of  the  fluid  is  transmitted  to  the  mercury.    The  gases  whose 
tension  we  wish  to  find,  being  often  of  a  temperature  suffi- 
ciently high  to  melt  the  cement  attached  to  the  apparatus, 
the  tube  A  G  is  filled  with  water,  which  receives  the  pres- 
sure, direct,  and  transmits  it  to  the  mercury. 

In  order  to  graduate  this  instrument,  A  being 
open  to  the  atmosphere,  that  point  where  the 
mercury  rests  in  the  tube  is  marked  1  (one  atmo- 
sphere). At  distances  of  thirty  inches,  the  num- 
bers 2,  3,  <fec.,  are  marked,  which  indicate  the 
number  of  atmospheres,  for  it  will  be  remembered, 
that  a  column  of  mercury  thirty  inches  in  height 
represents  the  atmospheric  pressure.  The  appa- 
ratus being  placed  in  connection  with  a  steam- 
boiler,  we  ascertain  the  pressure  to  which  it  is 
subjected  by  the  height  to  which  the  mercury 
rises  in  B  D  j  if  to  2-5,  the  pressure  is  2-5  atmo- 
spheres, or  37i  Ibs.  to  the  square  inch. 

280.  2d.    Manometer     -with      com- 
pressed air. — This  form  of  the  instrument 
consists  of  a  glass  tube  filled  with  dry  air, 
placed  in  a  cistern  of  mercury,  to  which  it 

is  cemented.    This  by  a  lateral  tube,  A,  fig.  f 
224,  communicates  with  the  vessel  contain- 
ing the  elastic  fluid  to  be  gauged. 

In  order  to  graduate  the  manometer,  such  a 
quantity  of  air  is  placed  in  the  tube,  that  when  A 
communicates  with  the  atmosphere,  the  level  of  the  mercury  is  the  same  in  the 
tube  as  in  the  cistern.  At  this  point,  therefore,  1  is  marked  upon  the  scale. 
Following  Mariotte's  law,  it  might  be  supposed  that  we  should  mark  for  two 


OF    GASES. 


22B 


atmospheres,  at  a  point  in  the  middle  of  the  tube,  but  when  the  column  of  air  is 
reduced  half,  the  tension  of  two  atmospheres  is  increased  by  the  weight  of  the 
column  of  mercury  raised  in  the  tube,  and  therefore  the  middle  point  of  the  tube 
would  represent  a  pressure  greater  than  two  atmospheres.  The  true  position  for 
the  second  mark  is  at  a  point  a  little  below  the  middle  of  the  tube,  where  the 
elastic  force  of  the  compressed  air,  added  to  the  weight  of  the  column  of  mer- 
cury, is  equal  to  two  atmospheres. 

The  true  position  of  the  points,  indicating  3,  4,  &c.,  atmospheres,  is  determined 
on  the  scale  of  the  manometer  by  calculation.  This  is  not  a  very  desirable  form 
of  manometer,  because  the  volume  of  air  growing  smaller,  the  divisious  must 
continually  diminish  in  size,  and  therefore,  even  considerable  variations  of  pres- 
sure are  not  easily  observed  in  the  upper  portion. 

Bourdon's  metallic  barometer,  described  in  $  163,  is  much  used  as  a 
manometer  or  gauge  for  steam-boilers.  It  is  sometimes  called  Ash- 
croft's  gauge,  and  is  the  best  instrument  in  use  for  the  purpose. 

[For  the  diffusion,  effusion,  and  transmission  of  gases,  the  mixture 
of  gases  and  liquids,  and  the  absorption  of  gases,  see  the  Author's 
"  Chemistry."] 

281.  Bellows. — The  most  common  instrument  for  producing  a  cur- 
rent of  air  is  the  ordinary  bel- 
lows, fig.  225,  consisting  of  two 
leaves  of  wood  united  by  leather, 
and  terminating  in  a  metallic 
tube  t.  A  valve  s  is  placed  in 
the  lower  leaf,  opening  up- 
wards. 

When  the  leaves  are  pressed  together,  the  valve  s  closes,  and  the  contained 
air  escapes  through  t.  But  when  the  226 

leaves  are  separated,  air  rushes  in 
through  the  valve  and  also  through 
the  tube,  through  which  last  it  is  again 
ejected  upon  pressing  the  leaves  to- 
gether. 

Allows  with  a  continuous 

;t. — In  the  ordinary  bellows, 
the  blast  of  air  is  intermittent. 
Where  a  continuous  jet  is  wanted, 
as  at  a  smith's  forge,  a  double 
blast  bellows  is  used,  fig.  226. 

This  consists  of  three  pieces  of  wood, 
of  which  one,  D,  is  immovable,  the 
others  are  connected  with  this  by 
means  of  leather.  The  apparatus  is 
divided  into  two  compartments,  U  V.  The  blast-pipe  communicates  with  tho  one 
above ;  in  the  lower  one,  air  is  introduced  through  the  lower  valve,  S.  When 


224 


THE    THREE    STATES    OF    MATTER. 


the  lever  is  drawn  down,  as  shown  by  the  arrow,  the  valve  S  closes,  and  the 
air  being  compressed,  passes  into  U  through  the  valves  r  r,  raising  C  B,  and  par- 
tially escaping  through  the  tube.  With  the  reverse  motion  (accelerated  by  the 
weight  P),  the  valves  r  r  close,  and  the  exterior  air  enters  V  by  the  valve  S. 
During  this  time,  the  upper  weight,  P',  causes  C  B  to  descend,  and  thus  there  is 
continually  an  escape  of  air  by  the  blast-pipe.  The  weight  may  be  replaced  by 
a  spring. 

282.  Furnace  blowers. — In  blast,  or  high  furnaces,  blowing  ma- 
chines are  employed,  by  means  of  which  a  large  volume  of  air  is  forced 
into  the  fire ;  these  machines  are  of  very  various  construction. 

Fig.  227  represents  one  of  them  ;  it  consists  of  a  cast  iron  cylinder,  containing 
a  piston,  p,  of  which  the  rod,  t,  passes,  air  tight,  through  a  packing-box,  d  ; 
there  are  four  valves,  two  of  which  227 

a  a'  opening  inwards,  draw  in  air  ; 
the  air  passes  out  through  the 
valves  b  b'  which  open  outwards. 
The  piston  is  set  in  motion  by 
a  steam-engine  or  water-wheel; 
during  its  descent  the  valves  a  and 
b'  only  are  opened ;  through  the 
first,  air  is  drawn  in,  through  the 
second,  it  is  expelled ;  during  the 
ascent  of  the  piston,  the  other 
valves  a'  and  6,  act  in  the  same 
manner.  The  expired  and  com- 
pressed air  is  received  into  the 
tube  g  h,  through  which  it  is  con- 
veyed to  the  furnace.  In  the  great 
blowing  machines  at  Scranton,  Pa. 
the  blast  is  used  under  a  pressure 
of  five  pounds  to  the  square  inch, 
driven  by  two  engines  of  1200 
horse  power  each. 

283.  Escape    of  compressed    gases. — When    a   compressed   gas 
escapes  from  an  opening   in  a  thin  wall,  the  velocity  of  its  escape 
depends  on  the  difference  of  the  interior  and  exterior  pressures,  and 
on  the  density  of  the  gas  passing  out.     It  has  been  proved,  4fc 

1.  That  with  the  same  gas  at  the  same  temperature,  the  velocity  of  flow 
into  a  vacuum  is  the  same  at  any  pressure. 

That  is,  if  we  had  a  vessel  filled  with  air,  compressed  at  1,  2,  3,  or  1000  atmo- 
spheres, and  allowed  it  to  escape  by  a  small  orifice,  the  velocity  of  its  flow  would 
be  the  same  during  the  whole  time  of  its  discharge.  But  the  quantity  of  the 
gas  that  could  escape  in  the  same  time  would  vary,  being  evidently  proportional 
to  the  density  of  the  gas,  that  is,  to  the  pressure.  If  the  escape  took  place  in  a 
gas,  as  air,  instead  of  in  a  vacuum,  the  velocity  is  then  proportional  to  the  dif- 
ference between  the  elastic  force  of  the  interior  and  exterior  air. 

2.  The  velocity  of  the  escape  of  gases  into  a  vacuum  is  in  inverse  ratio 
to  the  square  root  of  their  densities. 


OF   OASES. 


225 


Where  the  gas  escapes  through  long  tubes  instead  of  through  orifices  in 
N  thin  wall,  the  velocity  is  very  much  diminished,  because  of  the  friction, 
and  is  less  in  proportion  as  the  tube  is  longer  and  its  diameter  smaller. 

284.  Pneumatic   ink-bottle. — In   the   pneumatic   ink-bottle,   fig. 
228,  the  ink  in  the  tube  c  is  kept  constantly  at  nearly  the  same  level. 
By  inclining   the   bottle  it  may  be  filled  as  228 

seen  in  A.  The  ink  in  A  tends  to  force  itself 
in  the  tube  C,  but  is  opposed  by  the  atmo- 
spheric pressure,  which  is  much  greater  than 
the  pressure  of  the  column  of  ink  in  A.  As 
the  ink  in  C  is  consumed,  its  surface,  falling, 
will  allow  a  small  bubble  of  air  to  enter  A, 
where  it  will  exert  an  elastic  pressure,  and  cause  the  ink  in  C  to  rise  a 
little  higher.  This  effect  will  be  continually  repeated  until  the  bottle 
is  emptied  of  ink.  Bird-cage  fountains  are  constructed  on  a  similar 
principle. 

285.  The  syphon. — The  syphon  used  for  decanting  liquids,  depends 
for  its  operation  on  the  principle  of  atmospheric  pressure.     It  consists 
of  a  bent  tube,  6  &',  fig.  229,  having  one  of  its  arms  longer  than  the  other. 
It  may  be  filled  by  turning  it  over,  and  pour-         229  230 

ing  the  liquid  in,  or  by  immersing  the  shorter 
arm  in  a  vesssel  of  water,  and  applying  the 
mouth  at  6/ ';  upon  exhausting  the  air,  the 
water  will  be  forced  up  by  atmospheric  pres- 
sure, to  supply  the  place  of  the  air  withdrawn, 
and  there  will  then  be  a  continual  discharge 
until  the  vessel  is  emptied. 

The  two  branches  being  filled  with  liquid,  the 
pressures  exerted  at  the  points  6  and  n  will  be 
equal,  for  they  are  on  the  same  level ;  but  the  pres- 
sure exerted  at  b'  will  be  greater,  because  of  the 
column  n  b',  and  the  liquid  will  escape  from  this 
long  branch  because  of  this  excess  of  pressure,  and  will  draw  after  it  the  liquid 
in  the  shorter  branch ;  if  the  end  of  this  be  immersed,  there  will  be  a  continual 
discharge  as  long  as  b  is  below  the  surface  of  the  liquid,  for  the  atmospheric 
pressure  will  cause  the  liquid  to  ascend,  to  supply  the  place  of  that  which  is 
passing  out ;  otherwise  there  would  be  a  vacuum  produced. 

It  is  evident  that  water  could  not  be  raised  by  means  of  a  syphon 
more  than  thirty-four  feet :  for  a  column  of  water  of  that  height  is  in 
equilibrium  with  the  pressure  of  the  atmosphere  (261).  The  velocity 
of  the  flow  from  a  syphon  will  be  the  same  as  if  the  liquid  fell  freely 
from  a  height  equal  to  the  distance  between  the  level  of  the  liquid  in 
the  vessel  and  the  end  of  the  long  arm.  To  avoid  the  necessity  of  filling 
22 


226 


THE    THREE    STATES    OF    MATTER. 


a  syphon  by  pouring,  the  form  represented  in  fig.  230  is  employed.  To 
use  this  instrument,  the  open  end,  &',  of  the  longer  limb  is  closed  by  the 
finger,  while  a  partial  vacuum,  created  by  sucking  at  the  small  ascending 
tube,  t  a,  occasions  the  liquid  to  pass  over  as  in  the  ordinary  syphon. 

Intermittent  syphon.  Tantalus'  vase. — Fig.  231  consists  of  a 
vessel,  A,  containing  a  syphon,  of  which  one  of  the  branches  opens  below  the 
bottom  of  the  vessel ;  the  other  is  curved.  When  water  is  poured  into  the  vessel 
A,  it  will  rise  to  the  same  height  in  the  interior  231  232 

of  the  tube  as  it  attains  outside.  The  tube  will 
not  act  as  a  syphon  until  the  vessel  is  filled  to 
the  height  n,  but  when  it  reaches  that  point, 
the  water  will  flow  through  a  into  the  long 
branch,  filling  it  completely,  and  the  syphon 
being  now  supplied,  will  discharge  water  until 
the  vessel  is  emptied.  The  syphon  may  be 
concealed  in  a  little  image,  fig.  232,  B,  repre- 
senting Tantalus,  so  that  just  before  the  water 
touches  his  lips  the  syphon  is  filled,  and  the 
vessel  is  emptied. 

286.  Intermittent  springs. — There*  exist  in  nature  intermittent 
springs,  the  water  flowing  regularly  for  a  time,  and  then  suddenly 
ceasing.  In  these  springs  the  opening,  234 

as  at  a,  fig.  233,  communicates  with  a 
subterranean  cavity,  C,  by  means  of  a 
channel,  a  n  b,  which  has  the  form  of  a 
syphon.  This  cavity  is  gradually  filled, 
until  at  last  the  water  attains  the  level 
n  n,  when  the  syphon  is  filled,  and 
the  water  escapes.  If  the  syphon  dis- 
233 


cf — = 


chargers  the  water  faster  than  it  flows  into  C,  after  a  time  its  level  would 


OF    GASES. 


227 


be  lowered  to  6 ;  air  would  then  rush  in  by  the  syphon,  the  flow  of  water 
would  cease,  and  would  not  recommence  until  it  had  again  attained  the 
level  nn. 

Intermittent  fountain. — The  intermittent  fountain  consists  of  a 
vessel  of  glass,  C,  fig.  234,  whose  aperture  for  the  admission  of  water 
is  hermetically  sealed  by  an  accurately-ground  stopper. 

A  glass  tube  A,  passes  through  the  vessel  C,  its  upper  end  terminating  above 
the  surface  of  the  liquid;  its  lower  end  rests  in  a  copper  cistern,  B,  which  has  a 
small  aperture  for  the  escape  of  water.  The  globe  being  partially  filled,  the 
water  escapes  through  the  capillary  orifices  of  the  tube  at  D,  in  consequence  of 
the  atmospheric  pressure  transmitted  through  the  lower  end  of  the  tube  A. 
When  the  end  of  this  tube  becomes  covered  with  water,  which  after  a  time  hap- 
pens (because  the  orifice  in  the  cistern  B  does  not  allow  so  great  a  flow  of  water 
as  can  escape  from  the  tubes  at  D),  the  exterior  air  cannot  enter  the  globe,  and 
in  consequence  the  flow  ceases.  The  water  continuing  to  escape  from  D,  in  a 
little  time  the  surface  is  so  much  lowei'ed,  that  the  end  of  the  tube,  A,  is  out  of 
water;  the  air  then  entering  the  globe,  the  escape  recommences,  and  so  continues 
at  intervals  until  C  is  emptied  of  water. 

287.  Air-pump. — The  air-pump,  designed  to  produce  a  vacuum  in 

235 


any  confined  space,  was  invented  by  Otto  v.  Guericke,  burgomaster  of 
Magdeburg,  in  1650.     Fig.  235  exhibits  a  very  excellent  form  of  the 


228 


THE    THREE    STATES    OF    MATTER. 


air-pump,  manufactured  by  Ritchie  of  Boston,  usually  called  the 
form  of  air-pump.  The  essential  part  of  the  air-pump  is  the  cylinder 
shown  in  section  in  fig.  236.  This  cylinder  communicates  with  the  bell 
glass,  by  means  of  a  tube,  shown  in  fig.  235,  and  with  the  external  air  by 
means  of  the  tube  g  h  (fig.  236).  There  are  three 
valves,  a,  b,  and  c,  all  opening  upward.  The 
piston-rod  passes  through  a  packing-box,  d,  in 
which  it  moves  air-tight,  and  the  power  is  ap- 
plied by  means  of  a  lever,  as  shown  in  fig.  235. 
Suppose  the  piston  to  be  standing  at  the  bot- 
tom of  the  cylinder,  when  we  depress  the  lever, 
the  air  from  the  receiver  expands,  rushing 
through  the  valve,  a,  into  the  empty  space 
formed  in  the  bottom  of  the  cylinder,  while  the 
air  above  the  piston  is  forced  out  through  the 
valve  c  and  the  tube  g  h.  With  the  reverse 
motion  the  valves  a  and  c  close,  excluding  the 
external  air  from  the  cylinder,  and  preventing 
the  return  of  air  from  the  cylinder  to  the  receiver. 
At  the  same  time  the  piston-valve,  b,  opens  and 
allows  the  air  below  the  piston  to  pass  through  into  the  upper  part  of 
the  cylinder.  When  the  piston  rises  again,  this  new  volume  of  air 
which  has  passed  above  the  piston  is  forced  out  through  the  valve  c,  into 
the  external  atmosphere,  while  another  portion  of  rarefied  air  from  the 
receiver  expands  into  the  cylinder  below  the  piston,  to  pass  upward  and 
be  forced  out  through  the  valve  c  at  the  next  stroke  of  the  piston ;  and 
so  on  continuously,  as  long  as  the  rarefied  air  in  the  receiver  and  cylinder 
has  sufficient  tension  to  open  the  valves.  At  each  stroke  of  the  piston 
the  air  undergoes  renewed  rarefaction  until  the  amount  remaining  in  a 
good  instrument  is  about  one-thousandth  of  the  original  quantity,  and 
the  space  within  the  receiver  may  be  regarded  as  a  vacuum.  The 
pump  here  figured  is  furnished  with  a  barometric  manometer,  seen  in 
the  left  of  fig.  235,  by  which  the  degree  of  exhaustion  is  directly  indi- 
cated. The  efficiency  of  the  air-pump  depends  in  a  great  measure  upon 
the  valves,  which  are  best  made  of  oiled  silk. 

The  construction  of  the  upper  valve,  c,  as  made  by  Ritchie,  is  shown  in  fig. 
237.     The  disk  of  oiled  silk,  t,  is  kept  in  place  by  the  pin  237 

e,  and  the  whole  is  protected  by  the  dome-shaped  covering 
c.  The  tube  rj  h  (fig  236)  discharges  the  air,  and  the  oil 
which  escapes  with  it  is  collected  in  a  reservoir  placed 
below  the  pump. 

An  air-pump  with  two  cylinders  is  commonly  used  in  France,  the 


OF    OASES. 


229 


pistons  of  which  are  alternately  -raised  and  depressed  try  a  rack  and 
pinion  motion. 

Degree  of  Exhaustion. — It  is  plain,  on  a  moment's  reflection,  that  by 
mechanical  means  alone,  it  is  impossible  to  produce  a  perfect  vacuum.  There 
must  always  remain  a  certain  volume  of  air,  inferior  in  tension  to  the  gravity 
and  friction  of  the  pump  valves.  By  employing  an  atmosphere  of  dry  hydrogen 
to  rinse  out  the  residue  of  common  air  from  an  exhausted  receiver,  an  approach 
to  a  perfect  vacuum  is  made,  inversely  as  the  density  of  the  two  gases.  Also 
by  using  carbonic  acid  for  the  same  end,  and  absorbing  the  residue  of  this  gas 
by  dry  quick-lime  previously  placed  on  the  pump  plate,  a  perfect  vacuum  may 
be  produced;  but  by  chemical  and  not  by  mechanical  means. 

288.  Compressing  machine. — This  machine- is  used  to  compress 
the  air  or  any  other  gas ;  it  238 

is  constructed  like  the  air- 
pump,  the  only  difference 
being  that  its  valves  open  in 
a  contrary  direction,  viz. : 
downwards. 

Fig.  238  shows  a  very  neat 
form  of  the  condensing  pump 
as  constructed  by  Ritchie,  to 
illustrate  the  Mariottiah  law 
(275)  and  to  liquefy  gases. 

289.  Water  -  pumps. — 
Pumps     are     machines     de- 
signed to  elevate  liquids  above  their  former  level.     They  are  of  two 
classes :  1st,  those  acting  by  atmospheric  pressure ;  2d,  those  which 
act  independent  of  such  pressure.     They  are  commonly  called  either 
suction,  or  forcing  pumps,  or  both  united. 

290.  Suction-pumps. — The  suction-pump,  ng.  239,  is  composed  of 
a  tube,  A,  whose  lower  end  is  immersed  in  the  water  to  be  elevated 
This  is  attached  to  the  body  of  the  pump,  C,  which  contains  a  piston 
furnished  with  a  valve,  r,  opening  upward.     The  upper  extremity  of 
the  tube  A,  also  contains  a  valve,  o,  opening  in  the  same  direction. 

When  the  piston  is  elevated  from  the  lower  part  of  the  pump  by  working  the 
handle,  L,  the  valve  r  closes,  and  a  partial  vacuum  is  produced,  but  the  elastic 
force  of  the  air  in  A  causes  the  valve  o  to  open,  and  part  of  the  air  thus 
passes  into  C.  The  air  in  the  tube  is  thus  rarefied,  and  the  water  rushes  up 
to  such  a  height,  that  the  weight  of  the  column  of  water  raised,  added  to  the 
elasticity  of  the  interior  air,  keep  it  in  equilibrium  with  the  atmospheric  pres- 
sure. When  the  piston  descends,  the  valve  o  closes  by  its  weight,  and  pre- 
vents the  return  cf  the  air  from  the  body  of  the  pump,  C,  into  the  tube  A. 
The  compressed  air  opens  the  valve  r,  and  thus  escapes  into  the  atmosphere 
through  B.  After  a  number  of  strokes  of  the  piston,  fewer  as  the  capacity  of 
the  tube  a  is  less,  the  water  will  be  elevated  above  the  lower  valve ;  now  when 
22* 


230 


THE    THREE    STATES    OF    MATTER. 


the  piston  is  lowered,  the  valve  r  will  open  and  the  water  pass  above  it.     Upon 
elevating  the  piston,  r  closes,  and  the  water  is 
raised  in  B,  and  escapes  through  the  spout  S. 

As  in  this  and  the  following  pump, 
the  water  is  elevated  to  the  top  of  the  s 
tube  by  means  of  atmospheric  pressure, 
it  is  evident,  that  even  in  the  most  per- 
fectly constructed  pumps,  the  distance 
from  the  level  of  the  water  to  the  top 
of  the  pump  must  not  exceed  thirty- 
four  feet  (261),  but  those  of  ordinary 
construction  contain  defects,  so  that 
generally  we  do  not  gain  a  greater 
height  than  twenty-six  or  twenty-eight 
feet.  But  after  the  water  has  passed 
above  the  piston,  the  height  to  which  wo 
may  elevate  it,  is  limited  only  by  the 
power  applied  at  the  piston  ;  for  it  is 
the  ascensional  force  of  this  which  ele- 
vates the  water. 

291.  Suction  and  lifting  pump. — 

Sometimes  the  water  raised  above  the 

piston,  instead  of  passing  upwards   in 

the  tube   in  which  the   piston  works,  rises  by  a  lateral   ascensional 

tube,  S,  furnished  with  a  valve  which  prevents  241 

the  return  of  the  water,  as  is  shown  in  a,  r,  S, 

tig.  239. 

That  the  rising  of  the  water 
in  the  tube  is  due  to  the  at- 
mospheric pressure,  may  be 
demonstrated  by  the  appara- 
tus, fig.  240.  After  forming 
a  vacuum  in  the  reservoir 
which  contains  the  vessel  of 
water,  the  liquid  will  not  rise 
in  the  tube  when  the  piston 
in  the  pump,  P,  is  raised,  but 
upon  admitting  the  air  it  is 
i;;pidly  elevated,  as  usual. 


240 


£92.  Forcing-pump. — In 
the  forcing-pump,  the  piston 
has  no  valve.  The  lower  part  of  the  cylinder  in  which  it  works  is 


OF    GASES. 


231 


placed  in  the  water  to  be  elevated,  so  that  the  valve  r,  fig.  241,  which 
opens  upward,  is  always  immersed.  The  ascending  tube  a  6  contains 
a  valve,  S,  also  opening  upwards,  and  an  air  chamber, 


242 


When  the  piston  is  raised,  S  is  closed,  and  water  is  introduced  by  the  open 
valve  r;  upon  the  descent  of  the  piston,  r  closes,  and  the  water  is  forced  into 
the  ascending  tube,  a  b.  The  reservoir,  m  n,  filled  with  air,  is  designed  to  ren- 
der the  jet  of  water  continuous.  When  the  water  is  forced  by  the  piston  into 
the  tube,  the  air  is  compressed  in  m  n  ;  reacting  afterwards  by  its  elasticity,  it 
continues  to  drive  the  water  into  the  upper  part  of  the  tube,  after  S  is  closed 
'and  while  the  piston  is  rising. 

It  is  found  necessary  to  have  the  air-chamber  twenty-three  times  the 
capacity  of  the  body  of  the  pump,  in  order  to  render  the  jet  continuous. 

293.  Rotary  pump. — The  rotary  pump  is  a  mechanical  contrivance 
for  raising  water  by  a  continuous  rotary  movement.  Fig.  242  repre- 
sents one  of  the  most  successful  of  these  pumps  (Gary's).  Within  a  fixed 
cylinder  is  included  a  mova- 
ble drum,  B,  attached  to  the 
axis,  A,  and  moving  with  it. 
The  heart-shaped  cam  sur- 
rounding A,  is  immovable. 
The  revolution  of  B  causes 
the  plates  or  pistons  C  C  to 
move  in  and  out,  in  obedi- 
ence to  the  form  of  the  cam. 
The  water  enters  and  is  re- 
moved from  the  chamber 
through  the  ports  or  valves, 
L  and  M  ;  the  directions  are 
indicated  by  the  arrows. 

The  cam  is  so  placed  that  each  valve  is  in  succession  forced  back  into  its 
seat  when  opposite  E,  while  at  the  same  time  the  other  valve  is  driven  fully 
into  the  cavity  of  the  chamber  j  thus  forcing  before  it  the  water  already  there, 
into  the  exit  pipe  H,  and  drawing  after  it,  through  the  suction  pipe  F,  the 
stream  of  supply.  When  the  pump  is  set  in  action,  the  suction-pipe  is  gradually 
exhausted  of  air,  in  which,  consequently,  the  water  ascends,  and  being  thrown 
into  the  cylinder,  it  is  there  carried  around  by  the  plates  C  C,  in  the  manner  just 
described. 

This  is  a  form  of  pump  often  employed  in  the  steam  fire-engines  now 
coming  into  general  use. 

294.  Fire-engine. — In  order  to  obtain  a  continuous  and  powerful 
jet  of  water  from  fire-engines,  they  are  usually  constructed  with  two 
forcing-pumps,  which  are  alternately  discharging  water  into  a  common 
air-chamber.  The  pistons  are  moved  by  brakes,  having  an  oscillating 
motion.  The  water  from  both  pumps,  forced  into  the  air-chamber, 


232 


THE    THREE    STATES    OF    MATTER. 


escapes  through  a  long  leathern  hose,  terminated  by  a  metal  tube, 
which  serves  to  direct  the  jet. 

295.  Hiero's  fountain. — In  this  apparatus  we  also  obtain  a  jet  of 
water  by  means  of  air,  compressed  in  this  case  by  a  column  of  water. 
A  common  form  of  this  apparatus  is  repre-  243 

sented  by  fig.  243. 

It  consists  of  a  metallic  cistern  and  two  globes 
of  glass.  The  cistern,  D,  communicates  with  the 
lower  part  of  the  globe  N,  by  the  tube  B ;  a  second 
tube,  A,  joins  the  globes,  ending  in  the  upper  part 
of  both;  M  is  partially  filled  with  water;  and 
lastly,  a  third  tube  passes  through  the  cistern,  arid 
terminates  at  the  bottom  of  M.  The  upper  extremity 
of  this  tube  has  a  small  orifice,  from  which  the  jet 
of  water  issues. 

Upon  pouring  water  into  the  cistern  D,  the 
liquid  descends  to  N,  by  the  tube  B,  conse- 
quently the  water  in  the  lower  globe,  N,  sup- 
ports, besides  the  atmospheric  pressure,  the 
pressure  of  the  column  of  water  in  the  tube. 
This  pressure  is  transmitted  to  the  air  in  the 
globe,  M,  which,  reacting  on  the  water,  forces 
it  out  through  the  jet,  as  seen  in  the  figure. 
If  there  was  no  friction,  and  no  resistance 
from  the  air,  the  water  would  spout  to  a 
height  equal  to  the  difference  in  level  of  the 
water  in  the  two  globes. 

296.  Hydraulic  ram. — In  the  hydraulic 
ram,  the  momentum  of  a  part  of  the  fluid  in 
motion,  is  effective  in  raising  another  portion. 
A  simple  form  of  this  apparatus  is  seen  in 
fig.  244.    The  water  descends  from  the  spring 
or  brook,  A,  through  the  pipe  B,  near  the  end  of  which  is  an  air-cham- 
ber, D,  and  rising  main, 
F.     The  orifice  at  the  ex- 
treme end  of  B,  is  opened 
and  closed  by  a  valve,  E, 
opening  downwards. 

When  the  valve  E  is  open, 
the  water  flows  through  B, 
until  the  current  becomes 
sufficiently  rapid  to  raise  the 
valve  E,  and  thus  to  close 
the  orifice.  The  water  in  B  having  its  motion  thus  suddenly  checked,  exerts  a 


244 


OF    GASES. 


233 


great  pressure,  and  having  raised  the  valve  C,  will  rush  into  the  air-vessel  D, 
where  it  compresses  the  air.  The  compressed  air  in  D,  because  of  its  elasticity, 
causes  the  water  to  rise  in  the  pipe  F,  until  the  water  in  A  B  is  brought  to  rest. 
When  this  takes  place,  the  pressure  is  again  insufficient  to  sustain  the  weight 
of  the  valve  B,  which  opens  (descends),  the  245 

water  in  B  is  again  put  in  motion,  and  the 
same  series  of  effects  ensue  as  have  already  been 
described. 

The  hydraulic  ram,  when  well  con- 
structed, is  capable  of  utilizing  about  60 
per  cent,  of  the  moving  power. 

297.  Chain-pump. — The    chain-pump 
acts  independent  of  atmospheric  pressure. 
It  consists  of  a  cylinder,  fig.  245,  whose 
lower  end  is  immersed  in  the  water  of  the 
reservoir  B,  and  whose  upper  part  enters 
into  the  bottom  of  a  cistern,  C,  into  which 
the  water  is  to  be  raised.     An   endless 
chain  is  carried  around  the  wheels  above 
and  below,  and  is  furnished,  at  equal  dis- 
tances,  with    circular    plates,    which    fit 
closely  into  the  cylinder.     As  the  wheel 
is  revolved  by  means  of  power  applied 
usually  by  a  winch,  the  circular  plates 
successively  enter  the  cylinder  and  carry 
the  water  up  before  them  into  the  cistern, 
from  which  it  passes  out  by  a  spout. 

298.  Archimedes'  screw. — This  machine  is  said  to  have  been  in- 
vented by  Archimedes  in  Egypt,  to  246 

aid  the  inhabitants  in  clearing  the 
land  from  the  periodical  overflowings 
of  the  Nile.  The  instrument  varies 
in  its  form,  according  to  the  manner 
and  purposes  of  its  application.  To 
render  the  principle  upon  which  it 
works  intelligible,  let  us  suppose  a 
tube  bent  in  the  form  of  a  cork- 
screw, and  inclined  in  the  manner 
shown  in  fig.  246.  If  a  ball  be 
placed  in  A,  it  will  fall  to  B,  and 
there  remain  at  rest ;  if  the  screw 
be  now  turned  so  that  the  mouth  A  is  placed  in  its  lowest  position, 
the  point  B,  during  such  a  motion,  will  ascend,  and  will  assume  the 


234 


THE    THREE    STATES    OF    MATTER. 


highest  position  it  can  have.  The  ball  will  then  fall  to  C  ;  by  continu- 
ing the  revolution  of  the  screw,  the  ball  will  ascend  in  the  tube,  and 
finally  will  be  discharged  from  the  upper  mouth.  The  same  would 
happen  with  a  portion  of  liquid.  If  the  lower  extremity  of  the  screw 
was  immersed  in  a  reservoir  of  liquid,  it  would  gradually  be  carried 

247 


along  the  spiral  as  the  screw  was  turned,  to  any  height  to  which  the 
screw  might  extend.  In  practice,  the  screw  is  more  commonly  formed 
of  a  cylinder,  to  the  walls  of  which  is  attached  a  spiral  thread,  as 
shown  in  fig.  247.  Besides  liquids,  these  machines  are  used  for  ele- 
vating ores  in  mines,  or  grain  in  breweries,  &c.  They  are  commonly 
used  at  an  inclination  of  about  45°,  but  may  be  used  at  60° ;  revolving 
100  to  200  times  a  minute. 


Problems  on  Pneumatics. 
Atmospheric  Pressure. 

134.  What  weight  could  be  lifted  by  the  apparatus  shown  in  fig.  202,  if  the 
mouth  of  the  jar  is  5  inches  in  diameter,  and  the  air  within  the  jar  is  exhausted, 
so  as  to  leave  it  but  one  hundredth  part  its  normal  density? 

135.  What  force  would  be  required  to  separate  two  Magdeburg  hemispheres, 
having  an  internal  diameter  of  ten  inches,  if  a  perfect  vacuum  were  formed 
within  ? 

136.  A  mass  of  metal,  whose  specific  gravity  is   11-35,  weighs  in  a  vacuum 
735  grains  ;  how  much  will  its  weight  be  diminished  if  weighed  in  the  open  air  ?* 

*  In  these  problems  the  barometer  is  supposed  to  stand  at  30  inches,  and  the 
thermometer  at  the  freezing  point. 


OP   GASES.  285 

137.  A  mass  of  iron  (Sp.  Gr.  7-8)  weighed  in  air  with  brass  weights  (Sp.  Gr. 
8-3)  460  grains,  what  would  it  weigh  in  a  vacuum  ? 

138.  A  glass  globe,  from  which  the  air  has  been  exhausted,  weighs  254-735 
grammes ;  when  full  of  air,  it  weighs  5422-737  grammes ;  when  full  of  another 
gas,  651-175  grammes  j  what  is  the  capacity  of  the  globe,  and  what  is  the  specific 
gravity  of  the  gas  ? 

Barometer  and  Balloons. 

139.  To  what  height  will  sea  water  (Sp.  Gr.  =  1-026)  rise  in  a  Torricellian 
tube,  when  the  barometer  stands  at  28-75  inches  ? 

140.  When  the  mercury  barometer  stands  at  30   inches,  what  must  be  the 
length  of  a  water  barometer  inclined  to  the  horizon  at  an  angle  of  30°  ? 

141.  What  would  be  the  height  of  a  sulphuric  acid  barometer  (Sp.  Gr.  sul- 
phuric acid,  1-85)  when  the  mercurial  barometer  stands  29-35  inches? 

142.  Measurement  of  the  height  of  the  highest  peak  of  the  Smoky  Mountain, 
(Lat.  36°  N.)   in  North  Carolina,  September  8,  1859,  by  Prof.  A.  Guyot.     By 
observation  at  8£  A.  M. 

Barometer.     Temperature  Temperature 
Eng.  inches,  of  Barometer.        of  air. 
Lower  station,  R.  Collins'  house,  4  ft.  above 

ground, h  =  27"862,  T  =  66°-4,  t  =  65°-l. 

Upper  Station,  Smoky  Dome,  4  feet  below 

summit, A'  =  23'963,  T'  =  51°-S,  «'  =  51°-4. 

Mr.  Collins*  house  being  2500-2  feet  above  the  ocean. 

Calculate  from  these  data  the  height  of  Smoky  Dome  above  the  ocean. 

Altitude  calculated  by  Prof.  Guyot,  6655-85  feet. 

143.  What  is  the  ascensional  force  of  a  spherical  balloon,  30  feet  in  diameter, 
filled  with  common  illuminating  gas  (Sp.  Gr.  -485),  the  weight  of  the  balloon  and 
car  attached  being  200  Ibs.  ?     What  if  it  were  two-thirds  filled  with  hydrogen 
(Sp.  Gr.  of  hydrogen,  0-069)  ? 

144.  A  balloon  entirely  filled  with  illuminating  gas  (Sp.  Gr.  -500),  is  so  bal- 
lasted that  it  rises  to  an  elevation  where  the  mercury  stands  at  15  inches.   Suppose 
one-half  the  gas  is  now  liberated,  will  the  balloon  rise  or  fall  ?  and  what  amount 
of  ballast  should  be  put  in,  or  thrown  out,  to  cause  the  balloon  to  remain  sta- 
tionary, at  the  same  elevation  as  before  any  gas  was  liberated  ? 

Mariotte's  Law.     (Regarded  as  invariable.) 

145.  What  proportion  of  a  tube,  34  feet  high,  can  be  filled  with  water,  the 
contained  air  being  assumed  to  be  compressed  at  the  bottom  of  the  tube  ? 

146.  A  faulty  barometer  (containing  air)  indicated  29-2  and  30  inches,  when 
the  indications  of  a  correct  instrument  were  29-4  and  30-3  inches  respectively; 
find  the  length  of  tube  which  the  air  in  the  column  would  fill  under  the  pressure 
of  30  inches  ? 

147.  A  glass  globe,  10  c.  m.  in  diameter,  hermetically  sealed,  weighs  45-120 
gram,  when  the  barometer  stands  at  74  5  c.  m.     What  would  it  weigh  if  the 
barometer  stood  at  76  c.  m.  ? 

•  148.  A  glass  globe  hermetically  sealed,  30  c.  m.  in  diameter,  suspended  to  one 
arm  of  the  balance,  is  poised  by  320-422  gram,  in  brass  weights,  when  the  baro- 
meter stands  at  76-21  c.  m.  After  a  time,  it  is  found  to  have  lost  in  weight 
0-022  gram.  What  is  now  the  height  of  the  barometer,  supposing  the  tempera- 
ture not  to  have  changed  ? 


236  THE    THREE    STATES    OF    MATTER. 


CHAPTER  V. 

OF  UNDULATIONS. 
§  1.    Theory  of  Undulations. 

299.  Origin  of  undulations. — By  the  operation  of  certain  forces, 
the  different  parts  of  all  bodies  are,  ordinarily,  held  in  a  state  of  equi 
librium  or  rest.     If  the   molecules  of  a   body  are  disturbed  by  any 
extraneous  force,  they  will,  after  a  certain  interval,  return  to  the  state 
of  repose.     This  return  is  effected  by  the  particles  approaching  the 
position  of  equilibrium,  and   receding   from   it,  alternately,  until   at 
length  the  body,  by  the  resistance  of  the  medium  in  which  it  is  placed, 
and  by  other   causes,  is  gradually  brought  to  rest.     The   alternate 
movements  thus  produced,  are  variously  expressed  by  the  terms  vibra- 
tions, oscillations,  waves,  or  undulations,  according  to  the  state  or  form 
of  the  body  in  which  such  movements  occur,  and  the  character  of  the 
motions  which  are  produced. 

300.  Progressive    undulations. — Undulatory   movements   are  of 
two  kinds,  progressive  and  stationary.    In  progressive  undulations,  the 
particles  which  have  been  immediately  excited  by  the  disturbing  cause, 
communicate  their  motion  to  the  particles  next  them,  and  as  this  move- 
ment of  the  particles  is  successive,  the  position  they  assume  at  any 
particular  moment  during  their  motion,  appears  to  advance  from  one 
place  to  another. 

This  kind  of  undulation  is  observed  in  a  cord  made  fast  at  one  end,  while 
the  other  is  smartly  shaken  up  and  ^  248 

down ;  the  portion  of  the  cord  nearest     { 
the  hand  will  assume  the  position  in 
fig.  248,  I,  m  d  E  0.     Such  a  wave 
docs  not  continue  stationary;    the    II 
moment   it   is  formed,  it  advances 
toward  the  other  extremity  of  the 
«ord,   II,  on    reaching  which,  III,   lllm — — 
an  inverted  curve  is  produced,  IV, 
and   the   wave   returns,   V,   to   the   l 
position  from  which  it  started,  the 
relative   position   of   the   elevation 
and  depression  being  reversed.  This    V  m 
alternate  movement  may  be  repeated  a  number  of  times  before  the  cord  comes 
to  rest.     These  are  sometimes  called  waves  of  translation. 


OF    UNDULATIONS. 


237 


301.  Mechanical   illustration  of  undulations. In  fig.  249  is 

shown  Powell's  apparatus  for  illustrating  progressive  undulations.     A 
series  of  balls  are   so   mounted  249 

upon  metallic  rods  that  they 
have  freedom  of  motion  only  in 
a  vertical  direction.  On  a  shaft 
turned  by  a  crank,  shown  in  the 
lower  part  of  the  figure,  are 
placed  a  series  of  eccentric 
wheels  (one  under  each  rod)  so 
arranged  as  to  raise  the  rods  one 
after  the  other.  When  one  rod 
is  rising  another  is  falling,  and 
the  wave  appears  to  travel  from 
one  end  of  the  series  to  the  other. 
As  soon  as  one  wave  disappears 
another  is  formed,  and  these 
waves  succeed  each  other  like 
the  undulations  of  a  cord. 

302.  Stationary  undulations. — Undulations  are  termed  stationary 
when  all  parts  of  the  body  assume  and  complete  their  motion  at  the 
same  time. 

Thus,  when  a  cord  stretched  between  A  B,  fig.  250,  is  drawn  at  the  middle 
from  its  rectilinear  position,  it  ultimately  recovers  its  original  position,  after 
performing  a  series  of  vibrations,  in  which  all  parts  of  the  cord  participate. 

303.  Isochronous  vibrations. — Those  vibrations  that  perform  their 
journey  on  either  side  of  their  normal  position  in  equal  times,  are 
termed  isochronous  (from  iffoq,  equal,  and  /povoq,  time). 

The  movements  of  a  pendulum  furnish  a  perfect  illustration  of  such  vibra- 
tions (78). 

304.  Phases  of  undulations. — In   every  complete  oscillation,  or 
perfect  wave,    the   following   parts   may  be    recognised.     The   curve 

250  251 


3tf$^^--~---^-~^-~-^^3p 
" -"-~-~-v 55-  —. -~_v_v_i" ~-~- -""-"-"-"'"' '  L_ 


d  ' 


i 


aebdc,  fig.  251,  is  called  a  wave.  The  part  aeb,  which  rises  above 
the  position  of  equilibrium,  is  called  the  phase  of  elevation  of  the  wave, 
e  being  the  point  of  greatest  elevation ;  the  curve  b  d  c  is  called  the 
phase  of  depression  of  the  wave,  the  point  d  being  that  of  greatest 
23 


238 


THE    THREE    STATES    OF    MATTER. 


depression.  The  distance  ef,  of  the  highest  point  above  the  position 
of  equilibrium,  is  called  the  height  of  the  wave,  and  in  like  manner  the 
distance  g  d,  of  the  lowest  point  below  the  position  of  equilibrium,  is 
called  the  depth  of  the  wave.  The  distance  a  c,  between  the  beginning 
of  the  elevation  and  end  of  the  depression,  is  called  the  length  of  the 
wave,  the  distance  a  b  the  length  of  the  elevation,  and  6  c  that  of 
depression. 

305.  Nodal  points. — When  a  body,  as  a  string,  is  made  to  assume 
a  series  of  stationary  vibrations,  the  points  where  the  phases  of  eleva- 
tion and  depression  intersect,  are  always  at  rest. 

Let  the  cord  stretched  between  A  B,  fig.  252,  be  temporarily  fixed  at  the  points 
C  and  D,  and  the  three  parts  be  drawn  at  the  same  moment  equally  in  contrary 
directions,  so  that  the  cord  will  252 

assume  the  undulating  form  repre- 
sented  in  the  figure  ;  if  now  the 
fixed  points  at  G  and  D  be  removed, 
no  change  will  take  place  in  the 
vibratory  motion  of  the  cord;  but  as  it  continues  to  vibrato,  the  points  C  and 
D,  although  free,  will  be  in  a  state  of  rest. 

Pieces  of  paper  resting  upon  these  points  will  be  undisturbed,  while, 
if  placed  on  the  intermediate  positions,  they  would  be  thrown  off  imme- 
diately. These  are  called  nodal  points  (Latin,  nodus,  a  knot). 

\  2.    Undulations  of  Solids. 

306.  Solid  bodies. — All  solid  bodies  exhibit  the  phenomena  of 
vibration  in  various  forms  and  degrees,  varying  in  an  infinite  variety 
of  ways,  according  to  the  form  of  the  body,  and  the  manner 

in  which  the  force  producing  the  vibration  is  applied. 

307.  Forms  of  vibration. — Bodies  of  a  linear  form, 
as  tense  strings,  fine  wire,  &c.,  are  susceptible  of  three 
kinds  of  vibration,  which  are  called  (1st)  the  transverse, 
(2d)  the  longitudinal,  and  (3d)  the  torsional  vibrations. 
A  simple  apparatus  to  exhibit  these  effects  experimentally, 
contrived  by  Prof.  August,  is  represented  in  fig.  253.     It 
consists  of  a  spirally  twisted  wire,  stretched  from  a  frame 
by  a  weight.     If  the  weight  be  raised  to  A,  and  then  let 
fall,  it  will  advance  and  recede  from  its  normal  position,  ,^ 
the  wire  performing  a  series  of  longitudinal  vibrations. 

Transverse  vibrations  are  produced  by  confining  the  lower  end  of  the 
wire  by  a  clamp.  The  wire  is  then  drawn  from  its  position  of  equili- 
brium and  suddenly  let  go.  The  vibrations  which  it  then  makes,  shown 
by  the  dotted  lines,  are  transverse  to  the  axis  of  the  wire.  Torsional 
vibrations  are  produced  by  turning  the  weight  around  its  vertical  axis ; 


253 


OF    UNDULATIONS.  239 

upon  letting  it  go,  the  torsion,  or  twist  of  the  wire,  causes  it  to  turn  back, 
its  inertia  carrying  it  beyond  its  position  of  equilibrium,  until  arrested 
by  the  resistance  of  the  wire,  and  these  alternate  twistings  will  continue 
with  a  constantly  decreasing  energy,  until  gravity,  and  the  molecular 
forces  of  the  solid,  restore  the  equilibrium. 

308.  Vibration  of  cords. — Cords  and  wires,  as  is  familiarly  seen 
in  stringed   instruments,  have  their  elasticity  developed   by  tension. 
The  transverse  vibrations  of  a  body  are  well  illustrated  by  the  simple 
apparatus  annexed. 

Thus  if  the  cord  af  b,  fig.  254,  be  drawn  out  in  the  middle  to  a  c  6,  upon  being 
let  go,  its  elasticity  causes  it  to  return  254 

to   its  former   position.     This    movement  

is  effected  with    an   accelerated  velocity,  gj^*~^~~  y 

and  is  at  its  maximum  when  the  cord  has 

reached  the  line  of  equilibrium  af  b,  con- 

sequently  it  passes  with  a  constantly  decreasing  velocity   to   a  d  b,  where  its 

motion  Ls  nothing;  it  then  returns  to  af  b,  and  so  continues. 

One  complete  movement,  (as  from  a  cb  to  a  d  b,}  is  termed  an  oscil- 
lation or  vibration,  and  the  time  occupied  in  performing  it  is  called  the 
time  of  oscillation.  The  vibrations  of  tense  strings  are  isochronous. 

309.  Laws  of  the  vibration  of  cords. — Calculation  and  experi- 
ment have  demonstrated,  that  the  vibration  of  cords  is  in  accordance 
with  the  four  following  laws. 

1.  The  tension  being  the  same,  the  number  of  vibrations  of  a  cord  is  in 
inverse  ratio  to  its  length. 

That  is,  if  an  extended  cord,  as  of  a  violin,  makes  in  a  certain  time  a  number 
of  vibrations,  represented  by  1,  then,  in  order  to  make  a  number  of  vibrations, 
represented  respectively  by  2,  3,  4,  the  cord  must  be  £,  J,  J  as  long. 

2.  The  tension  being  the  same,  the  number  of  vibrations  in  cords  of 
the  same  material,  is  in  the  inverse  ratio  of  their  thickness  or  diameter. 

That  is,  if  we  take  two  cords  or  wires  of  the  same  length,  of  copper  or  steel, 
as  those  of  a  piano,  one  of  which  is  twice  the  diameter  of  the  other,  and  which 
vibrate  equal  lengths,  the  small  one  will  make,  in  the  same  time,  twice  as  many 
vibrations  as  the  larger. 

3.  The  number  of  vibrations  of  a  cord  is  proportional  to  the  square 
root  of  the  stretching  weight. 

That  is,  if  we  represent  by  1  the  number  of  vibrations  made  by  a  cord, 
extended  by  a  weight  of  ],  then  the  number  of  vibrations  made  by  a  similar  cord 
of  the  same  length,  in  the  same  time,  becomes  respectively  2,  3,  4,  &c.,  when  the 
weight  is  increased  to  4,  9,  16,  &c.  Thus,  if  we  would  cause  a  given  cord,  as 
of  a  violin,  to  vibrate  with  a  four-fold  velocity,  it  is  necessary  to  strain  it  to 
sixteen-fold  the  original  tension. 

4.  All  other  things  being  equal,  the  number  of  vibrations  of  a  cord  is 
inversely  proportional  to  the  square  root  of  its  density. 


240  THE    THREE    STATES    OF    MATTER. 

Thus,  if  we  take  a  cord  of  copper  which  has  a  density  of  9,  and  one  of  cat- 
gut, whose  density  is  about  1,  the  number  of  vibrations  of  the  last  in  the  same 
time  will  be  three  times  that  of  the  former. 

It  is  evident  that  these  laws  apply  only  to  homogeneous  cords,  am' 
not  to  those  cords  which  are  covered  with  another  material,  as  a  har£ 
string  of  cat-gut,  covered  with  metallic  wire. 

310.  Vibrations  of  rods. — Rods,  like  cords,  vibrate  both  in  longi 
tudinal  and  transverse  directions.     If  they  are  fixed  firmly  by  one  of 
their  extremities,  as  in  a  vice,  they  will  give,  when  set  in  motion,  a 
series  of  isochronous  vibrations. 

Elastic  rods  may,  like  strings,  be  divided  by  stationary  undulations 
into  several  vibrating  parts.  The  nodal  points  may  be  ascertained  by 
placing  upon  the  rods  light  rings  of  paper ;  these  will  be  thrown  off  as 
long  as  they  rest  upon  any  point  except  a  node,  but  when  they  reach  a 
node,  they  will  remain  there  unmoved. 

The  space  between  the  free  extremity  and  the  first  nodal  point  is  equal  to 
half  the  length  contained  between  two  nodal  points,  but  it  vibrates  with  the 
same  velocity.  Thus  a,  fig.  255,  being  the  fixed,  255 

and  b  the  free  end,  the  part  between  b  and  c  is  ^ 

half  the  distance  c  c'.     The  nodal  points  may  be  ^<^"      *^KT^   '^^<-       '^ 
rendered  sensible  by  sand  strewn  upon  the  hori- 
zontal surface  of  the  vibrating  rod ;  the  sand  is  seen  to  move  to  certain  points, 
where  it  remains  stationary ;  these  are  the  nodes. 

Rods  may  also,  like  cords,  vibrate  longitudinally,  and  the  nodal 
points  are  formed  in  the  same  manner.  It  has  been  observed  in  elastic 
rods  of  the  same  nature,  that  the  number  .of  longitudinal  vibrations  is 
in  the  inverse  ratio  of  their  length,  whatever  may  be  their  diameter 
and  the  form  of  their  transverse  section. 

A  prismatic  bar,  vibrating  longitudinally,  undergoes  a  very  consi- 
derable increase  of  length,  which,  in  the  state  of  repose,  could  not  be 
produced  except  by  a  very  strong  tension,  while  the  vibratory  movement 
is  obtained  by  a  very  feeble  force. 

The  number  of  vibrations  by  torsion  in  rods,  is  in  the  inverse  ratio 
of  their  length,  and  is  proportional  to  their  thickness,  the  substance  in 
all  cases  remaining  the  same. 

311.  Paths  of  vibration. — The   motion   performed  by   vibrating 
rods  is  often  very  complex.     This  may  be  beautifully  seen  by  the  con- 
trivance of  Prof.  Wheatstone,  consisting  of  a  polished  bead  fastened  on 
the  extremity  of  an  elastic  rod,  as  of  a  knitting-needle,  firmly  fixed  in 
a  board  or  vice. 

Upon  making  the  rod  vibrate,  the  bead,  by  reflection,  will  produce  a  continu- 
ous line  of  light.  It  will  be  seen  that  the  arc  described  is  not  circular,  but  the 
rod  appears  to  be  impressed  at  the  same  time  with  two  vibratory  movements,  at 


OF    UNDULATIONS. 


241 


256 


right  angles  to  each  other,  and  moves  in  a  curve  produced  by  the  composition  of 
these  forces. 

$12.  Vibration  of  elastic  plates. — Vibrations  are  readily  excited 
in  elastic  plates  by  the  friction  of  a  violin-bow  or  by  blows.  The  plato 
may  be  confined  either  at  its  centre 
or  from  one  corner,  in  the  vice,  fig. 
256,  resting  upon  a  cone  of  cork,  c, 
and  pressed  by  the  screw  a,  tipped 
with  cork. 

In  the  vibration  of  plates,  nodal  I 
lines  will  be  formed,  which  do  not 
participate  in  the  movements  of  the 
plane,  but  remain  in  a  state  of  rest. 

313.  Nodal  lines. — These  nodal 
lines  answer  to  the   nodal  points  in 
linear  vibrations,  and  if  we  suppose 
the  plane  to  be  made  up  of  a  series 

of  rods,  these  lines  will  answer  to  their  nodal  points.  They  run  in 
various  directions  across  the  vibrating  surface,  the  contiguous  ones 
moving  in  contrary  directions,  dividing  the  planes  into  numerous  por 
tions  in  opposite  phases  of  vibration. 

This  is  shown  in  fig.  257,  by  the  signs  -)-  and  — ,  A  B  being  the  vibrating 
plane.  The  dimensions  of  these  internodes  (vibrating  portions),  are  regulated 
in  the  same  manner  as  those  of  vibrating  rods.  257 

The  outside  ones,  a  b,  a  b,  are  always  half  the  Q 

size  of  those  in  the  interior.  The  nodal  lines 
vary  in  their  number  and  position,  according  to 
the  form  of  the  plates,  their  elasticity,  the  num- 
ber of  vibrations,  the  mode  of  vibrating,  &e. 

314.  Determination  of  the  position 
of  the  nodal  lines. — The  position  of  the 
nodal  lines  may  be  determined  by  scatter- 
ing sand   or  other  fine  material  over  the 
plate,   and   vibrating,    as   by    means  of  a     ~" 
violin-bow  drawn  across   the   edge  of  the 

plate;  the  grains  of  sand  will  remain  upon  the  points  which  are  ;•{ 
rest,  and  which  are  therefore  nodal  points.  Those  which  are  upon 
vibrating  portions,  will  be  thrown  aside  until,  after  a  time,  they  will 
settle  quietly  down  upon  the  nodal  lines. 

It  is  observed  that  if  lycopodium,  or  some  other  very  light  powder,  is  placed 
upon  the  plates,  it  will  accumulate  on  those  parts  which  are  in  greatest  vUra- 
tion.  Mr.  Faraday  proved  that  this  phenomenon  was  due  to  small  currents  of 
air  produced  during  the  vibration  of  the  plate,  and  which  drew  the  powder  with 
them  j  for  in  a  vacuum,  the  powder  of  lycopodium  is  disposed,  like  sand,  upon 
23* 


242 


THE    THREE    STATES    OF    MATTER. 


the  nodal  lines,  and  for  the  same  reason ;  if  the  plate  covered  with  sand  ia 
vihrated  under  water,  the  sand  collects  upon  the  most  agitated  portions  of  the 
plate,  because  of  the  similar  currents  excited  in  the  water  by  the  vibrations. 

315.  Laws  of  the  vibration  of  plates. — Observation  has  deter- 
mined that  the  vibration  of  plates  of  the  same  substance,  and  having 
the  same  degree  of  rigidity,  are  subject  to  the  following  laws : — 

1.  That  the  number  of  the  vibrations  is  independent  of  the  breadth  of 
the  la-mince. 

2.  It  is  proportional  to  their  thickness. 

3.  The  thickness  being  the  same,  it  is  in  inverse  ratio  of  the  square  of 
their  length. 

316.  Method  of  delineating  nodal  lines. — As  these  nodal  lines 
assume  various  and  complicated  figures,   difficult   to   delineate  with 
accuracy  by  common  drawing,  Savart  replaced  the  sand  by  powdered 
litmus,  previously  mixed  with  gum  water,  dried  and  pulverized  to  a 
uniform  size.    The  acoustic  figures  being  produced  with  this  powder,  a 
paper  moistened  with  gum  water  was  then  gently  pressed  upon  them, 
thus  giving  an  exact  transfer. 

This  method  gave  great  facilities  for  the  comparison  and  study  of  these  fugi- 
tive figures,  so  difficult  to  produce  with  perfect  identity,  and  enabled  the  inventor 
to  determine  the  exact  limits  of  the  nodal  lines  and  areas  of  unequal  vibration. 

258 


JXC 


.U-4 


317.  Nodal  figures.— Nodal  (or  acoustic)  figures  have  always  a  great 
symmetry  of   form,    and  259 

their  lines  are  generally 
as  much  more  numerous 
as  the  number  of  vibra- 
tions is  greater.  *  The 
same  plate  may  furnish 
an  infinite  variety  of  fig- 
ures, which  pass  from  one 
to  another  in  a  continu- 
ous manner,  and  not  by 
sudden  changes.  Thus  the 
inures  abcdef,  fig.  258, 
pass  into  one  another 
without  intermission. 

Many  hundred  forms  of  nodal  figures  have  been  figured.     Fig.  259  represents 
a  few  of  those  obtained  on  square  plates.     Triangular  and  polygonal  plates  all 


OF    UNDULATIONS. 


give  symmetrical  figures,  analogous  to  those  obtained  with  square  plates,  as  is 
seen  in  fig.  260.     With  circular  plates  it  is  observed  that  the  nodal  lines  distri- 

260 


bute  themselves  in  the  direction  of  the  diameter,  dividing  the  circle  into  an 
equal  number  of  parts,  or  into  more  or  less  regular  circular  forms,  having  the 
centre  of  the  plate  as  their  common  centre,  or  in  both  of  these  forms  combined. 
Fig.  261  represents  these  different  varieties  of  form. 

261 


O 


L 


r 


;o 


318.  Vibration  of  membranes. — The  flexibility  of  membranes 
does  not  permit  us  to  vibrate  them  unless  they  are  stretched  as  in  a 
drum.  They  present  modes  of  262 

vibration  which  have  much  ana- 
logy to  those  of  solid  plates, 
vibrating  either  by  concussion, 
as  in  the  drum,  or  by  the  influ- 
ence of  vibrations  in  the  air. 
If  we  stretch  over  the  top  of  a 
funnel  a  piece  of  moistened 
bladder,  and  when  it  is  dry, 
suspend  the  apparatus  by  a 
knotted  hair,  passed  through 
the  centre  of  the  membrane,  we 
can  produce  symmetrical  nodal 
lines  upon  its  surface,  strewed 
with  sand,  by  passing  the  fin- 
gers, covered  with  resin,  over  the  hair.  The  same  phenomenon  may  be 


Jxc 


u/ 


244 


THE    THREE    STATES    OF    MATTER. 


observed,  if  we  bring  the  membrane  near  a  bell  while  it  is  vibrating. 
The  acoustic  figures  obtained  by  the  vibration  of  membranes  are  ex- 
tremely varied.  Savart  has  observed  that  square  membranes  are 
divided  by  their  nodal  lines  into  the  same  forms  as  square  plates  under 
the  same  circumstances,  with  this  difference,  that  the  vibrating  parts 
in  the  vicinity  of  the  edges  are  smaller  for  the  last,  while  they  are 
equal  to  the  others  in  membranes.  Fig.  262  represents  a  few  of  the 
forms  produced  in  the  vibration  of  membranes.  It  has  been  found 
that  wood  and  metals,  in  very  thin  laminae,  vibrate  like  membranes. 

\  3.    Undulations  of  Liquids. 

319.  Production  of   "waves. — Liquids   are   capable  of  assuming 
undulatory  movements,  similar  to  the  vibrations  of  solids,  differing 
from  them,  however,  in  some  respects,  in  consequence  of  the  different 
physical  arrangement  of  their  atoms.    If  a  depression  be  made  at  any 
point  in  the  surface  of   a  fluid  in   a  state  of  rest,  by  the  dropping 
in  of  a  solid,  as  of  a  pebble  into  water  or  by  immersing  and    then 
withdrawing  the  solid,  a  circular  undulation  will  be  produced.    Around 
the  point  of  depression  there  first  rises  a  circular  elevation  above  the 
level  of  the  liquid  when  in  equilibrium,  and  immediately  beyond  this 
is  a  circular  depression,  and  so,  alternately,  successive  elevations  and 
depressions.     Thus  the  initial  motion  will  be  gradually  propagated  in 
a  series  of  progressively  widening  circles ;  wave  follows  wave,  until 
opposing  causes  allow  the  equilibrium  to  be  regained.     Thus,  in  fig. 
263,  the  light  circles  D  and  F  represent  the  elevations,  and  the  shaded 
ones,  C,  E,  G,  the  depressions  of  these  263 

circular  waves. 

As  in  the  case  of  the  vibrations  of 
solids,  an  entire  undulation  consists  of  a 
phase  of  depression,  and  another  of  ele- 
vation. This  may  be  rendered  more  in- 
telligible by  conceiving  a  vertical  plane, 
A  B,  to  pass  through  the  point  C,  whence  ** 
the  waves  originate.  It  is  plain  that  a 
progressive  lineal  undulation  will  arise 
on  it,  re'sembling  that  of  the  cord,  fig. 
248.  This  section  is  seen  in  fig.  264, 
A'  C'  B',  and  the  nomenclature  used  for 
the  cord  applies  to  it,  with  this  difference 
only,  that  by  the  breadth  of  the  wave  is  meant  the  periphery  of  its  circle,  and  by 
its  length,  the  length  of  both  the  elevated  264 

and  depressed  portions.     (Peschell.)  j — i  i — i 

320.  Progressive  undulations  in 
liquids. — In  a  movement  of  the  kind 

just  indicated,  the  fluid  appears  as  if  its  entire  mass  advanced   pro 


OF    UNDULATIONS.  245 

gressively  from  the  point  of  excitation  ;  but  this  is  a  delusion.  Float, 
ing  bodies,  as  pieces  of  wood,  are  not  hurried  forward  on  the  sur- 
face of  the  water,  but  merely  rise  and  fall,  alternately,  as  the  waves 
pass.  The  true  nature  of  the  motion  is  such,  that  each  particle  of  the 
fluid  describes  a  vertical  circle  about  the  spot  where  it  may  happen  to 
be,  revolving  in  the  direction  in  which  the  wave  is  advancing.  The 
particle  thus  returns  to  its  former  position  in  the  same  plane,  one-half 
being  above,  and  the  other  half  below  the  level  of  the  fluid.  Each 
particle  of  fluid  thus  set  in  motion,  imparts  a  similar  movement  to  its 
contiguous  particle,  this  again  to  the  next,  and  so  on.  But  as  a  certain 
time  must  elapse  for  this  transmission  of  motion,  the  different  particles 
will  be  describing  different  portions  of  tfceir  circular  movement  at  the 
same  moment.  Some  will  be  at  the  highest  point  of  their  vertical  circle, 
while  others  are  in  an  intermediate  position,  and  others  at  the  lowest, 
giving  rise  to  a  wave  which  advances  a  distance  equal  to  its  whole 
length,  while  each  particle  performs  one  entire  revolution. 

For  the  sake  of  simplicity,  we  will  consider  only  eight  of  the  many  particles 
which  we  may  conceive  as  occupying  the  horizontal  surface  between  a  and  m, 
fig.  265.  Imagine  the  particle  a  to  be  at  rest,  when  a  descending  wave  strikes 
it.  It  will  be  depressed,  and  will  begin  to  revolve  in  a  vertical  circle  in  the 
direction  of  the  arrow.  If  we  consider  eight  such  particles  .to  be  situated  on  the 

265 


line  a  m,  and  that  each  particle  begins  its  motion  J  of  a  revolution  later  than  its 
neighbor  next  on  the  left  hand;  then  at  the  instant  when  a  has  completed  one 
entire  revolution,  the  second  will  be  one-eighth  behind  it,  viz. :  at  7 ;  the  3d, 
two-eighths  behind  it,  viz. :  at  6  ;  and  the  fourth,  fifth,  sixth,  seventh,  and^ighth, 
at  the  points  5,  4,  3,  2,  and  1  respectively,  whilst  the  9th  particle  is  but  just 
beginning  to  move.  Connect  the  points  a,  7,  6,  5,  4,  3,  2,  1,  m,  and  the  line  will 
represent  the  form  of  the  fluid  surface  at  that  precise  moment  of  the  undulation. 

The  diameter  of  the  circle  which  each  particle  describes,  is  the  ampli- 
tude or  intensity  of  the  wave,  c6  its  depth,  and  #2  its  height,  each  of 
whicTi  is  equal  to  the  radius  of  a  circle  which  any  particle  describes 
during  one  oscillation.  This  radius  is  longer  or  shorter  according  to 
the  amplitude  of  the  wave.  It  is  sometimes  twenty  feet,  which  makes 
a  very  high  wave,  probably  the  largest  which  ever  occurs  on  the  ocean 
in  a  violent  storm,  unless  it  be  those  waves  which  have  been  increased 
by  the  accumulation  of  wave  upon  wave. 

321.  Stationary  waves. — Stationary  undulations  may  be  produced 
by  exciting  waves  in  a  circular  vessel,  from  its  central  point.  The 
waves  being  reflected  from  the  circular  wall,  will  produce  another  series, 


246  THE    THREE    STATES    OF    MATTER. 

which,  combined  with  the  first,  will  produce  the  effect  of  a  stationary 
undulation.  So  also  they  may  be  produced  on  a  surface  of  a  liquid 
confined  in  a  straight  channel  by  exciting  a  succession  of  waves,  sepa- 
rated by  equal  intervals,  moving  against  the  side  or  end  of  the  channel, 
and  reflected  from  it. 

322.  Depth  to  which  waves   extend. — Waves,  or  undulations, 
are  not  only  propagated  laterally,  but  also  in  all  other  directions.     It 
has  been  ascertained  (by  the  Messrs.  Webber)  that  the  equilibrium  of 
the  liquid  is  not  disturbed  to  a  greater  depth  than  about  three  hundred 
and  fifty  times  the  altitude  of  the  wave. 

323.  Reflection  of  waves. — If  a  series  of  progressive  waves  are 
arrested  by  impinging  against  any  solid  surface,  they  will  be  reflected 
again  from  that  surface  under  the  same  angle  at  which  they  struck  it. 
This  reflection  of  waves  is  occasioned  by  elasticity,  and  obeys,  precisely, 
the  laws  which  regulate  the  impact  of  elastic  bodies. 

Since  this  law  applies  to  all  the  rays  which  constitute  the  breadth  of 
a  wave,  the  path  of  a  reflected  wave  may  readily  be  determined  by  a 
knowledge  of  the  surface  and  the  angle  of  incidence.  If  the  wave  is 
linear,  (that  is,  if  the  line  resting  upon  the  highest  point  of  the  elevation 
at  right  angles  to  the  direction  in  which  it  is  moving,  is  a  straight  line), 
and  it  meets  a  plane  surface,  it  will  be  reflected,  and  return  in  the  same 
path.  If  it  meet  the  surface  at  an  angle  of  20°  or  30°,  it  will  be  reflected 
at  the  same  angle,  on  the  other  side  of  the  perpendicular  to  the  reflect- 
ing surface. 

324.  Waves  propagated  from  the  foci  of  an   ellipse. — If  the 
vessel  is  in  the  form  of  an  ellipse,  and  a  wave  originate  at  one  of  the 
foci,  all  the  rays  will  converge  so  as  to  fall  266 
simultaneously,  after  reflection,  on  the  other 

focus. 

Fig.  266  represents  an  ellipse,  of  which  F  and 
F'  are  the  foci,  which  have  the  following  property. 
If  lines  be  drawn  from  the  foci  to  any  points, 
P,  P,  P,  in  the  ellipse,  these  lines  will  form  equal 
angles  with  the  ellipse  at  P,  and  their  lengths 
taken  together,  will  he  equal  to  the  major  axis 
A  B.  If  we  suppose  a  series  of  circular  progres- 
sive waves  propagated  from  the  focus  F,  their  rays 
will  strike  successively  and  at  equal  angles  upon  the  elliptical  surface,  as  at  the 
points  P  P  P  ;  they  will  be  reflected  in  the  direction  P  F',  towards  the  other  focus. 
But  as  all  the  points  of  the  same  wave  move  with  the  same  velocity,  they  will 
all  reach  the  focus  F  at  the  same  time,  for  the  distances  they  pass  over  are  equal. 
Hence  it  follows,  that  each  circular  wave  that  expands  around  F,  will,  after  it 
has  been  reflected  from  the  surface  of  the  ellipse,  form  another  circular  wave 
around  F'  as  a  centre. 

325.  Waves  propagated  from  the  focus  of  a  parabola. — If  the 


OF    UNDULATIONS. 


247 


267 


surface  be  a  parabola,  and  a  wave  originate  at  its  focus,  all  the  rays 
will,  after  reflection,  pass  in  parallel  lines.  Or,  if  the  rays  impinge  in 
parallel  lines,  they  will,  after  reflection,  converge  to  the  focus. 

Fig.  267  represents  the  parabolic  curve.  The  point  V  is  its  vertex,  the  line 
V  M  its  axis.  The  point  F,  upon  the  axis,  is  the  focus,  and  has  the  following 
property.  If  lines  be  drawn  from  the  focus  to  any  points, 
P,  in  the  curve,  and  other  lines  be  drawn  from  the  points,  P, 
severally  parallel  to  the  axis  V  M,  meeting  lines  W  W,  drawn 
perpendicular  to  the  axis,  the  lines  F  P  and  P  p  will  be  in- 
clined at  equal  angles  to  the  curve  at  the  point  P,  and  the 
sum  of  their  lengths  will  be  everywhere  the  same.  Hence 
it  may  be  demonstrated,  as  in  the  case  of  the  ellipse,  that  if 
a  series  of  progressive  waves  be  propagated  from  the  focus 
F,  these  waves,  after  striking  the  curve,  will  be  reflected,  so 
as  to  form  a  series  of  parallel  straight  waves. 

Moreover,  it  is  evident  that  if  two  parabolas  face 
each  other,  so  as  to  have  their  axes  coincident,  a  sys- 
tem of  progressive  circular  waves,  issuing  from  one  focus,  will  be  fol- 
lowed by  a  corresponding  system,  having  for  its  centre  the  other  focus. 
For  if  a  series  of-  parallel  straight  waves  strike  a  parabolic  surface, 
their  reflection  would  form  a  series  of  circular  waves,  of  which  the 
centre  would  be  the  focus. 

Rays  reflected  from  spherical  surfaces,  whose  extent  is  small  com- 
pared with  their  diameter,  will,  in  their  direction,  approximate  closely 
to  those  reflected  from  a  parabolic  boundary. 

326.  Circular  waves  reflected  from  a  plane. — If  the  diverging 
rays  of  a  circular  wave  fall  upon  a  plane  surface  at  right  angles  to  it, 
their  path,  after  reflection,  is  the  same  as  it  would  have  been  had  they 
originated  from  a  point  on  the  opposite  side  of  268 

the  plane,  and  as  far  back  as  the  point  of  origin 
itself;  that  is,  the  form  of  the  reflected  wave 
will  be  the  reverse  of  the  incident  wave,  for  the 
rays  which  first  strike  the  surface  will  be  re- 
fleeted  first,  and  will  have  returned  to  the  same 
distance  from  the  surface  at  the  time  when  the 
last  rays  meet  it,  that  these  last  rays  were  at  the 
moment  when  the  first  were  reflected. 

Thus,  suppose  the  wave  g  a  d,  proceeding  from  the  centre  c,  fig.  268,  impinges 
on  the  plane  surface,  ef.  The  form  of  the  wave,  after  reflection,  will  be  the 
same  that  it  would  have  been  had  it  proceeded  from  c',  on  the  other  side  of  ef, 
(at  the  same  distance).  It  is  evident  that  with  a  circular  wave,  all  its  points 
cannot  impinge  at  the  same  time  on  a  plane,  therefore,  the  portions  in  advance  will 
impinge  first,  and  will  first  be  reflected;  and  when  a  impinges,  the  rays  at  d  and 
g  have  still  to  go  through  the  distances  d  e  and  gf,  before  they  can  be  reflected  ; 
but  in  the  space  of  time  required  for  this,  the  ray  at  a  will  have  returned  to  the 


248 


THE    THREE    STATES    OF    MATTER. 


point  k.  In  the  same  way  it  may  be  shown  that  the  intermediate  rays  will 
return  to  intermediate  positions,  and  be  found  in  the  line  e  kf,  symmetrically 
situated  to  the  line  e  nf,  in  which  they  would  have  been  had  they  not  been 
reflected  from  the  plane.  And  it  further  follows,  that  the  centre,  e',  of  the 
reflected  wave  d  k  g,  is  as  far  from  cf,  as  is  the  centre,  c,  of  the  incident  wave, 
e  nf,  but  on  the  opposite  side  of  the  median  plane,  e  af. 

327.  Combination  of    waves. — Where   two    systems   of  waves, 
coming  from  different  centres,  meet  each  other,  several  effects  may  fol- 
low, according  to  the  mode  of  meeting,  which  curiously  illustrate  the 
principles  of  undulation  in  all  departments  of  physics.     1st.  If  the 
elevations  of  the  two  waves  coincide,  and,  consequently,  their  depressions 
also,  then  a  new  wave  will  be  formed,  whose  elevations  and  depressions 
will  be  the  sum  of  those  of  the  two  originals.     2d.  If  the  two  waves 
of  equal  amplitude  are  so  superimposed  that  the  reverse  of  the  last  case 
is  true,  i.  e.,  that  the  elevation  of  one  fits  the  depression  of  the  other, 
then  both  waves  disappear,  and  the  surface  remains  horizontal.     Or, 
3d,  if  one  wave  has  greater  amplitude  than  the  other,  and  the  two 
waves  meet  in  the  same  phase,  then  the  resulting  wave  will  have  a 
height  equal  to  the  difference  between  the  greater  and  the  less. 

Combinations,  and  interference  of  waves,  are  of  universal  occurrence 
in  all  media,  in  which  force  of  any  kind  is  propagated  by  undulations. 

328.  Interference  in  an  ellipse. — The  two  systems  of  waves  formed 
by  an  elliptical  surface,  and  propagated,  one  directly  around  one  of  the 
foci,  and  the  second  formed  by  reflec-  269 

tion  around  the  other,  exhibit  not 
only  the  phenomena  of  reflection, 
but  also  of   interference.      These 
phenomena  are  represented  in  fig. 
269,  where  a  and  b  are  the  two  foci. 
The  strongly  marked  lines  are  the 
elevations,  the  more  lightly  traced  j 
lines  are  the  depressions,  the  points 
where   the   more  strongly  marked 
circles   intersect  the   more  faintly 
marked   circles,   are  points  where 
an  elevation  coincides  with  a  de- 
pression, and  are  therefore  points 
of  interference.     The  series  of  these  points  form  lines  of  interference 
which  are  indicated  in  the  diagram  by  dotted  lines,  which,  as  will  be 
seen,  arrange  themselves  regularly  in  the  form  of  hyperbola  and  ellipse? 
about  these  foci. 

329.  Undulations  of  the  waters  of  the  globe. — The  undulations 
produced  in  the  oceans,  lakes,  rivers,  and  other  large  collections  of 


OP   UNDULATIONS.  249 

water  upon  the  surface  of  the  globe,  are  of  extreme  importance  in  the 
economy  of  nature.  Did  not  water  possess,  as  a  consequence  of  the 
mobility  of  its  particles  among  each  other,  the  property  of  being  thus 
set  in  motion,  the  ocean  would  soon  be  rendered  putrid  by  the  decom- 
position of  the  mass  of  organized  matter  it  contains.  The  principal 
physical  cause  which  produces  these  undulations  on  a  moderate  scale, 
is  the  motion  of  the  atmosphere.  On  a  large  scale  they  are  produced 
by  the  combined  effects  of  the  attraction  of  the  sun  and  moon  upon 
the  surface  of  the  ocean,  which  causes  the  ebb  and  flow  of  tides. 
Differences  in  temperature  and  density  of  the  waters  of  different  parts 
of  the  ocean,  cause  currents,  by  the  efforts  of  these  waters  to  assume  a 
state  of  equilibrium  ;  and  lastly,  the  rotation  of  the  earth  upon  its  axis, 
originating  the  constant  easterly  current.  A  full  discussion  of  these 
interesting  questions  belongs  to  Physical  Geography. 

I  4.   Undulations  of  Elastic  Fluids. 

330.  Waves  of  condensation  and  rarefaction. — The  undulations 
of  liquids  already  described  (319)  are  surface  waves.     Undulations  of 
the  same  kind  may  also  be  produced  in  elastic  fluids.     Elastic  fluids 
are  also  subject  to  undulations  of  a  totally  different  kind  called  waves 
of  condensation  and  waves  of  rarefaction.     Such  undulations  are  due 
to  elasticity,  and  are  produced  in  air  and  gases  by  any  disturbance  of 
density.     If  any  elastic   fluid   be   compressed,    and   again   suddenly 
relieved  from  compression,  it  will  expand,  and  in  its  expansion  exceed 
its  former  volume  to  a  certain  extent ;  after  which  it  will  again  con- 
tract, and  thus  oscillate  alternately  on  either  side  of  the  position  of 
repose.    It  is  obvious  that  we  must  regard  these  undulations,  or  pulses 
of  air,  as  extending  equally  in  all  directions  in  the  free  air,  and  limited 
only  by  the  walls  of  the  containing  vessel  or  apartment  when  the  air  is 
confined.    Therefore,  the  effects  of  the  united  oscillations  extend  equally 
in  the  course  of  radii,  from  the  centre  to  every  point  of  the  surface  of 
a  sphere. 

331.  Undulations  of  a  sphere  of  air. — The  oscillations  of  air  will 
not  be  confined  to  the  sphere  in  which  they  commence.     When  air 
is  first  contracted,  an  aerial  shell,  bounding  the  sphere  of  contraction, 
expands,  and  becomes  thereby  less  dense  than  when  in  equilibrium. 
Again,  upon  the  expansion  of  the  original  sphere,  the  bounding  shell 
contracts,  and  becomes  more  dense,  in  virtue  of  its  inertia  and  elasticity. 
This  exterior  shell  of  air  thus  acts  upon  another,  external  to  it ;  this  in 
its  turn  on  another,  and  so  on,  and  thus  the  initial  force  is  propagated 
upon  successive  concentric  portions  of  air ;  its  effects  becoming  less 
marked  with  each  enlargement,  until,  like  the  ripple  of  a  wave  of 
water,  it  becomes  too  evanescent  to  be  appreciated.     Compare  \  653. 

24 


J50 


THE   THREE    STATES    OF    MATTER. 


This  alternate  condensation  and  expansion  of  an  elastic  fluid,  extending  spheri- 
cally around  the  original  centre  of  disturbance,  is  perfectly  analogous  to  a  series 
of  circular  waves  formed  around  a  point  on  the  surface  of  a  liquid.  The  conden- 
sation of  the  elastic  fluid  being  analogous  to  the  elevation  of  a  surface  wave,  and 
the  phase  of  rarefaction  being  analogous  to  the  phase  of  depression. 

The  radius  of  the  hollow  sphere,  or  the  distance  the  undulation  had  traversed 
when  the  first  particles  resumed  a  position  of  rest,  is  called  the  length  of  a  wave ; 
the  entire  sphere  comprised  within  these  limits  constitutes  a  wave,  and  the  time 
of  vibration  is  equal  to  the  time  in  which  motion  is  propagated  through  the  entire 
length  of  a  wave.  If  the  cause  which  excited  the  undulation  continues  to  operate, 
the  first  wave  will  expand,  and  there  will  arise  a  second  and  third  wave,  <fcc., 
within  the  first,  and  concentric  with  it. 

This  radial  propagation  of  undulations  in  air  can  takfe  place  with  equal  velo- 
city in  all  directions,  only  when  the 
atmosphere  is  of  uniform  density,  so 
far  as  the  vibrations  extend.  If  this 
is  not  the  case,  such  a  wave  cannot 
have  a  spherical  form. 

Let  fig.  270  represent  a  section  of  a 
sphere  of  air,  or  other  elastic  fluid,  in 
which  waves  of  condensation  and  rare- 
faction have  extended  outwards  from 
the  centre  C ;  then  the  heavy  lines, 
a  efg,  bhik,  and  d I p  q,  will  represent 
the  phases  of  greatest  condensation,  the 
finer  intermediate  lines  will  represent 
the  spaces  of  greatest  rarefaction,  and 
the  distances  m  n,  and  n  o,  between  cir- 
cles of  greatest  condensation,  will  be 
the  length  of  the  waves. 

Mechanical  illustration.— Pro- 
fessor Snell  has  contrived  the  apparatus,  represented  in  fig.  271,  to  illustrate  these 
undulations.     It  consists  of  a  shaft  turned  by  the  crank  seen  at  the  left,  on 
which  are  elliptical  grooves,  inclined  to  271 

the  axis,  in  which  the  rods  carrying  the 
white  balls  are  made  to  vibrate  from 
right  to  left  and  back  again.  These 
grooves  are  so  arranged  that  each  suc- 
cessive ball  moves  to  the  left  later  than 
the  preceding.  Thus  the  balls  are  seen 
crowded  together  at  certain  parts  of  the 
series ;  and,  as  the  crank  is  turned,  the 

phases  of  greatest  condensation  travel  across  the  field  from  left  to  right,  while 
other  similar  waves  are  formed  and  continually  succeed  them. 

332.  Velocity  and  intensity  of  aerial  waves. — The  velocity  with 
which  such  undulations  are  propagated  through  the  atmosphere,  depends 
on,  and  varies  with,  the  elasticity  of  the  fluid.  Waves,  both  large  and 
small,  are  transmitted  with  an  equal  velocity,  so  long  as  the  elasticity 
remains  the  same.  The  intensity  of  vibration,  i.  e.,  the  dimensions  of 
the  spaces  which  the  individual  particles  traverse  while  in  this  state  oi 


OF    UNDULATIONS.  251 

movement,  depends  on  the  energy  of  the  disturbing  force,  which,  it  is 
also  evident,  is  a  measure  of  the  degree  of  compression  of  the  wave. 

333.  Interference  of  waves  of  air. — If  two  series  of  aerial  waves 
coincide  as  to  their  points  of  greatest  and  least  condensation,  a  new 
series  of  waves  will  be  formed,  whose  greatest  condensation  and  rare- 
faction is  determined  by  the  sum  of  these  points,  as  prevailing  in  the 
separate  undulations.     But  where  the  series  are  so  arranged  that  the 
point  of  greatest   condensation  of  one   coincides   with   the    point   of 
greatest  rarefaction  in  the  other,  the  resulting  series  will  have  conden- 
sations and  rarefactions  equal  to  the  difference  between  the  waves  which 
meet.     If  they  are  equal,  total  interference  takes  place,  as  in  the  case 
of  non-elastic  fluids,  and  silence  results,  if  the  waves  are  those  of  sound. 

Indeed  all  the  effects  described  in  the  case  of  waves  formed  upon  the 
surface  of  a  liquid  are  reproduced  under  analogous  conditions  in  the 
case  of  undulations  of  aeriform  bodies.  It  must,  however,  be  borne  in 
mind,  that  these  aerial  waves  have  always  a  spherical  form. 

334.  Intensity  of  waves  of  air  expanding  freely. — The  undu- 
lations produced'  in  air  form  progressively  increasing  spheres  (330), 
the  magnitude  of  whose  surfaces  are  to  each  other  as  the  square  of  their 
radii,  or  as  the  square  of  their  distance  from  their  respective  points  of 
impulse.     As  the  intensity  of  the  wave  is  diminished  in  proportion  to 
the  space  over  which  it  is  diffused,  it  follows,  that  the  effect  or  energy 
of  these  waves  diminishes  as  the  square  of  the  distances  from  the  centre 
of  propagation  increases.     So  soon,  however,  as  the  radial  extension 
of  the  wave  meets  with  any  resistance  which  reflects  the  rays  in  a 
parallel  or  concentric  direction,  this  rule  ceases  to  be  applicable. 


Problems. 
On  the- Laws  of  Vibrations. 

149.  If  a  cord  of  a  given  length  makes  48  vibrations  per  second,  what  must 
be  the  respective  lengths  of  similar  cords  to  make  63,  64,  72,  81,  and  90  vibra- 
tions per  second? 

150.  If  a  cord,  3  feet  long,  extended  by  a  weight  of  10  Ibs.,  makes  96  vibra- 
tions per  second,  with  what  force  must  a  similar  cord,  2  feet  long,  be  extended 
that  it  may  make  108  vibrations  per  second  ? 

151.  If  an  iron  wire,  one-tenth  of  an  inch  in  diameter  (Sp.  Gr.  7-8),  makes 
72  vibrations  per  second,  what  must  be  the  diameter  of  a  platinum  wire  of  the 
same  length  (Sp.  Gr.  21-23)  which  will  make  45  vibrations  per  second? 

152.  An  iron  rod,  vibrating  by  torsion,  makes  30  oscillations  per  second;  how 
much  longer  must  a  rod,  having  twice  the  diameter,  be  to  vibrate  (with  the 
same  force)  15  times  per  second? 


252  THE   THREE   STATES   OF    MATTER. 


CHAPTER  VI. 

ACOUSTICS. 
$  I.  Production  and  Propagation  of  Sound. 

335.  Acoustics. — Sound. — Acoustics  (derived  from  the  Greek 
verb,  dxoua),  to  hear),  teaches  the  science  of  sounds,  their  cause,  nature, 
and  phenomena.  Sound  is  the  impression  produced  on  the  sense  of 
hearing  by  the  vibrations  of  sonorous  bodies.  These  vibrations  are 
transmitted  to  the  ear  by  the  surrounding  medium,  which  is  ordinarily 
the  atmospheric  air. 

Sound  a  sensation. — It  will  be  understood,  therefore,  that  all 
sound,  whether  unmusical,  like  mere  noise,  or  musical,  like  what  is 
technically  called  a  tone  (a  sound  of  definite  and  appreciable  pitch), 
is  a  sensation;  and  the  causes  which  produce  this  sensation  may  exist 
without  the  sensation  itself — that  is,  without  sound.  The  cause  of 
sound  being  atmospheric  vibration,  if  there  be  no  delicately  constructed 
organ,  like  the  ear,  to  receive  the  impression  of  this  vibration,  there  is 
no  sound.  It  would  follow,  that  even  at  the  Falls  of  Niagara,  if  there 
were  no  ear  present  to  receive  the  impression,  those  gigantic  vibra- 
tions would  exist  only  as  such — without  sound. 

Key-note  of  nature. — The  aggregate  sound  of  nature,  as  heard  in 
the  roar  of  a  distant  city,  or  the  waving  foliage  of  a  large  forest,  is  said 
to  be  a  single  definite  tone,  of  appreciable  pitch.  This  tone  is  held  to 
be  middle  F  of  the  pianoforte — which  may  therefore  be  considered  the 
key-note  of  nature. 

Noise. — The  distinctive  character  of  mere  noise  is  determined  by 
the  nature  and  duration  of  the  irregular  vibrations  causing  it.  If  these 
vibrations  are  short  and  single,  the  effect  is  that  of  a  crack,  or  an  abrupt 
explosion,  as  in  the  snapping  of  a  whip,  or  the  explosion  of  cannon. 
If  they  are  continuous  and  prolonged,  the  effect  is  that  of  a  rattle,  or 
rumble,  like  the  rolling  of  thunder,  or  the  noise  of  carriages  over  a 
stony  road. 

Musical  sounds. — Sound,  in  a  musical  sense,  or  tone,  is  the  sensa- 
tion produced  by  a  scries  of  equal  atmospheric  vibrations.  Noise  is 
the  sensation  produced  by  unequal  vibrations.  If  we  throw  a  single 
stone  into  the  centre  of  a  placid  lake,  a  single  wave  circles  off  to 


ACOUSTICS. 


253 


273 


the  shore  :  such  is  the  effect  upon  the  air  when  a  tone  id  produced. 
If  a  handful  of  pebbles  is  thrown  into  the  lake,  each  separate  pebble 
produces  its  own  circle,  these  circles  intersect  each  other  and  become 
confused  to  the  eye  :  such  is  the  effect  upon  the  air  when  a  noise  is 
produced.  Pulling  the  string  of  a  harp  would  correspond  to  the  single 
stone  thrown  into  the  lake :  striking  a  table  or  chair,  where  the  sepa- 
rate fibres  of  the  wood  vibrate  unequally,  would  correspond  to  the 
handful  of  pebbles. 

A  church-bell,  to  a  cultivated  ear,  is  noisy,  or  musical,  according  as  the  tones 
in  the  vibrating  metal  (for  every  bell  produces  more  than  one  distinguishable 
tone)  chance  to  be  at  musical  or  unmusical  intervals.  If  the  intervals  are  (mu- 
sically considered)  dissonances,  the  bull  will  be  discordant ;  if  they  are  con- 
cords, the  bell  will  be  harmonious.  Again,  if  in  these  concordant  tones  the 
intervals  be  "major,"  the  bell  will  be  cheerful;  if  they  be  "minor,"  the  bell 
will  be  sad. 

336.   All  bodies   producing  sound   are   in  vibration. — If  the 

sonorous  body  is  solid,  and  presents  a  large  surface,  as  a  bell-jar,  the 
vibrations  may  be  shown  by  suspending  a  small  ivory 
ball,  i,  by  a  thread  in  the  interior  of  the  jar  A  B,  in- 
clined in  the  position  seen  in  fig.  272.  When  the  jar 
resounds  with  a  blow,  the  ball  is  thrown  from  the  sides, 
as  shown  by  the  dotted  line,  and  returning,  is  again 
thrown  off,  and  so  continues  bounding,  in  consequence 
of  the  vibrations.  A  touch  from  the  hand  arrests  the 
vibratory  movement  in  the  glass :  the  sound  ceases, 
and  the  ivory  ball  remains  quiet. 

If  the  sonorous  body  is  a  plane 
surface,  its  vibrations  may  be  shown 
by  the  formation  of  nodal  lines  with 
grains  of  sand  scattered  upon  it. 
When  the  sound  is  produced  by  a 
stretched  cord,  the  vibrations  may 
be  felt  by  touching  the  cord  lightly 
with  the  hand,  or  may  be  seen  by 
placing  bands  or  rings  of  paper 
upon  the  vibrating  cord.  In  wind 
instruments,  it  is  the  air  which  they  contain,  whose  vibrations  produce  the 
musical  sounds. 

This  may  be  proved  by  an  organ-pipe,  or  by  a  glass  tube,  fig.  273,  when  a 
current  of  air  is  passed  into  it  through  the  foot,  0.  A  small  membrane  of  gold- 
beater's skin,  extended  on  a  circle  of  pasteboard,  B,  is  placed  within  the  tube, 
and  sustained  in  a  horizontal  position  by  means  of  a  thread.  Grains  of  sand 
strewed  upon  the  membrane,  will  be  arranged  in  nodal  figures,  proving  that  the 
membrane  obeys  the  vibratory  movement  of  the  air  which  surrounds  it.  That 
the  vibrations  are  not  due  to  an  ascending  current  of  air,  is  proved  by  the  fact, 
that  the  membrane  does  not  vibrate  when  it  is  placed  midway  of  the  length  of 
24* 


254  THE    THREE    STATES    OF    MATTER. 

the  tube  [a  nodal  point],  but  above  or  below  this  point  it  vibrates,  and  more 
strongly  as  it  is  further  removed  from  the  centre. 

337.    Sound  propagated   by  waves. — Sound  is  propagated   by 
waves  of  condensation  and  rarefaction  (330),  as  shown  in  fig.  274.    The 

274 


vibrations  of  the  sounding  hell  are  communicated  to  the  surrounding 
medium,  and  by  vibrations  alternately  forwards  and  backwards.  Mo- 
tion is  communicated  to  an  ever  increasing  spherical  portion  of  the 
medium  until  it  reaches  the  ear,  by  which  the  sensation  of  sound  is 
perceived. 

338.  Co-existence  of  sound-waves. — Many  sounds  may  be  trans- 
mitted simultaneously  in  different  directions  by  the  same  medium  with- 
out destroying  each  other,  all  the  sounds  penetrating  and  crossing  in 
space  without  modification.     In  complicated  symphonies,  a  practiced 
ear  readily  distinguishes  the  sound  of  each  instrument.    A  very  intense 
sound  may  overpower  a  feeble  sound,  as  a  loud  noise  renders  the  human 
voice  inaudible. 

339.  Sound  is  not  propagated  in  a  vacuum. — The  vibrations  of 
elastic  bodies  do  not  produce  an  impression  on  the  ear,  unless  there 
exists  between  this  organ  and  the  sonorous  body  an  uninterrupted  elas- 
tic medium,  vibrating  with  it.     This  medium  is -ordinarily  the  atmo- 
spheric air,  but  other  gases,  vapors,  liquids,  and  solids,  transmit  sound, 
and  generally  with  a  facility  varying  with  their  density. 

To  prove  that  sound  is  not  propagated  in  a  vacuum,  place  under  the  receiver 
of  an  air-pump,  a  bell,  kept  in  constant  vibration  by  a  clock-work  movement, 
fig.  275.  The  bell  apparatus  should  be  placed  upon  wadding,  otherwise  the 
vibrations  would  be  communicated  to  the  plate  of  the  air-pump,  and  thus  to  thp 
air.  While  the  receiver  is  filled  with  air  at  the  ordinary  pressure,  the  sound 
is  distinct ;  as  the  air  is  gradually  exhausted,  the  sound  grows  more  and 
more  feeble,  until  finally,  when  a  vacuum  is  obtained,  it  ceases  to  be  heard, 
but  is  immediately  revived  by  admitting  air  again. 


ACOUSTICS 


255 


275 


340.  Sound   is    propagated  in  all  elastic  bodies.— If,  in   the 

experiment  just  described,  the  vacuum  is  supplied  with  hydrogen  gaa 
(density  0.0692),  or  any  gas  of  less  density 
than  atmospheric  air,  a  sound  will  be  trans- 
mitted from  the  bell,  very  feeble  for  the  hy- 
drogen, and  increasing  as  the  gas  is  more 
dense.  In  like  manner,  a  person  whose  lungs 
have  been  filled  with  hydrogen  gas,  utters 
only  a  shrill  piping  sound. 

Vapors,  water  and  other  liquids,  transmit 
sounds  like  gases,  but  with  much  more  energy. 
When  two  bodies  are  struck  under  water,  the 
sound  is  distinct  to  a  person  having  his  ear 
under  water,  or  communicating  with  the  water 
by  means  of  some  solid  substance.  The  conducti- 
bility  of  sound  is  so  great  in  solids,  that  if  we  apply 
the  ear  to  one  end  of  a  beam  of  wood,  the  slightest 
shock,  as  the  scratch  of  a  pin  at  the  other  extremity,  may  be  heard  distinctly- 
The  noise  of  cannon  has  been  heard  a  distance  of  more  than  two  hundred  and 
fifty  miles,  by  applying  the  ear  to  the  solid  earth.  In  several  mines  in  Corn- 
wall, England,  there  are  galleries  which  extend  under  the  sea,  where  the  sound 
of  the  waves  is  clearly  heard  when  the  sea  is  agitated,  rolling  the  pebbles  and 
boulders  over  the  rocky  bottom  of  the  ocean. 

The  music  from  a  company  of  musicians,  playing  in  orchestra  upon  numerous 
instruments,  has  been  transferred  to  an  apartment  in  another  house,  by  a  cord 
stretched  across  the  intervening  street,  connecting  at  one  end  with  a  sounding- 
board,  and  at  the  other  extremity  with  a  wooden  box.  On  placing  the  ear  at  an 
opening  in  the  box,  the  whole  musical  movement  was  heard,  reproduced  in 
miniature,  being  transmitted  by  the  vibrations  through  the  cord.  A  bystander 
in  the  same  apartment  was  unconscious  of  there  being  any  performance. 

341.  Hearing  is  a  sense  depending  upon  the  ear,  a  beautifully  con- 
structed instrument,  designed  to  gather  in  the  vibrations  of  the  sur- 
rounding air.    This  vibratory  movement  is  communicated  to  the  acoustic 
nerve  by  the  aid  of  organs  which  will  be  described  in  detail  at  the  close 
of  this  chapter. 

342.  Time  is  required  for  the  transmission  of  sound. — Expe- 
rience testifies  to  the  truth  of  this  statement.     We  hear  the  blows  of  a 
hammer  at  a  distance  a  very  sensible  interval  of  time  after  we  see  them 
struck.    An  appreciable  time  elapses  after  we  see  the  flash  of  a  cannon, 
at  a  little  distance  from  us,  before  we  hear  the  explosion.     The  report 
of  the  meteor  of  1783  was  heard  at  Windsor  Castle  ten  minutes  after 
its  disappearance. 

343.  The  velocity  of  all  sounds  is  the  same.* — The  velocity  of 
sound  is  the  space  that  it  traverses  in  a  second.     Theory  demonstrates 
that  the  velocity  of  the  vibrations  of  sonorous  bodies  in  the  same  me- 


*  See  note  in  Appendix,  p.  66 S. 


256  THE    THREE    STATES    OF    MATTER. 

dium,  is  the  same  for  all  sounds,  grave  or  sharp,  strong  or  feeble,  and 
Whatever  may  be  their  pitch.  Observation  confirms  this  result,  at  least 
for  those  distances  at  which  experiments  have  been  made.  There  is  no 
confusion  in  the  effects  of  music,  at  whatever  distance  it  may  be  heard. 

If  the  different  notes  simultaneously  produced  by  the  various  instruments  of 
an  orchestra,  moved  with  different  velocities,  they  would  be  heard  by  a  distant 
auditor  at  different  moments,  so  that  a  musical  performance,  except  to  those  in 
its  immediate  vicinity,  would  produce  only  discords.  M.  Biot,  in  playing  an 
air  upon  a  flute  at  the  extremity  of  a  pipe  of  the  aqueduct  of  Paris,  found  that 
the  sounds  came  to  the  other  end,  having  exactly  the  same  interval,  demon- 
strating that  the  different  sounds  travelled  with  the  same  velocity. 

344.  Velocity  of  sound  in  air. — Numerous  experiments  have  been 
made  for  estimating  the  velocity  of  sound ;  that  is,  the  space  that  it 
travels  over  in  a  second.  The  most  extensive  and  accurate  system  of 
experiments  were  those  made  in  1822,  by  the  Board  of  Longitude  of 
France,  conducted  by  Messrs.  Prony,  Arago,  Humholdt,  Gay  Lussac, 
and  others. 

Two  pieces  of  cannon  were  used,  one  placed  at  Montlhery,  the  other  at  Mout- 
martre,  between  which  the  distance  is  18,612  m.  (=  61,063-8  feet),  or  more  than 
ten  miles.  The  discharges  were  reciprocal,  so  as  to  avoid  the  influence  of  the 
wind.  At  each  station  were  numerous  observers,  furnished  with  chronometers, 
who  noticed  the  time  between  the  appearance  of  the  light,  and  the  arrival  of  the 
sound.  This  time  may  be  called  that  which  the  sound  requires  to  pass  from  one 
station  to  another,  for  the  time  occupied  by  the  passage  of  the  light  between 
the  two  points  is  wholly  inappreciable.  The  mean  time  required  to  transmit  the 
sound  was  54-6  seconds.  By  dividing  the  distance  between  the  two  stations  by 
this  number,  the  velocity,  per  second,  is  obtained.  The  velocity  of  sound  at 
61°  F.  (16°  C.),  that  being  the  temperature  of  the  atmosphere  during  the  ex- 
periment, is  1118-3  feet  (340-88  m.),  (for  61,063-8-=-  54-6  =  1118-3  -f) ;  or  at 
the  temperature  of  32°  F.  it  would  be  about  1086-1  feet. 

Messrs.  Bravais  and  Martin,  in  1844,  have  determined  that  the  velo- 
city of  sound  between  the  summit  and  base  of  the  Faulhorn  (a  lofty 
mountain  in  the  Swiss  Alps)  is  the  same,  whether  ascending  or  descend- 
ing, and  that  it  is  1090-47  feet  per  second  at  32°  F. 

It  has  been  determined,  1.  That  the  velocity  of  sound  decreases  with 
the  temperature;  at  50°  F.  (10°  C.),  it  is  1106-091  feet  (337  m.)  So 
that  as  the  temperature  is  lowered,  sound  diminishes  in  velocity  about 
one  foot  and  a  tenth  for  every  degree.  2.  That  at  the  same  tempera- 
ture the  velocity  of  sound  is  not  materially  affected,  whether  the  sky  is 
bright  or  cloudy,  the  air  clear  or  foggy,  the  barometric  pressure  great 
or  small,  provided  the  air  is  tranquil.  All  of  these  circumstances, 
however,  exert  a  great  influence  on  the  intensity  of  the  sound  as  it 
reaches  the  ear  from  a  given  distance.  Fogs,  snow,  &c.,  prevent  the 
free  propagation  of  sound,  but  do  not  materially  affect  its  velocity.  3. 
That  its  velocity  varies  with  the  velocity  and  direct!  ^n  of  the  wind. 


ACOUSTICS.  257 

345.  Velocity  of  sound  in  different  gases  and  vapors.— The 

velocity  of  sound  in  the  different  gases,  is  in  the  inverse  ratio  of  the 
square  root  of  their  densities. 

Dulong  has  determined  by  calculation  the  velocity  of  sound  in  the  following 
gases,  at  the  temperature  of  32°  F.  Carbonic  acid  860  feet  (262  m.),  oxygen 
1040  feet  (317  m.),  olefiant  gas,  1030-2  feet  (314  m.),  air,  1092-54  feet  (333  m.), 
carbonic  oxyd,  1105  6  feet  (337  m.),  and  hydrogen,  4163  feet  (1269  m.),  each 
in  a  second.  The  theoretical  velocity  of  sound  in  vapor  of  alcohol  at  140°  is 
862  feet,  in  vapor  of  water  at  154°  is  1347  feet.  The  observed  velocities  are 
generally  not  very  far  from  those  given  by  calculation. 

346.  Calculation  of  distances  by  sound. — The  known  velocity 
of  sound  per  second  (1118  feet),  enables  us  to  obtain  a  close  approxi- 
mation of  the  distance  of  the  sonorous  body.     This  follows  as  a  conse- 
quence of  the  very  experiments  (344)  by  which  the  velocity  of  sound 
was  determined.    From  the  known  laws  of  falling  bodies  (71),  we  may 
also,  with  the  aid  of  the  known  velocity  of  sound,  obtain  an  approxi- 
mate estimate  of  the  height  of  a  precipice,  or  the  depth  of  an  abyss, 
from  the  time  occupied  by  the  sound  of  any  projectile,  let 'fall  from  the 
hand,  in  reaching  the  ear. 

347.  Velocity  of  sounds  in  liquids. — Sound  is  conveyed  through 
liquids  as  well  as  through  gases.     The  velocity  of  sounds  in  liquids 
is  much  greater  than  in  air.     In  1827,  Messrs.  Colladon  and  Sturm, 
experimenting  upon  the  velocity  of  sound  in  the  Lake  of  Geneva,  found 
it  to  be  4708  feet  (1435  m.)  per  second,  or  about  four  and  a  half  times 
greater  than  in  air,  at  the  temperature  of  46'6°  F. 

Agitation  of  the  water,  liquids,  <fec.,  did  not  affect  either  the  rapidity  or 
intensity  of  the  sound.  But  the  interposition  of  solid  bodies,  such  as  walls,  or 
buildings,  between  the  sounding  body  and  the  observer,  almost  destroyed  the 
transmission  of  sound  in  water ;  an  effect  which  does  not  take  place  nearly  to 
the  same  degree  in  air  (350). 

348.  Velocity  of  sounds   in   solids. — Sound   is   transmitted   by 
solid  bodies  with  much  greater  rapidity  than  by  air,  but  by  no  means 
with  equal  velocity,  varying  much  with  the  elasticity  and  density  of  the 
different  solids,  as  well  as  their  homogeneity  and  uniformity  of  structure. 

Want  of  homogeneity  in  any  medium  interferes  with  the  propagation  of  sonor- 
ous vibrations.  Let  a  tall  glass  be  half  filled  with  champagne  wine :  as  long 
as  there  is  effervescence,  and  the  wine  contains  air  bubbles,  a  stroke  on  the  glass 
gives  only  a  dead  disagreeable  sound ;  as  the  effervescence  subsides  the  tone 
becomes  clearer,  and  when  the  liquid  is  tranquil  the  glass  rings  as  usual.  The 
dullness  of  sound  alluded  to  is  owing  to  the  fact  that  the  wine  which  forms  part 
of  the  vibrating  system  lacks  homogeneity,  and  therefore  is  incapable  of  regular 
vibration. 

The  most  exact  experiments  have  been  made  by  M.  Biot,  with  a  series  of  water- 
pipes  in  Paris,  which  had  a  length  of  3120  feet  (951  in.).  A  bell  was  hung  at 
the  centre  of  a  ring  of  iron,  fastened  to  the  mouth  of  the  tube,  so  that  the 


258  THE    THREE    STATES    OF    MATTER. 

vibrations  of  the  ring  would  affect  only  the  metal  of  the  tube,  and  the  vibrations 
of  the  bell  only  the  included  air.  When  the  ring  and  bell  were  struck  simulta- 
neously, an  observer,  placed  at  the  other  end,  heard  two  sounds;  the  first 
transmitted  by  the  metal,  the  second  by  the  air.  By  noticing  the  interval  of 
time  between  the  arrival  of  the  two  sounds,  it  was  ascertained  that  the  velocity 
of  propagation  of  sound  in  cast  iron  is  about  10-4  times  that  observed  in  air; 
that  is,  11,609  feet  (3538'5  m.).  Similar  experiments  were  made  by  Hassenfratz 
on  the  velocity  of  sound  in  stone,  on  the  walls  of  the  galleries  of  the  catacombs 
which  underlie  Paris,  by  observing  the  interval  of  time  between  the  arrival  :f  a 
sound  transmitted  by  the  stones  and  of  that  transmitted  by  the  air  of  the  gallery. 

Were  the  earth  and  sun  connected  by  an  iron  bar,  nearly  three  years  would 
elapse  before  the  sound  of  a  blow  applied  at  the  sun  could  reach  the  earth. 

The  velocity  of  the  propagation  of  sound  has  been  determined  theoretically 
by  Savart,  Chladni,  Masson,  and  Wertheim,  from  the  number  of  longitudi- 
nal and  transverse  vibrations  of  the  bodies,  or  their  coefficient  of  elasticity. 
Chladni  found,  by  the  aid  of  longitudinal  vibrations,  that  in  wood,  the  velocity 
of  sound  is  from  ten  to  sixteen  times  greater  than  in  air.  In  metals,  the  velo- 
city is  more  variable,  being  from  four  to  sixteen  times  as  great  as  in  air. 

349.  Interference  of  sound. — When  two  series  of  sonorous  undu- 
lations  encounter   each   other   in   opposite   phases   of  vibration,   the 
phenomena  of  interference  are  produced.    The  undulations  will  become 
mutually  checked,  and  if  the  two  sounds  are  of  equal  intensity,  instead 
of  producing  a  louder  sound,  as  might  be  expected,  they  will  altogether 
destroy  each  other  and  produce  silence.    If,  however,  one  of  the  sounds 
ceases,  the  other  is  heard  immediately. 

If  two  sounding  bodies  were  placed  in  the  foci  of  an  ellipse,  fig.  269,  no  sound 
would  be  heard,  if  an  ear  was  placed  on  any  of  the  lines  of  interference  indi- 
cated by  the  dotted  lines,  but  if  one  sound  was  stilled,  the  other  would  be  heard, 
or  if  the  ear  was  placed  between  the  lines  of  interference,  then  both  sounds 
would  be  heard  simultaneously,  and  would  be  louder  than  either  alone. 

The  interference  of  sounds  may  be  shown  by  means  of  a  common 
tuning-fork.  276 

When  in  vibration,  its  branches  recede  from,  and  ap- 
proach each  other,  as  shown  by  the  dotted  lines  in  fig. 
276.  If  the  instrument,  when  vibrating,  is  placed  about 
a  foot  from  the  ear,  with  the  branches  equidistant,  both 
sounds  will  be  heard ;  for  the  waves  of  sound  combine 
their  effects ;  but  as  it  is  slowly  turned  around,  the  sound 
will  grow  more  and  more  feeble,  until  at  length  a  posi- 
tion will  be  found  in  which  it  will  be  inaudible.  For,  as 
the  tuning-fork  is  turned,  the  waves  of  sound  interfere,  and 
produce  partial  or  total  silence.  This  may  also  be  illustrated 
by  attaching  a  tuning-fork,  lengthwise,  to  any  rotating  sup- 
port. When  the  fork  is  vibrating,  no  sound  will  be  heard  so 
long  as  it  continues  to  rotate, 

350.  Acoustic  shadow. — Persons  cut  off  from  ob- 
servation by  a  wall,  or  other  obstacle,  still  hear  sounds 

distinctly,  although  with  a  diminished  volume.    Thus  a  band  of  music 


ACOUSTICS.  259 

in  an  adjacent  house,  or  neighboring  street,  is  readily  followed  in  the 
softest  melody.  Intervening  obstacles,  therefore,  however  opaque  to 
light,  do  not  cast  perfect  shadows  to  sound.  The  sound  is  not  entirely 
cut  off,  because  the  obstacle  is  elastic,  and  propagates  the  vibrations  it 
receives  in  a  manner  analogous  to  light  passing  through  a  translucent 
medium. 

To  a  distant  observer,  the  roar  of  a  railway  train  is  instantly  bushed  on 
entering  a  tunnel,  and  as  suddenly  renewed  on  its  emergence. 

Acoustic  shadows  are  much  more  distinctly  recognised  when  large 
masses,  as  edifices  or  rocks,  intervene ;  so  large  as  not  to  enter  into 
vibration. 

Although  there  is  not  complete  silence  in  the  acoustic  shadow,  still  it 
is  analogous  to  the  shadow  of  light,  for  there  is  never  complete  obscurity 
in  the  latter  case,  even  when  we  take  the  utmost  precaution,  for  the 
light  spreads  behind  the  obstacles  which  arrest  it. 

351.  Distance  to  which  sound  may  be  propagated. — The  dis- 
tance at  which  sounds  are  audible  does  not  admit  of  precise  measure- 
ment. In  general,  it  may  be  stated,  that  a  sound  will  be  heard  further, 
the  greater  its  original  intensity,  and  the  denser  the  medium  in  which 
it  is  propagated.  It  also  depends,  greatly,  on  the  delicacy  of  hearing 
of  different  individuals/  The  intensity  of  sound,  like  that  of  all  forces 
acting  in  lines,  diminishes  in  the  inverse  ratio  of  the  squares  of  the 
distance  of  the  sounding  body.  Thus,  if  the  linear  dimensions  of  a 
theatre  be  doubled,  the  volume  of  the  performers'  voices  at  any  part  of 
the  circumference  will  be  diminished  in  a  fourfold  proportion. 

That  this  difference  of  the  agitating  impression  is  the  true  cause,  is  shown  by 
confining  the  air  on  all  sides  in  a  tube.  Biot  experimented  with  2860  feet  of  the 
water-pipes  of  Paris.  At  this  distance  the  lowest  whisper  made  at  one  end  was 
accurately  heard  at  the  other  extremity  of  the  tube. 

A  powerful  human  voice  in  the  open  air,  at  the  ordinary  temperature,  is 
audible  at  the  distance  of  seven  hundred  feet.  In  a  frosty  air,  undisturbed  by 
winds  or  current,  sound  is  heard  at  a  much  greater  distance  with  surprising 
distinctness.  Lieut.  Forster,  in  the  third  polar  expedition  of  Capt.  Parry,  held 
a  conversation  with  a  man  across  the  harbor  of  Port  Bowen,  a  distance  of  ono 
and  a  quarter  miles.  Dr.  Young  states,  on  the  authority  of  Derham,  that  the 
watchword  "  all's  well"  has  been  distinctly  heard  from  Old  to  New  Gibraltar,  a 
distance  of  ten  miles.  The  marching  of  a  company  of  soldiers  may  be  heard, 
on  a  still  night,  at  from  five  hundred  and  eighty  to  eight  hundred  and  thirty 
paces ;  a  squadron  of  cavalry  at  foot  pace,  at  seven  hundred  and  fifty  paces ; 
trotting,  or  galloping,  one  thousand  and  eighty  paces  distant.  When  the  air  is 
calm  and  dry,  the  report  of  a  musket  is  audible  at  eight  thousand  paces.  The 
Bound  of  the  cannonading  at  Waterloo  was  heard  at  Dover. 

Sounds  travel  further  on  the  earth's  surface  than  through  the  atmosphere.  Thus 
it  is  said,  that  at  the  siege  of  Antwerp  in  1832,  the  cannonading  was  heard  in  the 
mines  of  Saxony,  which  are  about  three  hundred  and  seventy  miles  distant.  The 


260 


THE    THREE    STATES    OF    MATTER 


277 


cannonading  at  the  battle  of  Jena  was  heard  feebly  in  the  open  fields  near  Dres- 
den, 92  miles  distant,  but  in  the  casemates  of  the  fortifications  it  was  heard  with 
great  distinctness.  The  noise  of  a  sea  fight  between  the  English  and  the  Dutch 
in  1672,  was  heard  at  Shrewsbury,  a  distance  of  two  hundred  miles.  Sound 
has  been  carried  by  the  atmosphere  to  the  distance  of  three  hundred  and  forty- 
five  miles,  as  it  is  asserted,  that  the  very  violent  explosions  of  the  volcano  at 
St.  Vincent's  have  been  heard  at  Demarara. 

Sir  Stamford  Raffles  records  however  a  similar,  though  much  more  extraor- 
dinary, fact.  The  eruption  in  Tombers,  in  Sumbawa,  was  perhaps  the  most 
violent  volcanic  action  recorded ;  occasional  paroxysms  were  heard,  he  says, 
more  than  nine  hundred  miles  distant. 

352.  Reflection  of  sound. — When  the  waves  of  air  on  which  sound 
is  being  borne  impinge,  in  the  course  of  their  expansion,  on  a  solid 
surface,  they  will  be  reflected  from  it,  agreeably  to  the  laws  regulating 
the  impact  of  solid  bodies  (112).  Their  return  is  made  with  equal  velo- 
city, and  under  an  equal  but  opposite  angle,  to  that  under  which  they 
advanced. 

Let  a  spherical  wave  whose  centre  is  at  S,  fig.  277,  encounter  obliquely  a 
plane  surface,  a  0,  separating  two  media  of  different  density,  a  portion  of  the 
sound  will  be  reflected  as  though  it  emanated  from 
the  point  S',  as  far  behind  0  as  S  is  in  front  of  it, 
and  while  a  n  would  have  been  the  surface  of  the 
wave  if  the  reflecting  medium  had  not  intervened, 
a  n'  will  be  the  wave  surface  of  the  reflected  sound. 
Take  any  portion  of  the  incident  wave,  as  b  m,  let 
bp  =  m  a,  when  the  surface  of  the  incident  wave 
reaches  a,  a  wave  starting  from  a  new  centre  of  vi- 
bration, b,  will  have  extended  to  the  circumference 
described  upon  bp  ;  similarly  a  new  vibration  start- 
ing from  c,  will  describe  the  circle  of  which  c  q  is 
the  radius.  In  the  same  manner,  vibrations  start- 
ing from  every  point  of  the  line  a  0,  will  make  up 
the  compound  wave  surface  a  n',  whose  centre  is  at 
S',  and  which  is  tangent  to  all  the  wave  surfaces, 
whose  radii  are  c  q,  b p,  &c. 

353.  Echo. — An  echo  is  the  repetition  of  a 
sound  reflected  by  a  sufficiently  distant  object, 
so  that  the  reflected  is  not  confounded  with 
the  direct  sound. 

The  ear  cannot  distinguish  one  sound  from  ano- 
ther, unless  there  is  an  interval  of  one-ninth  of  a  ''<ii 
second  between  the  arrival  of  the  two  sounds.  Sounds  must,  therefore,  succeed 
each  other  at  an  interval  of  one-ninth  of  a  second,  in  order  to  be  heard  dis- 
tinctly. Now  the  velocity  of  sound  being  eleven  hundred  and  eighteen  feet  a 
second,  in  one-ninth  of  a  second  the  sound  would  travel  one  hundred  and  twenty- 
four  feet. 

To  have  a  perfect  echo,  therefore,  the  reflecting  surface  must  be  at 
least  sixty-two  feet  from  the  sounding  body.  (62X2=124.)  If  we 


ACOUSTICS.  261 

speak  a  sentence  at  the  distance  of  sixty-two  feet  from  the  reflecting 
surface,  we  shall  hear  the  echo  of  the  last  syllable  only.  If  twice, 
thrice,  or  four  times  the  distance,  two,  three,  or  four  of  the  syllables 
will  bdfechoed,  the  direct  sounds  and  reflected  sound  of  the  other  syl- 
lables of  the  sentence,  being  confounded  with  each  other.  If  the  re- 
flecting surface  is  at  a  less  distance  from  the  sounding  body  than  sixty- 
two  feet,  the  direct  sound  and  the  reflected  sound  become  confused,  so 
that  words  and  tones  cannot  be  heard  distinctly.  The  original  sound 
will  then  be  prolonged  and  strengthened ;  an  effect  which  we  express 
by  saying  there  is  resonance.  If  the  distance  is  comparatively  small, 
as  in  a  common-sized  room,  the  sounds  reflected  from  the  walls,  the 
ceiling  and  the  floor,  reach  the  ear  at  almost  exactly  the  same  time  as 
the  direct  sound,  and  the  apparent  power  of  the  voice  is  strengthened, 
besides  preserving  its  delicacy.  Where,  however,  the  apartment  is 
larger,  the  direct  sound  only  partially  coincides  with  the  reflected 
sound,  and  more  or  less  confusion  arises.  Voices  are  heard  in  a  re- 
markably sonorous  manner,  in  large  apartments  with  hard  walls,  while 
draperies,  hangings,  carpets,  &c.,  about  a  room,  smother  the  sound, 
because  these  are  bad  reflectors.  A  crowded  audience  has  a  similar 
effect,  and  increases  the  difficulty  of  speaking,  by  presenting  surfaces 
unfavorable  to  reflection. 

354.  Repeated  echoes. — Repeated  or  multiplied  echoes,  are  those 
which  repeat  the  same  sound  many  times.     This  happens  when  two 
obstacles  are  placed  opposite   to   one  another,  as  parallel  walls,  for 
example,  which  reflect  the  sound  successively. 

A  striking  and  beautiful  effect  of  echo  is  produced,  in  certain  locali- 
ties, by  the  Swiss  mountaineers,  who  contrive  to  sing  their  Ranz  des 
Vaclies  in  such  time,  that  the  reflected  notes  form  an  agreeable  accom 
paniment  to  the  air  itself. 

There  is  a  surprising  echo  between  two  barns  at  Belvidere,  Allegheny  county, 
N.  Y.  It  repeats  eleven  times,  a  word  of  either  one,  two,  or  three  syllables ; 
and  has  been  heard  to  repeat  it  thirteen  times.  By  placing  oneself  in  the  centre, 
between  the  two  barns,  a  double  echo  is  heard,  one  in  the  direction  of  each  barn, 
and  a  monosyllable  is  thus  repeated  twenty-two  times. 

At  Ademach,  in  Bohemia,  there  is  an  echo  which  repeats  seven  syllables 
three  times  j  at  Woodstock,  in  England,  there  is  one  which  repeats  a  sound 
seventeen  times  during  the  day,  and  twenty  times  during  the  night.  An^icho  in 
the  Villa  Smionetta,  near  Milan,  is  said  to  repeat  a  sharp  sound  thirty  times 
audibly. 

The  most  celebrated  echo  among  the  ancients,  was  that  of  the  Metelli  at  Rome, 
which,  according  to  tradition,  was  capable  of  repeating  the  first  line  of  the 
./Eneid,  containing  fifteen  syllables,  eight  times  distinctly. 

355.  Change  of  tone  by  echo. — Dr.  Chas.  G.  Page  describes  an  echo  in 
Fairfax  county,  Virginia,  which  gives  three  distinct  reflections,  the  second  echo 
much  the  most  distinct.     Twenty  notes  played  upon  a  flute,  are  returned  with 
perfect  clearness.     But  the  most  singular  property  of  this  echo  is,  that  soin^ 


262 


THE    THREE    STATES    OF    MATTER. 


notes  in  the  scale  are  not  returned  in  their  places,  but  are  supplied  with  other 
notes,  which  are  either  thirds,  fifths,  or  octaves. 

356.  Whispering  galleries. — Whispering  galleries  are  so  called, 
because  a  low  whisper,  uttered  at  one  point  in  them,  may  ta4  heard 
distinctly  at  another  and  distant  point,  while  it  is  inaudible  in  other 
positions. 

Such  galleries  are  always  domed,  or  of  ellipsoidal  shape ;  the  best  form  is 
that  of  the  ellipsoid  of  revolution.  In  such  a  chamber,  whispering  in  one  focus, 
is  very  audible  to  a  person  at  the  other  focus,  because  the  undulations  striking 
upon  the  walls,  are  reflected  to  the  point  where  the  hearer  is  placed,  while  in 
any  other  position,  a  feeble  sound,  or  none  at  all,  will  be  heard,  because  only  a 
part  of  the  reflected  sound  will  reach  the  ear  at  one  time.  (See  fig.  266.) 

One  of  the  halls  of  the  museum  of  antiquities,  of  the  Louvre,  at  Paris,  fur- 
nishes an  example  of  such  an  apartment.  In  the  dome  of  the  Rotunda  of  the 
Capitol  at  Washington,  is  a  fine  whispering  gallery.  The  principal  room  of  the 
Merchants'  Exchange,  in  New  York,  is  of  a  similar  character,  and  at  the  same 
time  affords  a  painful  example  of  confused  echoes. 

The  new  Halls  of  Congress,  at  Washington,  and  the  Lecture  room  at  the 
Smithsonian  Institution,  have  been  designed  with  special  reference  to  the  best 
form  for  public  speaking,  and  to  this  end  an  elaborate  series  of  experiments  and 
observations,  upon  the  best  proportions  and  forms  of  public  halls,  have  been 
undertaken  by  Profs.  Henry  and  Bache,  by  order  of  the  government,  the  results 
of  which  are  recorded  by  the  former,  in  the  Proceedings  of  the  American  Asso- 
ciation for  1856,  p.  119,  and  Smithsonian  Report  for  1856,  p.  221. 

357.  Refraction  of  sound. — Although  sound  is  reflected  by  any 
surface  of  different  density  from  that  in  which 

it  originates,  the  sound  also  enters  the  second 
medium  by  means  of  new  vibrations  origi- 
nating at  the  interposed  surface. 

We  have  seen  (345,  347)  that  the  velocity  of 
sound  is  not  the  same  in  different  media.  Let  a 
sound-wave  originating  at  S,  fig.  278,  meet  with 
another  medium  in  which  sound  moves  slower  than 
in  the  first,  and  let  a  0  be  the  surface  of  the  second 
medium.  Let  the  difference  of  velocity  be  such 
that  while  the  new  vibration,  originating  at  6, 
would  advance  to  p',  if  the  medium  were  like  the 
first,  it  can  move  only  to  e  in  the  new  medium : 
it  is  evident  that  if  a  n  be  the  wave  surface  with 
the  velocity  unchanged,  a  N  will  be  the  wave  sur- 
face -^Uh  the  retarded  velocity,  and  the  ray  S  6 
will  enter  the  second  medium  in  the  direction  b  R, 
more  nearly  perpendicular  to  the  surface  a  0,  than 
its  direction  in  the  first  medium. 

For  a  fuller  discussion  of  the  laws  of  refrac- 
tion, see  the  chapter  on  Optics. 

The  phenomena  of  refraction  of  sound  are  in 
accordance  with  theory.  The  researches  of  Pois- 
Bon  and  Grreen  have  placed  this  beyond  doubt. 


Sondhauss  has  demonstrate-! 


ACOUSTICS. 


263 


the  same  thing  by  the  following  experiment : — A  cell,  cCm  n,  fig.  279,  was  formod 
of  two  films  of  collodion,  united  at  the  edges  by  a  rim  of  iron.  The  two  films, 
m  and  n,  were  made  spherically  convex,  and  when  inflated,  the  instrument  took 


279 


the  form  of  a  lens,  like 
those  employed  in  opti- 
cal experiments.  This 
apparatus  was  filled  with 
carbonic  acid  gas,  by 
means  of  an  opening  at 
a.  He  placed  a  watch  at 
S,  in  the  axis  of  the  lens 
that  is  in  the  line  S  r 
which  passes  through 
the  centres  of  the  two 
surfaces  m  and  n.  When 
an  observer  placed  his 
ear  on  the  opposite  side  in  the  axis  of  the  lens,  the  ticking  of  the  watch  was 
distinctly  heard,  if  at  a  proper  distance  from  the  lens  :  this  distance  was 
less  in  proportion  as  the  watch  was  farther  removed.  If  the  lens  was  raised 
up,  the  sound  ceased  to  be  heard;  and  the  result  was  the  same  if  the  ear 
was  removed  from  the  axis  S  r.  Having  replaced  the  watch  by  an  organ-pipe, 
having  an  opening  like  a  flute,  instead  of  the  ear  he  employed  the  bent  tube 
fc,  having  gold-beater's  skin  extended  over  the  opening  c,  and  fine  sand  placed 
upon  it.  When  this  apparatus  occupied  the  positions  in  which  the  ear  heard 
the  sound  of  the  watch,  the  sand  was  agitated ;  but  on  removing  the  lens  the 
sand  remained  at  rest. 

To  comprehend  how  these  experiments  demonstrate  the  refraction  of  sound, 
we  must  refer  to  the  principles  of  optics,  in  which  multiplied  experiments  have 
rendered  the  explanation  very  complete,  and  easy  to  be  understood. 

358.  The  speaking-trumpet  is  an  instrument  employed  to  convey 
the  voice  to  a  great  distance.  This  instrument  consists  of  a  conical 
tube  0  P,  fig.  280,  terminated  by  a  bell-shaped  extremity,  P.  At  0 
is  a  mouth-piece  which  surrounds  the  lips  without  interfering  with 
their  movements.  The  trumpet,  it  is  said  by  history,  was  used  by 

280 


0 


Alexander  the  Great  for  commanding  his  army.  At  the  present  day 
it  is  employed  at  sea  to  cause  the  voice  of  the  commander  to  b.e  heard 
above  the  roar  of  the  winds  and  waves.  On  land  it  is  used  by  firemen. 
To  explain  the  augmentation  6f  sound  by  the  trumpet,  it  was  formerly  sup- 
posed that  the  sound  was  reflected  by  the  sides  of  the  trumpet,  so  that  the  vibra- 
tions issued  in  the  direction  of  the  axis  of  the  instrument,  and  that  this  effect 


264  THE    THREE    STATES    OF    MATTER. 

vras  also  aided  by  the  vibration  of  the  walls  of  the  instrument  itself.  It  was 
shown  by  Lambert  in  1763  that  the  vibration  of  the  instrument  tended  to  render 
articulate  sounds  confused. 

The  explanation  by  reflection  of  the  rays  of  sound  is  inadmissible.  In  reality 
(he  form  of  the  extremity  has  considerable  influence,  but  on  the  theory  of  reflec- 
tion it  should  be  without  effect.  On  the  contrary,  the  conical  form  should  be  all 
important,  but  Hassenfratz.has  shown  that  a  cylindrical  tube,  with  a  bell-shaped 
extremity,  strengthens  the  sound  as  much  as  a  conical  tube.  In  fact,  when  the 
interior  of  the  trumpet  is  lined  with  cloth,  so  that  the  reflection  must  be  very 
foeble  or  almost  null,  the  intensity  of  the  sound  transmitted  remains  unchanged. 
We  may  add  that  the  sound  transmitted  through  a  speaking-trumpet  is  increased, 
not  merely  in  the  direction  to  which  it  is  pointed,  but  in  every  direction,  whether 
:he  extremity  is  bell-shaped  or  otherwise.  The  efficacy  of  the  trumpet  is,  there- 
fore, not  due  to  the  reflection  of  sound  from  its  walls,  but  simply,  as  stated  by 
Hassenfratz,  to  the  greater  intensity  of  the  pulsations  produced  in  the  column 
of  confined  air  which  vibrates  in  unison  with  the  voice  at  the  mouth-piece.  A 
considerable  effect  is  produced  by  the  bell-shaped  extremity  of  the  trumpet,  but 
the  nature  of  this  influence  has  not  been  satisfactorily  explained. 

359.  Ear-trumpet. — The  hearing-trumpet,  fig.  281,  intended  to 
assist  persons  hard  of  hearing,  is  in  form  and  application  the  reverse 
of  the  speaking-trumpet,  although  in  principle  the  same.  It  consists 
of  a  conical  tube,  turned  in  any  281 

convenient  direction,  so  that  the 
opening,  o,  may  enter  the  ear. 
The  strengthening  of  the  sound 
by  this  instrument  was  formerly 
attributed  to  reflection  of  sonorous  waves  caused  to  converge  to  the 
oar,  and  it  was  sought  to  obtain  the  form  most  favorable  to  fulfill  this 
condition ;  thus  the  cone  was  replaced  by  a  paraboloid,  having  its 
focus  at  the  point  o.  But  these  different  forms  have  no  effect  upon  the 
result.  Moreover,  the  nature  of  the  walls,  and  the  condition  of  the 
interior  surface,  whether  rough  or  polished,  or  lined  with  cloth,  has  no 
effect  upon  the  intensity  of  the  sound.  The  only  essential  condition  is 
that  the  exterior  opening  should  be  greater  than  that  which  enters  the 
oar.  The  effect  of  the  ear-trumpet  is  explained  as  follows: — The  por- 
tions of  compressed  or  dilated  air,  which  arrive  at  the  exterior  opening, 
transmit  their  compression  or  dilatation  to  portions  of  air  smaller  and 
smaller,  and  consequently  transmit  it  with  increasing  intensity.  In 
this  manner  the  portion  of  air  at  o  receives  and  transmits  to  the  mem- 
brane of  the  tympanum  a  compression  or  dilatation  of  much  greater 
intensity  than  in  the  absence  of  the  instrument.  Holding  the  hand 
concave  behind  the  ear,  as  deaf  persons  are  seen  to  do,  concentrates 
sound  in  the  manner  of  an  ear-trumpet.  The  form  of  the  external  ear 
in  animals  favors  the  collection  of  sound. 

360.  The  siren. — This  ingenious  instrument  was  invented  by  M. 


ACOUSTICS. 


265 


Cagniard  de  Latour,  for  the  purpose  of  ascertaining  the  number  of 
vibrations  of  a  sonorous  body,  corresponding  to  any  proposed  musical 
sound. 

Fig.  282  shows  the  siren  mounted  on  a  wind  chest,  E,  designed  to  supply  a 
current  of  air.    Figs.  283,  284,  show  the  interior  details  of  the  apparatus.    The 

282  283  284 


siren  is  constructed  entirely  of  brass.  It  consists  of  a  tube,  0,  about  four  inches 
in  diameter,  terminating  in  a  smooth  circular  plate,  B,  fig.  284,  which  contains, 
at  regular  intervals  near  its  circumference,  small  holes,  which  are  pierced  through 
the  plate  in  an  oblique  direction.  Another  plate,  A,  turning  very  easily  upon 
its  axis,  is  placed  as  near  as  possible  to  B,  without  being  in  contact  with  it.  This 
plate  is  pierced  with  the  same  number  of  oblique  orifices  as  those  in  the  plate, 
B,  but  inclined  in  an  opposite  direction,  as  shown  in  fig.  283,  n,  A ;  m,  B. 

When  a  current  of  air  arrives  from  the  bellows,  it  passes  through  the  holes 
of  the  first  plate,  and  imparts  a  rotary  movement  to  the  second  plate,  in  the 
direction  n,  A,  fig.  283.  As  the  upper  plate  revolves,  the  current  of  air  is  alter- 
nately cut  off,  and  renewed  rapidly  by  the  constantly  changing  position  of  the 
holes.  In  consequence  of  this  interruption,  when  the  plate  A  moves  with  a 
uniform  velocity,  a  series  of  puifs  of  wind  will  escape  at  equal  intervals  of  time. 
These  puffs  will  produce  undulations  in  the  air  surrounding  the  instrument,  and 
when  the  wheel  revolves  with  sufficient  rapidity,  a  musical  sound  is  produced, 
which  increases  in  acuteness  as  the  velocity  of  the  wheel  becomes  greater. 

A  counter  (like  that  on  a  gas  meter)  is  connected  with  the  upper  plate,  by 
which  the  number  of  revolutions  is  indicated.  Pressure  upon  the  buttons,  C  D, 
fig.  284,  causes  the  toothed  wheels  to  be  set  in  communication  with  the  endless 
screw  upon  the  spindle,  T.  The  revolution  of  these  wheels  is  recorded  by  the 
motion  of  the  hands  upon  the  dials  in  fig.  282.  To  determine  the  number  of 
vibrations  corresponding  to  a  given  sound,  a  blast  of  wind  is  forced  from  the 
bellows  into  the  siren,  until  it  gives  a  corresponding  note.  The  hands  on  the 
dials  being  brought  to  their  respective  zeros  at  the  commencement  of  the 
experiment,  "their  position,  at  the  end  of  any  known  interval,  will  indicate  the 
25* 


2G6  THE    THREE    STATES    OF    MATTER. 

number  of  puffs  of  air  which  have  escaped  from  the  revolving  plate,  and  will, 
consequently,  determine  the  number  of  undulations  of  the  air  which  correspond 
to  the  sound  produced. 

The  siren,  with  equal  velocity,  gives  the  same  sound,  excepting  the  timbre,  in 
tlia  different  gases,  and  in  water,  as  it  does  in  air,  which  proves,  that  the  height 
of  any  sound  depends  on  the  number  of  vibrations,  and  not  on  the  nature  of 
iha  sonorous  body. 

361.  Savart's   toothed   wheel. — Savart    has    employed    another 
•  >paratus  to  count  the  "number  of  vibrations  corresponding  to  any 
•  oposed  pitch. 

[t  consists,  fig.  285,  of  a  toothed  wheel,  D,  to  be  revolved  as  regularly  as  pos- 
*J>le,  by  means  of  the  wheel  R,  and  endless  band  r.  The  toothed  wheel,  D, 

285 


i  volving  rapidly,  makes  the  tongue,  C,  vibrate,  producing  in  the  air  corre- 
sponding undulations,  the  effect  of  which  is  *a  musical  sound.  As  the  tongue  i.s 
.-•ruck  on  the  passage  of  each  tooth,  the  number  of  vibrations  in  a  second  will 
'•  '^respond  with  the  number  of  teeth  which  have  struck  the  tongue  in  the  sarno 
f:  ie.  This  is  learned  from  the  dial  plate,  0,  which  indicates  the  number  of 
i  (  volutions  of  the  axis,  and  multiplying  this  by  the  number  of  teeth,  we  have 
(.': ;  whole  number  of  vibrations  in  a  given  time.  Upon  revolving  the  wheel 
si  >wly,  we  may  hear  the  successive  shocks  of  the  teeth  against  the  tongue,  and 
:i  -  we  increase  the  velocity,  we  obtain  a  more  and  more  elevated  sound. 

362.  Music  halls. — Music  halls,  theatres,  &c.,  should  be  so  con- 

;ucted  as  to  convey  the  sounds  that  are  uttered,  throughout  the  space 

mpied  by  the  audience,  unimpaired  by  any  echo  or  conflicting  sound. 

;  i  theoretical  grounds,  the  best  form  for  the  walls  would  be  that  of  a 

,'irabola.     Ornaments,  pillars,  alcoves,  vaulted  ceilings,  all  needless 

.-  -How  and  piojecting  spaces,  break  up  and  destroy  the  echoes,  and 

ve  jonances.     The  height  of  a  room  for  public  speaking  should  be  not 

m  >re  than  from  thirty  to  thirty-five  feet;  for  at  this  point,  called  the 

liuiit  of  perceptibility,  the  reflection  and  the  voice  will  blend  together 

well,  and  thus  strengthen  the  voice  of  the  speaker  ;  if  it  is  higher  than 


ACOUSTICS.  267 

this,  the  direct  sound  and  the  echo  will  begin  to  be  heard  separately, 
and  produce  indistinctness. 

§  2.  Physical  Theory  of  Music. 

363.  Qualities  of  musical  sounds. — Musical  sound  is  the  result 
uf  equal  atmospheric  vibrations,  conveying  to  the  ear  tones  of  definite 
and  appreciable  pitch.    The  ear  distinguishes  three  particular  qualities 
in  sound.     1.  The  tone  or  pitch,  in  virtue  of  which  sounds  are  high  or 
low.     2.  The  intensity,  in  virtue  of  which  they  are  loud  or  soft ;  and 
3d,  quality  or  timbre,  in  virtue  of  which  sounds  of  the  same  intensity 
and  pitch  are  relatively  distinguishable. 

1.  Tone  or  pitch. — The  tone  or  pitch  of  a  musical  sound  is  high  or 
low.    It  depends  on  the  rapidity  of  the  vibratory  movement.    The  more 
rapid  the  vibrations  are,  the  more  acute  will  be  the  sound. 

2.  Intensity  or  loudness. — The  intensity,  or*  force  of  sound,  de- 
pends on  the  amplitude  of  the  oscillations ;  that  is,  upon  the  degree  of 
condensation  produced  at  the  middle  of  the  sonorous  wave. 

A  sound  may  maintain  the  same  pitch,  and  yet  possess  greater  or 
less  intensity,  according  as  the  amplitude  of  the  oscillations  varies. 

Thus,  if  we  vibrate  a  tense  cord,  the  intensity  or  loudness  of  the  tone  will 
vary,  as  the  distance  which  the  vibrating  parts  pass  on  each  side  of  the  line  of 

rest. 

3.  Qu^ity. —  Quality  is  that  peculiarity  in  sound  which  allows  us  to 
distinguish,  perfectly,  between  sounds  of  the  same  pitch,  and  the  same 
intensity. 

Thus,  the  sounds  produced  by  the  flute  and  clarionet  are  at  once  distinguish- 
able. The  quality  of  t*he  sound  of  instruments  appears  to  depend  not  only 
on  the  nature  of  the  sonorous  body,  and  the  surrounding  bodies  set  in  vibration 
by  it,  but  also  on  the  form  and  material  of  the  instrument ;  and  probably,  also, 
on  the  form  of  the  curve  of  vibration. 

364.  Unison. — Sounds  produced  by  the  same  number  of  vibrations 
per  second,  are  said  to  be  in  unison. 

Thus,  the  siren  (360)  and  Savart's  wheel  (361)  are  in  unison  when  we  cause 
them  to  make  the  same  number  of  vibrations  in  the  same  time. 

365.  Melody.— Harmony.— Vyhen  the  vibrations  of  a  progressive 
series  of  Dingle  musical  sounds  bear  to  each  other  such  simple  relations 
as  are  readily  perceived  by  the  ear,  an  agreeable  impression  is  pro- 
duced, called  melody.     When  two  or  more  sounds,  having  to  each  other 
such  simple  relations,  are  produced  simultaneously,  it  is  called  a  chord, 
and  a  succession  of  chords,  succeeding  each  other  in  melodious  order, 
constitutes  harmony. 

If  we  take  a  series  of  sounds,  the  ratios  of  whose  vibrations  are  as 


268 


THE    THREE    STATES    OF    MATTER. 


the  following  numbers— 1  :2:3:4:5:6:7:8:9:  10— we  have  the 
notes  which  will  produce  a  series  of  chords,  which,  commencing  with 
the  most  simple,  will  gradually  become  more  and  more  complicated, 
until  the  ear  can  no  longer  perceive  their  relations  ;  when  this  point  is 
reached,  they  will  cease  to  produce  chords  and  harmony. 

In  sounds  whose  vibrations  bear  to  each  other  the  relations  of 
1:2:4:8:  16,  every  vibration  expressed  by  the  lower  numbers  cor- 
responds with  similar  vibrations  in  the  higher  series.  The  interval 
between  such  sounds  is  very  great,  and  is  called  an  octave,  because 
other  sounds  having  simple  relations  may  be  so  placed  between  1  and  2, 
or  4  and  8,  as  to  form  with  the  two  extremes  a  series  of  eight  sounds 
having  agreeable  relations  to  each  other. 

Fig.  286  represents  the   relations  286 

of  such  tones   as  produce  the  most 
pleasing   effects    when    sounded   to- 
gether.    The    dots   represent  vibra-  Octave 
tions  ;  and  those  which  occur  siniul-      2  :  1 
taneously,    and    therefore    increase 
each  others'  powers,  are  connected 
by  vertical  lines.     On  the  left  of  the  Fifth 
figure  are  the  names  applied  to  these 
intervals,    as    explained   in    section 
371. 

366.  Musical  scale.  — Ga- 
mut.— The  tones  forming  a  me- 
lodious series  between  any  two 
adjacent  sounds  which  are  as 
one  to  two,  are  called  the  musical 
scale  or  gamut. 

It  is  generally  supposed  that  the 
musical  scale  was  invented  by  Guido 
of  Arezzio,  or  according   to    others  Minor    j 
that  it  was    an    improvement   upon      Third  j 
the   Grecian    scale,    and   called    the      6  :  5 
gamut  from  the  Greek  letter  gamma, 
as  an  acknowledgment  of  the  assistance  he  derived  from  that  nation. 

The  sounds  which  compose  the  ^nusical  scale  or  gamut,  are  the 
alphabet  of  music.  They  are  designated,  in  English,  by  the  letters  C, 
D,  E,  F,  G,  A,  B.  In  French  and  Italian,  by  the  words  ut,  or  do,  re, 
mi,  fa,  sol,  la,  si. 

"We  may  also  represent  the  notes  of  the  gamut  in  numbers.  In  order 
to  find  the  relation  which  exists  between  the  fundamental  note,  C,  or 
do,  and  the  other  notes,  the  sonometer,  or  monochord,  fig.  287,  is  em- 
ployed , 


•   •••••  <>••!•• 

T  *  t  *  t  *  t  ' 


<>    ••••   •    •••••• 

«>    ••+••!•• 


ACOUSTICS.  269 

367.  The  sonometer  or  monochord.— This  instrument  is  used  to 
study  the  transverse  vibrations  of  cords ;  and  by  it  we  ascertain  the 
relation  between  the  different  notes  of  the  musical  scale,  and,  with  the 
aid  of  the  siren  (360),  the  number  of  vibrations  by  which  they  are 
respectively  produced. 

Above  a  case  of  thin  wood,  a  cord,  or  metallic  wire,  A  D,  is  stretched  over  tho 
pulley  «,  by  the  weights  P,  on  the  pan  m,  fig.  287.  The  movable  bridge,  B,  can 

287 


be  placed  at  any  desired  point;  and  for  convenience  of  adjustment,  the  scale  is 
marked  off  beneath  the  wire,  commencing  with  C.  The  string,  A  D,  when 
vibrating  its  whole  length,  produces  the  note  C ;  in  order  to  produce  the  note  D, 
the  movable  bridge,  B,  must  be  advanced  toward  the  fixed  bridge  D,  until  the 
length  of  the  cord  is  but  eight-ninths  of  that  which  produces  the  note  C.  Pro- 
ceeding in  the  same  manner  for  the  other  notes,  it  will  be  found,  that  the  length 
of  the  cord  corresponding  to  each  note  is  represented  by  the  following  fractions  : 

Notes, CDEFGABC' 

Relative  length  of  cord,  .  •  1  f  i  \  f  f  f  J8S  i 
Continuing  to  move  the  bridge  on  the  sonometer,  it  will  be  found,  that  the 
eighth  sound,  the  octave,  is  produced  by  a  length  of  cord  half  that  of  the  funda- 
mental sound.  Upon  this  note,  an  octave  higher  than  the  fundamental  note,  we 
may  construct  a  scale,  each  note  of  which  is  produced  by  the  vibration  of  a  cord 
half  as  long  as  the  same  note  in  the  preceding  gamut.  In  the  same  manner  we 
may  have  also  a  third  and  a  fourth  scale. 

368.  Relative  number  of  vibrations  corresponding  to  each 
note. — In  order  to  ascertain  the  relative  number  of  vibrations  corres- 
ponding to  each  note  in  the  same  time,  it  is  sufficient  to  invert  the 
fractions  of  the  preceding  table.  For  by  the  principles  already  esta- 
blished (309),  the  number  of  vibrations  is  in  inverse  ratio  of  the  length 
of  the  string.  Representing,  therefore,  the  number  of  vibrations  cor- 
responding to  the  fundamental  note  C,  by  1,  proceeding  as  above,  wo 
vform  the  following  table : 

Notes,        /.        .         .        .CDEFGABC' 
Relative  number  of  vibrations,        Iff      $      I      f      */     ^ 


270  THE    THREE    STATES    OF    MATTER. 

Which  indicates,  that  in  producing  the  note  D,  nine  vibrations  are  made 
in  the  same  time  that  eight  are  made  by  the  fundamental  note  C.  So, 
when  the  note  E  is  sounded,  five  vibrations  are  made  for  four  of  C  ;  for 
B,  fifteen  to  eight  of  C,  &c. 

369.  Absolute  number  of  vibrations  corresponding  to  each 
note. — By  setting  the  siren,  or  Savart's  wheel,  in  unison  with  a  given 
sound,  we  obtain  the  absolute  number  of  vibrations  corresponding  to 
it.  If  we  set  the  siren  in  unison  with  the  fundamental  C,  in  order  to 
obtain  the  number  of  vibrations  corresponding  to  the  other  notes,  as  D, 
we  have  but  to  multiply  it  by  the  fraction  §,  &c.  But  the  fundamental 
C  varies  with  the  nature,  length,  and  tension  of  the  cord  of  the  sono- 
meter, and  therefore  the  number  of  vibrations  may  be  represented  by 
an  infinite  variety  of  numbers,  corresponding  to  the  different  scales. 
The  notes  of  the  scale  whose  gamut  corresponds  to  the  gravest  sound  of 
the  bass,  are  indicated  by  1.  To  notes  of  gamuts  more  elevated,  are  affixed 
the  indices  2,  3,  &c. ;  to  graver  -notes  are  affixed  the  indices  —  1,  —  2, 
&c.  The  number  of  simple  vibrations  corresponding  to  the  note  C,  is 
128,  and  in  order  to  obtain  the  number  of  vibrations  corresponding  to 
the  other  notes,  we  have  but  to  multiply  this  number  by  the  fractions 
indicated  in  (368),  which  gives  the  following  table: 

Notes G       D      E       F       G       A        B 

Absolute  number  of  simple 

vibrations,       .        .        .128    144    160    170|    192    213£    240 

The  absolute  number  of  vibrations  for  the  superior  gamut,  is  obtained 
by  multiplying  the  numbers  in  the  table  successively,  by  2,  by  3,  by  4, 
&c. ;  for  the  lower  gamut,  we  divide  the  same  numbers  by  2,  by  4,  &c. 
Thus,  the  number  of  vibrations  of  A3  is  214  X  4  =  856  simple  vibra- 
tions, or  428  complete  vibrations.* 

It  must,  however,  be  stated,  that  there  is  a  slight  difference  in  the  actual 
number  of  vibrations  producing  a  particular  note  as  performed  in  different  cities. 
Thus,  A3  of  the  pitch  adopted  at  different  orchestras,  which  by  the  above  table 
should  be  produced  by  426j|  vibrations,  varies  as  follows  : 

Orchestra  of  Berlin  Opera,          ......     437-32 

Opera  Comique,  Paris,       .          .       ' 427-61 

Academic  de  la  Musique,  Paris,  .....     431-34 

Italian  Opera,  in  1855, 449 

In  piano-fortes,  which,  for  private  purposes,  are  generally  tuned  below  concert 
pitch,  A3  is  produced  by  about  420  vibrations  in  a  second. 

There  has  been  a  curious  progressive  elevation  of  the  diapason  (pitch)  of 
orchestras,  since  the  time  of  Louis  XIV.,  when  the  la  in  the  orchestra  was 
(according  to  Sauveur)  810  simple  vibrations  (=405  complete  vibrations)  per 
second ;  the  number  at  the  grand  opera  is  now  898,  or  nearly  a  tone  higher. 
This  rise  has  taken  place  mainly  in  the  present  century^being  a  semitone  since 
1823.  The  causes  of  this  change  (which  is  still  in  progress)  are  doubtless  owing 

*  See  Appendix,  p.  668. 


ACOUSTICS.  271 

to  the  process  adopted  for  preserving  and  transmitting  the  true  pitch  of  the 
fundamental  note.  The  final  tuning  of  the  diapason  is  done  by  the  file,  and 
filing  a  diapason  heats  it;  at  the  moment  it  is  in  tune  with  the  standard  it  is 
thus  heated,  and  when  it  afterwards  cools  the  tone  rises.  When  this  second 
diapason  is  used  for  tuning,  there  is  another  similar  rise,  and  so  it  continues. 
This  gradual  elevation  of  pitch  becomes  quite  sensible  after  the  lapse  of  one  or 
two  generations.  (Am.  Jour.  Sci.  [2]  xx.  262.) 

370.  Length  of  sonorous  waves. — It  is  easy  to  ascertain  the  length 
of  a  sonorous  vibration,  if  we  know  the  number  of  vibrations  made  in  a 
second.     For,  as  sound  travels  at  the  rate  of  1118  feet  per  second,  if 
but  one  vibration  is  made  in  that  time,  the  length  of  the  wave  must  be 
1118  feet;  if  two  vibrations,  the  length  of  each  must  be  half  of  1118, 
=  559  feet,  &c. 

C  corresponds,  as  we  have  seen,  to  128  vibrations  per  second;  the  length  of 
its  waves  is,  therefore,  (1118  -~- 128)  =  8-73  feet. 

The  following  table  indicates  the  length  of  the  waves  corresponding  to  the 
C  of  successive  scales  : 

Length  of  waves  in  feet.        Number  of  vibrations  in  a  second. 

C_3 70-           16 

C_2 35-           32 

C_!  .......  17-5        64 

G!  8-73 128 

C2  4-375 256 

C3  2-187 512 

C4  1-093 1024 

371.  Interval. — Interval  is  the  numerical  relation  existing  between 
the  number  of  vibrations  made  in  the  same  time  by  two  sounds,  or  it  is 
that  which  indicates  how  much  one  sound  is  higher  than  another. 

Musical  intervals  are  named  from  the  position  of  the  higher  note 
counting  upwards  from  the  lower. 
C,  D,   E,    F,    G,     A,    B,   C',   D',     E',     F',     G',     A',     B',    C". 

i,  f,   f,    I,    I,     I    ¥,  2,    y,     ¥,     I,      f,     V,    ¥>     4. 

1st,  2d,  3d,  4th,  5th,  6th,  7th,  8th,  9th,  10th,  llth,  12th,  13th,  14th,  15th. 

i  v,  is,  i,  v,  §,  it,  t,   y,  it,    t,    v,    t>    if- 

In  the  above  table  are  given,  1st,  the  letters  by  which  successive  notes  are 
designated ;  2d,  the  relative  numbers  of  their  vibrations  as  compared  with  the 
lowest  note ;  3d,  the  names  of  the  notes  as  compared  with  the  first;  and  lastly, 
the  intervals  obtained  by  dividing  each  note  by  that  which  immediately  precedes 
it.  It  will  be  seen  that  there  are  but  three  different  intervals  between  succes- 
sive notes  of  the  scale ;  viz.  |,  which  (being  the  largest  interval  found  in  the 
scale)  is  called  a  major  tone,  y>  called  a  minor  tone,  and  jf  which  is  called  a 
semitone,  though  it  is  greater  than  one-half  of  the  interval  of  either  of  the  other 
tones.  This  last  is  also  called  a  diatonic  semitone,  to  distinguish  it  from  other 
divisions  made  for  particular  purposes.  The  difference  between  a  major  tone 
and  a  minor  tone  is  ^y  of  a  major  tone,  and  is  called  a  comma. 


272  THE    THREE    STATES    OF    MATTER. 

Comparing  the  notes  of  the  natural  scale  two  and  two,  we  obtain  a  variety 
«'  intervals  named  as  in  the  following  : — 

TABLE  OF  MUSICAL  INTERVALS. 

<ZD  =  FG  =  AB  =  | ;  major  tone. 

DB  =  G  A  =  V  =  f^  of  | ;  minor  tone. 

E  F  =  B  C  =  jf  =  |  f  of  f  4  of  f ;  diatonic  semi 

tone. 

CE  =  FA  =  GB  =  f;  major  third. 

EG=AC'=:BD'  =  f  «=  1 1  of  £  5  minor  tllird- 

DF  =  f  of  n  =  f?offf  off;  ff  of  a 

minor  third. 

CF  =  DG  =  EA  =  GO'  =  j;  fourth. 

AD'  =  |  =  |J  of  f  j  sharp  fourth. 

F  B  =  f  f  =  |f  of  f  £  of  |  j  iff  of  perfect 

fourth. 

C  G  =EB  =  FC'  =  GD'  =  AE'  =  f;  fifth. 

D  A  =  f  f  =  | »  of  f  ;  f «  of  a  perfect  fifth. 

B  F'  =  &jr  •  an  inharmonious  interval. 

CA=DB  =  FD'  =  GE'=  |;  sixth. 

AF'  =  BG'==  |  =  ||  of  | ;  minor  sixth. 

FD'  =  ^  ;  an  inharmonious  interval. 

C  B  =  F  E'  =  Y  )  seventh,  an  inharmonious  inter- 

val. 

D  C'  =  GF'  =  B  A'  =  y  .  flattened  seventh,  § |  of  | ;  de- 

cidedly more  harmonious  than  the 
seventh.* 

E  D'  =  A  G'  =  I  =  If  of  V  '  minor  seventh. 

C  C'  =  | ;  octave. 

372.  Compound  chords. — Perfect  concord. — It  is  evidently  easy 
to  take  three  or  four  notes  whose  vibrations  have  simple  relations  to 
each  other,  and  which  taken  two  and  two  produce  a  sensation  of  har- 
mony.    Such  combinations  are  called  compound  chords. 

If  we  take  the  three  notes  C,  E,  G,  whose  vibrations  are  to  each 
other  as  the  numbers  4,  5,  6,  compared  two  and  two  they  give  the 
relations  f,  f,  f,  which  constitute  by  their  union  three  harmonious 
intervals  called  the  perfect  major  accord.  If  we  take  the  three  notes 
E,  G,  B,  which  compared  two  and  two  give  the  relations  f ,  f ,  f ,  we  find 
it  differs  from  the  preceding  only  in  the  order  of  the  intervals.  This 
series  is  called  the  perfect  minor  accord. 

373.  A  new  musical  scale. — By  examining  the  preceding,  pages  it 
will  be  seen  that  the  relative  number  of  vibrations,  and  the  intervals 
between  different  notes  in  the  common  musical  scale,  are  made  up 
entirely  of  combinations  formed  from  the  three  prime  numbers  2,  3,  5. 
and  it  has  been  generally  stated  that  relations  founded  upon  the  prime 

*  The  ratio  |  is  claimed  to  belong  to  natural  mulic;  see  section  (373). 


ACOUSTICS. 


273 


7  were  too  complicated  to  be  appreciated  by  the  ear,  or  to  be  executed 
either  by  the  voice  or  by  instruments.  But  the  use  of  the  prime  seventh 
in  music  has  been  recently  pointed  out  by  H.  W.  Poole,  Esq.,  of  Wor 
cester,  Mass.* 

Multiplying  the  ratios  of  the  ordinary  scale  by  48,  we  have  the : — 

TRIPLE  DIATONIC  SCALE. 

(  With  Common  Chord  on  C,  £,  and  F.) 
C,         D,         E,         F,         G,         A,         B,         C'. 
48,       54,       60,       64,       72,        80,       90,         96. 

I'         V*       lf>         i        tf*         f*        If- 
By  introducing  the  prime  7,  Mr.  Poole  obtains  a  series  which  he  calls  the : — 

DOUBLE  DIATONIC  SCALE. 

(  With  Common  Chord  on  C,  and  Chord  of  7  and  9  on  G.) 
C,        D,         E,         (F),         G,         (A),        B,         C'. 
48,        54,        60,         63,          72,          81,         90,         96. 

f     v,   n>     f>     t>      v>    if. 

In  defence  of  this  introduction  of  the  prime  7  in  musical  composition,  it  is 
claimed  that  it  is  required  to  fill  up  the  series  1  to  10  (365),  as  all  the  other 
numbers  up  to  ten  are  universally  admitted.  It  is  further  claimed  that  it  is  of 
frequent  use  by  such  masters  as  Haydn,  in  the  "  Dead  March  of  Saul,"  Mozart, 
in  the  "0  dolce  Concento,"  and  that  it  also  occurs  in  the  compositions  of 
Rossini. 

It  may  also  be  mentioned  that  the  Chinese,  in  their  musical  scale,  employ  the 
flat  sevenths  instead  of  the  notes  in  use  with  us,  which  gives  G  to  B  as  72  to  84 
or  6  to  7,  and  B  to  C'  as  84  to  96  or  7  to  8,  the  very  harmony  contended  for. 

The  following  example  of  harmonies,  rising  through  the  entire  series  from 
1  to  10,  is  taken  from  the  essay  of  Mr.  Poole. 


Resolution 


Here  we  have  a  series  of  harmonies  beginning  with  the  common  chord  C,  E, 
G,  4,  5,  6,  and  rising  in  the  last  example  to  the  full  chord  of  the  10th,  all  of 
which  can  be  appreciated,  and  are  capable  of  giving  a  pleasing  effect  on  an 
instrument  of  perfect  intonation.  The  full  chord  of  the  10th  contains  the  fol- 
lowing series  of  vibrations  and  intervals  : — 


*  Am.  Jour.  Sci.  [2],  IX.,  p.  68;  also  Math.  Monthly,  II,  p.  16. 
26 


274  THE    THREE    STATES    OF    MATTER. 

E.   10     . 10 

r  MINOR  TONE. 

D.  9   ".        .        .        , 9  ; 

[  MAJOR  TONE. 

08  8 

[EXTENDED 

BK    r  7  J  SECOND  (?) 

{  DIMINISHED 

n       «  *  •>  THIRD  (?) 

G.     6     .        .        .        •        , 6  j 

[  MINOR  THIRD. 

E.  5 5J 

|  MAJOR  THIRD* 
C.     4 4  j 

[  FOURTH. 
G.     3 3, 

[  FIFTH. 
C.     2 .        .2 

I  OCTAVE. 
C.     1 1  J 

374.  Transposition. — Any  tone  of  the  common  scale,  or  any  pitch 
whatever,  may  be  taken  as  the  basis  of  another  similar  scale,  provided 
the  same  relative  intervals  are  preserved  between  the  successive  notes. 
Such  change  is  called  transposition  of  the  scale.     If  such  a  change  of 
pitch  is  made  on  an  instrument  tuned  to  play  the  natural  scale,  addi- 
tional notes  must  be  provided  in  one  or  more  of  the  intervals  already 
described.     Such  additional  notes  are  called  sharps  (jfr)  or  fiats  ([>), 
according  as  the  tone  corresponding  to  any  given  note  is  raised  or 
lowered.     When  new  notes  are  interpolated  in  every  major  and  minor 
tone  of  the  natural  scale,  there  are  obtained  twelve  intervals  in  the 
octave,  and  the  series  thus  formed  is  called  the  chromatic  scale. 

When  the  diatonic  semitone,  jf ,  is  taken  from  the  major  tone,  f,  the 
remaining  interval  is  called  a  chromatic  semitone.  When  the  diatonic 
semitone  is  taken  from  the  minor  tone,  y*,  the  interval  which  remains 
is  called  the  grave  chromatic  semitone. 

375.  Temperament. — In  transposing  the  scale,  so  as  to  commence 
on  any  note  of  the  natural  gamut,  it  is  supposed,  in  theory,  that  every 
note  may  be  raised  or  lowered  through  an  interval  of  a  diatonic  semi- 
tone, jf.     This  would  involve  the  addition  of  an  inconvenient  number 
of  new  notes ;  therefore,  in  the  construction  of  musical  instruments,  it 
is  assumed  that  such  notes  as  Q$  and  D\)  are  identical,  though  they 
are  not  strictly  the  same,  and  are  not  played  alike  on  a  violin  or  harp, 
in  the  hands  of  a  skillful  performer. 

temperament  is  a  device  by  which  the  multiplication  of  notes  beyond 
convenient  limits  is  avoided.  For  practical  purposes,  organs,  piano- 
fortes, and  other  instruments,  are  so  tuned  as  to  divide  the  octave  into 
12  equal  intervals,  called  chromatic  semitones,  of  equal  temperament. 


ACOUSTICS. 


275 


1/2  =  1.060. 


V  2*  =  1-260. 
=  1-498. 


In  this  system,  all  the  musical  intervals  employed,  except  the  octaves, 
differ  more  or  less  from  their  true  value,  as  given  by  theory,  and  as 
demanded  by  the  cultivated  ear. 

True  value.      Value  in  equal  temperament. 

Minor  semitone,  f  f  =  1-042, 

Major  semitone,  {f  =  1'067, 

Minor  third,  f  =  1-200,       }/&'=  1'189. 

Major  third,        *f  =  1-250, 

Fifth,  f  =  1-500, 

It4s  here  seen  that  the  minor  semitones  and  major  thirds  are  all  too 
sharp,  while  the  major  semitone,  minor  third,  and  the  fifths  are  all  too 
flat. 

Messrs.  H.  W.  Poole  and  J.  Alley  have  invented  an  organ,  on  which 
every  musical  interval  can  be  correctly  given 'without  tempering;  and 
the  perfect  musical  scale  can  be  performed  in  as  many  different  keys  as 
may  be  desired.  (Am.  Jour.  Sci.  [2],  Vol.  IX.,  p.  68.) 

The  subject  of  temperament  in  all  its  relations  is  too  extensive  to  be 
treated  in  this  work,  and  we  must  refer  the  reader  to  musical  treatises 
for  further  information.  . 

376.  Beating. — When  two  sounds  are  produced  at  the  same  time, 
which  are  not  in  unison,  alternations  of  strength  and  feebleness  are 
heard,  which  succeed  each  other  at  regular  intervals. 

This  phenomenon,  called  beating,  discovered  by  Savart,  is  easily  explained. 
Supposing  that  the  number  of  vibrations  of  288 

the  two  sounds  was  30  and  31 ;  after  30  vibra- 
tions of  the  first,  and  31  of  the  second,  there 
would  be  coincidence,  and  in  consequence,  beat- 
ing, while  at  any  other  moment,  the  sonorous 
waves  not  being  superimposed,  the  effect  would  be 
less.  If  the  beatings  are  near  to  each  other,  there 
is  produced  a  continuous  sound,  which  is  graver 
than  the  two  sounds  which  compose  it,  since  it 
comes  from  a  single  vibration,  while  the  other 
sounds  are  made  of  30  and  31  vibrations. 

The  nearer  the  vibrations  approach  to  exact 
unison,  the  longer  is  the  interval  between  the 
beats.  When  the  unison  is  complete,  then  no  beats 
are  heard  ;  when  it  is  very  defective,  they  produce 
the  effect  of  an  unpleasant  rattle. 

377.  Diapason,  tuning-fork. — The  dia- 
pason is  a  familiar  instrument,  with  which 
we  may  produce,  at  will,  an  invariable  note  ; 
its  use  regulates  the  tone  of  musical  instru- 
ments.    It  is  formed  from  a  bar  of  steel, 

curved,  as  seen  in  fig.  288.     It  is  often  sounded  by  drawing  through  it 


276  THE    THREE    STATES    OF    MATTER. 

a  smooth  rod  of  steel  large  enough  to  spring  open  the  limbs,  and  its 
vibrations  are  greatly  strengthened  to  the  ear  by  mounting  it,  as  in  the 
figure,  upon  a  box  of  thin  wood,  open  at  one  end.  A  diapason,  giving 
03,  or  256  vibrations  in  a  second,  produces  a  sound  comparable  with 
that  from  an  organ  tube. 

The  diapason  is  ordinarily  formed  to  produce  A3,  corresponding  to  428  vibra- 
tions in  a  second. 

The  whole  diatonic  scale  is  thus  conveniently  constructed,  by  a  series  of  dia- 
pasons, arranged  as  in  fig,  289,  upon  a  sounding-box,  A  A. 

378.  Sensibility  of  the  ear. — According  to  Savart,  the  most  grave 
note  the  ear  is  capable  of  appreciating,  is  produced  by  from  sev*n  to 
eight  complete  vibrations  per  second.  When  a  less  number  is  made, 
the  vibrations  are  heard  as  distinct  and  successive  sounds. 

The  most  acute  musical  sound  recognised,  was  produced  by  24,000  complete 
vibrations  per  second.     Savart  maintains,  however,  that  this  is  not  the  extreme 
limit  of  the  sensibility  of  the  ear,  289 
which    is    capable     of    wonderful 
training.     The  same  physicist  has 
also  demonstrated,  that  two   com- 
plete  vibrations   are    sufficient   to 
enable  the  ear  to  determine  the  ra- 
pidity of  these  vibrations  ;  that  is, 

the  height  of  the  sound  produced.   A|    "*       **      "»'•    •**     "*     Ja"    ":   "V 
If  his   wheel   made  24,000  vibra-         i  i  i 


tions  in  a  second,  the  two  require  but  yy.^jy^th  of  a  second.  The  ear  may, 
therefore,  compare  sounds  which  act  only  during  this  wonderfully  brief  interval. 
The  limit  of  perceptible  sound  depends  on  the  amplitude  of  the  vibrations.  By 
enlarging  the  dimensions  of  Savart's  toothed  wheel,  and  increasing  the  distances 
between  the  teeth,  more  rapid  vibrations  can  be  heard.  Despretz  was  enabled 
to  recognise  sounds  made  by  36,500  complete  vibrations  per  second. 

Many  insects  produce  sounds  so  acute  as  to  baffle  the  human  ear  to  distinguish 
them  ;  and  naturalists  assert,  that  there  are  many  sounds  in  nature  too  acute  for 
human  ears,  which  are  yet  perfectly  appreciated  by  the  animals  to  which  they 
are  notes  of  warning,  or  calls  of  attraction. 

The  natural  la  is  said  to  be  heard  by  rapidly  moving  the  head  j  owing  to  the 
motion  of  the  small  bones  of  the  ear.  See  g  393. 

g  3.  Vibration  of  Air  contained  in  Tubes. 

379.  Sonorous  tubes.— Mode  of  vibrating. — In  wind  instru- 
ments, with  walls  of  suitable  thickness,  the  column  of  air  contained  in 
the  tubes  alone,  enters  into  vibration. 

The  material  of  the  tube  has  no  influence  upon  the  pitch,  but  affects  the 
quality  (363)  in  a  striking  and  important  manner.  The  pitch  of  the  sound 
produced,  depends  partly  on  the  size  and  situation  of  the  embouchure ;  still  more 
on  the  manner  of  imparting  the  first  movement  to  the  air,  and  partly  also  on 
varying  the  length  of  the  tube  containing  the  column  of  air.  The  difference  in 
the  quality  of  the  tones  produced  by  pipes  of  different  materials  is  most  probably 
owing  to  a  very  feeble  vibration  of  the  materials  themselves. 


ACOUSTICS. 


277 


290 


291 


Sonorous  vibrations  are  produced  in  tubes  in  a  number  of  ways. 
1.  By  blowing  obliquely  into  the  open  end  of  a  tube,  as  in  the  Pan- 
dean pipe.  2.  By  directing  a  current  of  air 
into  an  embouchure,  or  near  the  closed  end  of 
the  tube.  These  tubes  are  called  mouth-pipes. 
3.  By  thin  vibrating  laminae  of  metal,  or  of 
wood,  called  reeds,  or  by  the  vibration  of  the 
lips,  acting  as  reeds.  4.  By  a  small  flame  of 
hydrogen  gas. 

380.  Mouth-pipes.—Fig.    290    represents 
the   embouchure  of  an  organ  tube,  fig.  291, 
that  of  a  whistle  or  flageolet.     In  these  two 
figures  the  air  is  introduced  by  the  opening,  i 
(called  the  lumiere) ;  6  o  is  the  mouth,  of  which 
the  upper  lip  is  beveled.    The  foot,  P,  fig.  291, 
connects  the  pipe  with  a  wind-chest.     When  a 
rapid  current  of  air  passes  through  the  inlet, 
it  encounters  the  edge  of  the  upper  lip,  which 

partially  obstructs  it,  causing  a  shock,  so  that  the  air  passes  through 
6  o  in  an  intermittent  manner.  These  pulsations  are  transmitted  to 
the  air  in  the  tube,  making  it  vibrate,  and  producing  a  sound. 

In  order  to  have  a  pure  sound,  there  must  exist  a  certain  relation  between  the 
dimensions  of  the  lips,  the  opening  of  the  mouth,  and  the  size  of  the  lumiere. 
Again,  the  length  of  the  tube  must  bear  a  certain  ratio  to  its  diameter.  In  those 
wind  instruments,  like  the  flute,  flageolet,  &c.,  in  which  various  notes  are  pro- 
duced by  the  opening  and  closing  of  holes  in  their  sides  by  means  of  fingers  or 
keys,  there  is  a  virtual  variation  in  the  length  of  the  tube,  which  determines  the 
pitch  of  the  various  notes  produced.  The  number  of  vibrations  depends  upon 
the  dimensions  of  the  tube  and  the  velocity  of  the  current  of  air. 

381.  Reed-pipes. — A  reed  is  an  elastic  plate  of  metal,  or  of  wood, 
attached  to  an  opening  in  such  a  manner,  that  a  current  of  air,  passing 
into  the  opening,  causes  the  plate  to  vibrate.     This  vibration  is  propa- 
gated to  the  surrounding  air.     Reeds  are  found  in  hautboys,  bassoons, 
clarionets,  trumpets,  and  in  the  Jews-harp,  which  is  the  most  simple 
instrument  of  this  species. 

Fig.  292  represents  a  reed  pipe,  mounted  on  the  box  of  a  bellows,  Q.  A  glass, 
E,  in  one  of  the  walls  of  the  tube,  allows  the  vibrations  of  the  reed  to  be  seen 
The  case,  H,  serves  to  strengthen  the  sound.  Fig.  293  represents  the  reed  sepa- 
rated from  the  tube.  It  is  composed  of  a  rectangular  case  of  wood,  closed  at  its 
lower  end,  and  open  at  the  top,  at  a  point  o.  A  plate  of  copper,  c  c,  contains  a 
longitudinal  opening,  designed  to  allow  the  passage  of  the  air  from  the  tube,  M  N, 
through  the  orifice  o.  •  An  elastic  plate,  »',  almost  closing  the  aperture,  is  confined 
at  its  upper  end.  The  sliding  rod,  >•,  curved  at  its  lower  end,  permits  the  regu- 
lation of  the  pitch,  by  alterations  in  the  length  of  the  vibrating  part  of  the  plate. 

When  a  current  of  air  passes  in  through  the  foot,  P,  the  reed  vibrates,  alter- 
26* 


278 


THE    THREE    STATES    OF    MATTER. 


nately  opening  and  closing  the  aperature.     The  vibrations  being 
sound  produced  varies  in  pitch  with  the  velocity  of  the  current. 


transmitted  to  the  exterior  air  through 
the  opening  o. 

In  this  kind  of  reed,  the  vibrating 
plate  passes  through  the  aperture,  with- 
out its  walls,  and  the  tone  is  remarkably 
pure  and  free  from  any  harshness.  The 
quality  of  the  tone  of  a  reed-pipe  depends 
much  on  its  figure,  also  upon  the  con- 
struction of  the  reed,  and  the  material 


292 


rery  rapid,  the 
This  sound  is 
293 


294 


of  which  it  is  composed. 
In  the  French  horn, 
the  trumpet,  and  other 
similar  instruments,  the 
sound  is  produced  by 
the  vibration  of  the  lips 
of  the  performer,  acting 
like  reeds. 

382.  Gas    jet.— 

A  jet  of  hydrogen, 
burned  within  a  tall 
tube  of  glass,  or 
other  material,  occa- 
sions, if  accurately 
adjusted,  a  musical 
note. 

A  simple  form  of  this  arrangement  is  seen  in  fig.  294,  where  hydrogen,  gene- 
rated by  the  action  of  dilute  sulphuric  acid  on  zinc  in  the  bottle,  is  burned  from 
the  narrow  glass  tube,  within  one  of  larger  dimensions.  It  is  better  to  take  the 
gas  from  a  reservoir,  or  gas  jet,  with  a  key  interposed,  to  regulate  the  volume 
of  the  flame.  The  cause  of  the  vibrations  and  sound  in  this  case  is  to  be  found 
in  the  successive  explosions  of  small  portions  of  free  g*as,  mingled  with  common 
air.  The  heat  occasions  a  powerful  ascending  current  of  air,  momentarily 
extinguishing  the  flame,  and  at  the  same  instant  permitting  the  mixture  of  the 
atmospheric  oxygen  with  a  portion  of  inflammable  gas.  The  expiring  flame 
kindles  this  explosive  mixture,  and  relights  the  jet.  As  these  successive  pheno- 
mena occur  with  great  rapidity,  and  at  regular  intervals,  the  necessary  conse- 
quence is  a  musical  note. 

•For  a  full  discussion  of  the  phenomena  of  singing  flames,  see  a  memoir  by 
Prof.  W.  B.  Rogers,  Am.  Jour.  Sci.  [2]  xxvi.  1. 

383.  Musical  instruments. — The  principles  already  explained  in 
this  chapter,  will  illustrate  the  peculiar  power  of  the  several  sorts  of 
musical  instruments  in  common  use.   It  is  inconsistent  with  our  limited 
space  to  describe,  in  detail,  these  several  instruments.     Such  details 
belong  to  a  special  treatise  on  music.    Musical  instruments  are  grouped 
chiefly,  under  the  heads  of  wind,  and  stringed  instruments,  and  those 
like  the  drum,  in  which  a  membrane  is  the  source  of  vibration. 


ACOUSTICS.  279 

Wind  instruments  are  sounded,  either  with  an  emboucjiure,  like  a  flute,  or  with 
reeds.  The  first  division  includes  the  flute,  pipe,  flageolet,  <fcc.,  and  in  the  second 
are  found  the  clarionet,  bassoon,  horns,  trombones,  &c.  The  organ  also  is  a 
wind  instrument,  and  is,  incomparably,  the  grandest  of  all  musical  instruments, 
as  its  power  and  majesty  is  without  parallel  in  instrumental  combinations. 

Stringed  instruments  are  all  compound  instruments.  The  sounds  produced  by 
the  vibration  of  the  cords  are  strengthened  by  elastic  plates  of  wood,  and 
enclosed  portions  of  air,  to  which  the  cords  communicate  their  own  vibrations. 
They  are  vibrated  either  by  a  bow,  as  in  the  violin,  by  twanging,  as  in  the  harp, 
or  by  percussion,  as  in  the  piano. 

Drums  are  of  three  sorts;  the  common  regimental  or  snare  drum,  which  is  a 
cylinder  of  brass,  covered  with  membrane,  and  beaten  on  one  end  only;  the 
bass,  or  double  drum,  of  much  larger  dimensions,  and  beaten  on  both  heads  ; 
and  thirdly,  the  kettle  drum,  a  hemispherical  vessel  of  copper,  covered  with 
vellum,  and  supported  on  a  tripod.  This  drum  has  an  opening  in  the  metallic 
case,  to  equalize  the  vibrations.  They  all  depend,  of  course,  upon  the  vibration 
of  tense  membranes  (318). 

384.   Vibration    of   air   in   tubes. — Laws    of    Bernoulli. — The 

following  laws  of  the  vibration  of  air  contained  in  tubes,  were  disco- 
vered by  Daniel  Bernoulli,  a  celebrated  geometrician  who  died  in  1782. 
We  may  divide  tubes  into  two  classes. 

a.  Tubes  of  which  the  extremity  opposite  the  mouth  is  closed. 

b.  Tubes  open  at  both  extremities. 

a.  Tubes  of  which  the  extremity  opposite  the  mouth  is  dosed. 

1st.  The  same  tube  may  produce  different  sounds,  the  number  of 
vibrations  in  which  will  be  to  each  other  as  the  odd  numbers,  1,  3,  5, 
7,  &c. 

2d.  In  tubes  of  unequal  length,  sounds  of  the  same  order  correspond 
to  the  number  of  vibrations,  which  are  in  inverse  ratio  of  the  length 
of  the  tubes. 

3d.  The  column  of  air,  vibrating  in  a  tube,  is  divided  into  equal 
parts,  which  vibrate  separately  and  in  unison.  The  open  orifice  being 
always  in  the  middle  of  a  vibrating  part,  the  length  of  a  vibrating  part 
is  equal  to  the  length  of  a  wave  corresponding  to  the  sound  produced. 

b.  Tubes  open  at  both  extremities. 

The  laws  for  tubes  open  at  both  extremities,  are  the  same  as  the  pre- 
ceding, excepting  that  the  sounds  produced  are  represented  by  the  series 
of  natural  numbers,  1,  2,  3,  4,  &c. ;  and  that  the  extremities  of  the 
tubes  are  in  the  middle  of  a  vibrating  part.  Again,  the  fundamental 
sound  of  a  tube  open  at  both  extremities,  is  always  the  acute  octave  of 
the  same  sound  in  a  tube  closed  at  one  extremity. 

Demonstration. — If  the  column  of  air  contained  in  a  tube  vibrates  as  a 
single  wave,  the  number  of  vibrations  will  evidently  be  equal  to  the  velocity 
of  sound,  represented  by  V,  divided  by  the  length  of  the  tube,  L,  or  by  the 

V 
quotient  — .     If  the  column  of  air  is  divided  into  a  number  of  segments,  each 


280  THE    THREE    STATES  *OF    MATTER. 

vibrating  separately,  let  I  represent  the  length  of  one  of  these  segments,  and 

V 
the  number  of  vibrations  per  second  will  evidently  be  =  — . 

(a)  If  the  pipe  containing  the  column  of  air  is  stopped  at  both  ends,  there  will 
be  a  node  at  each  end.     Let  n  represent  the  number  of  nodes  including  the  two 
ends  ;  the  number  of  vibrating  segments  will  be  n  —  1,  the  length  of  each  vibra- 
L 

ting  segment  will  be  I  = ,  and  the  number  of  vibrations  per  second  will  be 

n  —  1 

V  V 

=  (n  —  !)•— >  in  which  we  may  substitute  for  n  any  number  greater  than 
I  L 

V     V     V 

unity,  giving  the  series  of  possible  vibrations  1.— ,  2—,  3—,  Ac. 

L      L     L 

(6)  If  the  tube  is  closed  at  one  end,  that  end  must  be  regarded  as  a  node,  and 
the  open  end  of  the  tube  as  the  middle  of  a  vibrating  segment.  Therefore, 

2n  — 1 
2(n  —  1)  -{-  1  =  2n  —  1  will  be  the  number  of  half  segments,  and  will  be 

the  entire  number  of  vibrating  segments  contained  in  the  length,  L,  and  the 

2n  — 1  V 
number  of  vibrations  per  second  will  become  •-• 

Substituting  for  n  the  integers  1,  2,  3,  <fcc.,  we  obtain  the  following  series  of 
vibrations  for  the  different  tones  of  the  pipe  : — 
V        V        V 

i-z'*-!' «•!•** 

If  the  pipe  is  open  at  both  ends,  as  before  let  n  be  the  number  of  nodes.  The 
number  of  complete  ventral  segments  will  be  n  —  1,  and  there  will  be  a  half 
segment  at  each  end,  making  n  segments  in  the  length  L.  The  length  of  a  com- 

L 

plete  segment  will  therefore  be  — ,  and  the  number  of  vibrations  per  second  is 
n 

V 
»— ,  making  n  =  1,  2,  3,  Ac.  We  obtain  the  following  series  of  vibrations  cor- 

Jj 
responding  to  different  tones  of  the  pipe  : — 

V       V        V 
l-7;    2yj  3.-,  Ac. 
L        L        L 

The  series  of  vibrations  for  the  tones  produced  by  a  pipe  will  be  as  follows  : — 
In  a  pipe  open  at  both  ends,  or  closed  at  both  ends,     .     .     1,  2,  3,  4,  5,  <fec. 

In  a  pipe  open  at  only  one  end, |,  f,  f ,  |,  f .  " 

In  the  latter  case  the  fundamental  note  is  an  octave  lower  than  when  both 
ends  of  the  tube  are  open,  or  when  both  ends  are  closed.  The  particular  tone 
that  a  pipe  will  produce  in  either  of  these  series  depends  on  the  strength  of  the 
blast. 

385.  Construction  of  musical  instruments. — Practically,  the  end 
of  the  tube  where  sound  is  formed  is  never  entirely  closed,  and  usually 
the  embouchure  is  on  one  side  of  the  tube.  The  laws  of  Bernoulli 
adapted  to  these  conditions  give  for  the  construction  of  musical  instru- 
ments the  following  practical  rules : — 

1.  The  length  of  the  tube  is  equal  to  the  quotient  of  the  velocity  of 


ACOUSTICS.  281 

sound  divided  by  the  number  of  vibrations   and  diminished  by  twice 
the  breadth  of  the  tube. 

2.  The  number  of  vibrations  is  equal  to  the  quotient  of  the  velocity  of 
sound,  divided  by  the  length  of  the  tube,  increased  by  twice  its  breadth. 

3.  The  length  of  a  cylindrical  organ  tube,  flattened  at  the  embochure, 
is  equal  to  the  quotient  of  the  velocity  of  sound  divided  by  the  number 
of  vibrations,  and  diminished   by  five-thirds  the  diameter  of  the  tube. 
(Comptes  Bendus,  T.  L.  1860,  p.  176.) 

386.  Vibrating  dams. — Illustrations  of  the  vibration  of  air  in  tubes 
^/e  often  found  at  waterfalls.     The  horizontal  column  of  air  enclosed 
behind  the  descending  sheet  of  water  is  rarefied  by  friction  of  the  water 
which  carries  away  a  portion  of  the  air,  and  the  external  air  rushing 
in  at  the  sides  is  thrown  into  vibrations,  which  are  often  so  perceptible 
as  to  endanger  the  safety  of  persons  approaching  too  near  the  cataract. 

At  the  falls  of  Holyoke,  Mass.,  the  descending  sheet  of  water  has  a  breadth 
of  1008  feet,  with  a  fall  of  £0  feet,  and  varying  from  5  feet  to  3  inches  thick. 
The  pulsations  of  the  air  rushing  in  behind  the  waterfall  vary  from  82  to  258 
per  minute. 

Says  Professor  Snell,  who  has  described  these  phenomena  at  length,*  "At 
one  time,  when  I  witnessed  the  comparatively  slow  oscillations  of  82  per  minute, 
I  was  surprised  by  the  great  strength  of  the  current  of  air,  as  it  rushed  into  the 
opening  at  the  end  of  the  dam.  I  could  not  venture  within  the  passage  through 
the  pier,  lest  I  should  be  swept  in  behind  the  sheet;  nor  could  I  stand  at  the 
entrance  of  the  arch  without  bracing  myself,  by  placing  both  hands  on  the 
corners."  These  vibrations  are  shown  by  Professor  Snell  to  follow  the  laws  of 
Bernoulli  for  the  vibration  of  air  in  tubes. 

$  4.    Vocal  and  Auditory  Apparatus. 

I.     OF  VOICE  AND  SPEECH. 

387.  Voice  and  speech. — In  nearly  all  the  air-breathing  vertebrate 
animals,  there  are  arrangements  for  the  production  of  sound,  or  voice, 
in  some  part  of  the  respiratory  apparatus.    In  many  animals  the  sound 
admits  of  being  variously  modified  and  altered  during  and  after  its  pro- 
duction ;  and  in  man  one  of  the  results  of  such  modification  is  speech. 

388.  The  vocal  apparatus  of  man   consists  of  the  thorax,  the 
trachea,  the  larynx,  the  pharynx,  the  mouth,  and  the  nose,  with  their 
appendages. 

The  thorax,  by  the  aid  of  the  diaphragm  and  the  intercostal  muscles  acting 
ca  the  lungs  within,  Alternately  compressing  and  dilating  them,  performs  the 
part  of  the  bellows  producing  a  current  of  air  for  the  production  of  sound.  The 
trachea,  or  the  windpipe,  extending  from  the  larynx  to  the  lungs,  acts  as  a  tube 
to  convey  the  air  from  the  lungs  to  the  organs  more  immediately  corcerned  in 
the  production  of  voice  and  speech.  The  larynx,  which  may  be  coosidered  as 
the  musical  organ  of  the  voice,  corresponds  to  the  mouth-piece  or  that  part  of 
the  organ  tube  which  gives  the  peculiar  character  to  the  sound.  The  pharynx 

*  Am.  Jour.  Sci.  [2]  Vol.  XXVIII.  p.  228. 


282  THE    THREE    STATES    OF    MATTER. 

is  a  large  cavity  above  the  larynx,  which,  by  the  varying  form  and  tension  of 
its  walls,  modifies  the  tones  of  the  voice.  The  mouth  and  nasal  passages  corres- 
pond to  the  upper  part  of  an  organ  tube  from  which  the  vibrations  of  the 
column  of  air  are  thrown  into  the  atmosphere. 

The  larynx. — This  organ  is  composed  essentially  of  four  cartilages, 
called  respectively  the  thyroid,  crjcoid,  and  the  two  arytenoid  carti- 
lages. The  cavity  of  the  larynx  is  nearly  closed  by  two  pairs  of  mem- 
branes, called  the  vocal  cords,  the  openiDg  between  which  is  called 
the  glottis.  295 

In  fig.  295,  showing  a  vertical  section  through 
the  larynx  and  glottis,  the  position  of  the  thy- 
roid and  cricoid  cartilages  is  seen  in  b  b,  a  a. 
The  thyroid  cartilage  consists  of  two  flat  plates 
whose  upper  edges  are  curved  somewhat  like 
the  letter  S,  and  forms  a  prominent  projection 
on  the  throat  of  man,  visible  exteriorly,  and 
vulgarly  called  Adam's  Apple.  The  cricoid 
cartilage,  a  <t,  lies  below  the  thyroid  cartilage, 
and  is  in  fact  only  an  enlargement  of  one  of 
the  cartilaginous  rings  forming  the  wind-pipe. 
The  position  of  the  arytenoid  cartilages  is  over 
the  cricoid  cartilages.  These  several  cartilages, 
with  the  hyoid  bone,  serve  as  points  of  attach- 
ment for  the  muscles  forming  the  proper  vocal 
apparatus.  The  two  chief  tongues  a£  the  glottis, 
or  proper  vocal  cords,  c  c,  extend  from  the 
thyroid  cartilage  to  the  arytenoid  cartilages, 
and  leave  between  them  a  fissure,  the  runa 
vocalis,  or  glottis,  shown  better  in  fig.  297.  This  fissure  leads  on  one  side  into 
the  trachea,  which  lies  below  the  larynx,  and  on  the  other  into  the  cavity  of  the 
larynx  itself,  which  communicates  with  the  cavities  of  the  mouth  and  nose. 

Besides  the  proper  vocal  cords,  there  are  the  ventricular  cords,  d  d,  situated 
a  small  distance  above  them  in  the  epiglottis;  they  are  less  developed  than  the 
first.  The  ventricular  cords  have  no  part  in  the  production  of  vocal  sounds, 
which,  however,  they  doubtless  serve  to  modify  and  strengthen  in  the  same  way 
as  the  conical  ease  surmounting  an  organ  tube. 

Between  these  two  sets  of  cords  are  seen  the  deep  depressions,  called  the 
ventricles  of  the  glottis. 

The  voice  is  produced  in  the  larynx  ;  for  if  an  opening  is  pierced 
into  the  trachea,  below  the  larynx,  the  air  escapes  by  this  opening, 
and  it.  is  not  possible  to  produce  any  vocal  sound.  If  an  opening 
is  made  above  the  larynx,  it  does  not  prevent  the  formation  of 
sound.  Magendie  mentions  the  case  of  a  man  who  had  a  fistulous 
opening  in  his  trachea,  and  who  could  not  speak  unless  he 
closed  it,  or  wore  a  tight  cravat. 

The  glottis. — A  clear  idea  may  be  obtained  of  the  form 
and  action  of  the  glottis,  by  supposing  two  pieces  of  India 
rubber  stretched  over  the  orifice  of  a  tube,  so  that  .a  small  fissure  is  left 
between  them,  fig.  296. 


ACOUSTICS. 


283 


By  forcing  air  through  such  a  tube,  sounds  will  be  produced,  varying  with 
the  tension  of  the  membranes  and  the  dimensions  of  the  aperture.  The  glottis 
is  a  fissure-like  opening,  bounded  by  similar  membranes.  By  means  of  a  series 
of  small  muscles,  the  vocal  cords  may  be  extended  or  relaxed  at  pleasure,  while 
other  muscles  afford  the  power  of  altering  the  width  of  the  vocal  fissure. 

The  vocal  ligaments  being  thicker  at  their  free  edges  than  elsewhere,  they 
vibrate  like  cords,  but  as  they  also  extend  like  plates  to  the  sides  of  the  larynx, 
their  vibrations  are  very  nearly  allied  to  the  vibration  of  reeds.  There  has  been 
much  controversy  as  to  whether  the  larynx  and  glottis  are  to  be  considered  as 
a  reed,  or  as  a  stringed  instrument.  It  is  probably  more  correct  to  say  that  it 
acts  upon  the  principles  of  both  combined. 

389.  Mechanism  of  the  voice. — The  formation  of  sound  in  the 
larynx,  as  has  been  already  suggested,  is  produced  by  the  vibration  of 
the  vocal  cords,  acting  as  a  species  of  membranous  reed,  under  the 
influence  of  air  from  the  lungs.     The  sound  being  produced  as  in  ordi- 
nary reeds  (381)  by  tht)  intermittent  current 

of  air. 

The  glottis  is  the  original  seat  of  the  sound, 
and,  although  other  parts  of  the  respiratory 
apparatus  have  a  certain  influence  in  modifying 
the  tone,  they  have  no  share  whatever  in  the 
production  of  the  sounds,  or  in  determining 
their  pitch. 

When  at  rest,  the  lips  of  the  glottis  are 
wrinkled  and  plicated,  so  that  the  air  in  respi- 
ration passing  through  the  fi'ssure  fails  to  put 
the  membranes  in  vibration.  But  as  the  musi- 
cian tunes  his  instrument  by  increasing  or  di- 
minishing the  tension  of  its  vibrating  strings,  so  something  like  this 
occurs  with  the  human  larynx.  The  two  conditions  of  the  glottis  are 
beautifully  shown  by  the  two  parts  of  fig.  297,  from  Miiller.  The 
upper  shows  the  organ  at  rest,  the  vocal  cords,  cc,  being  relaxed,  while 
in  the  lower,  these  cords  are  shown  as  in  the  act  of  vibrating ;  the  small 
air  passage,  o,  opening  into  the  trachea,  is  never  closed.  When  sounds 
are  to  be  produced,  the  fissure  is  contracted  and  the  membranes  receive 
the  degree  of  tension  necessary  for  vibration.  The  sound  varies  accord- 
ing to  the  tension  of  the  membranes,  the  magnitude  of  the  fissure,  and 
the  form  and  magnitude  of  the  passages  through  which  the  air  thus  put 
into  vibration,  passes  before  it  issues  into  the  atmosphere. 

390.  Range  of  the  human  voice.— In  speaking,  the  range  of  the 
human  voice  is  subject  to  but  very  little  variation,  being  generally 
limited  to  half  an  octave.     The  entire  range  of  voice  in  an  individual  is 
rarely  three  octaves,  but  the  male  and  female  voice  taken  together  may 
be  considered  as  reaching  to  four. 


284  THE    THREE    STATES    OF    MATTER. 

There  are  two  kinds  of  male  vxoices,  called  bass  and  tenor,  and  two 
kinds  of  female  voices,  called  contralto  and  soprano,  all  differing  from 
each  other  in  tone.  The  strength  of  the  bass  voice  is  in  general  greater 
on  the  low  tones  than  the  tenor.  The  contralto  is  also  stronger  on  the 
low  tones  than  the  soprano.  But  bass  singers  can  sometimes  go  very 
high,  and  the  contralto  frequently  sings  the  high  notes  like  soprano. 

The  essential  difference  between  the  bass  and  tenor  voices,  and 
between  the  contralto  and  soprano,  consists  in  the  tone  or  "  timbre" 
which  distinguishes  them  even  when  they  are  singing  the  same  note. 
The  barytone  is  intermediate  between  bass  and  tenor,  and  the  inezzo- 
soprano  is,  in  like  manner,  found  between  the  contralto  and  soprano. 
These  two  qualities  of  voice  have  a  middle  position  as  to  pitch  in  the 
scale  of  male  and  female  voices. 

The  different  qualities  of  tenor  and  bass,  and  «.vf  alto  and  soprano  voices, 
probably  depend  on  some  peculiarities  of  the  ligaments,  and  the  membranous 
and  cartilaginous  parietes  of  the  laryngeal  cavity  which  are  not  at  present 
understood.  We  may  form  some  idea  of  these  peculiarities,  by  recollecting  that 
musical  instruments  made  of  different  materials,  e.  g.,  metallic  wires  and  gut- 
strings,  may  be  tuned  to  the  same  note,  but  that  each  will  have  a  peculiar  quality 
or  "  timbre." 

The  following  are  the  limits  of  the  different  classes  of  voice,  as  determined  by 
Cagniard  de  Latour,  Savart,  and  others,  the  numbers  annexed  being  the  num- 
ber of  double  vibrations  of  the  glottis  produced  in  a  second  of  time. 

Soprano,  j  ^jjj        .Mezzo-soprano,  j  f^         Contralto,  j  ™£ 

f  528,  f  352,  f  220, 

Tenor,      j  m  Barytone,  j^         Bass,  j    ^ 

391.  Ventriloquism,  stuttering,  &c. —  Ventriloquism  is  supposed  by 
many  investigators  to  consist  chiefly  in  the  use  of  inspiratory  sounds;  this  is 
true  only  to  a  certain  extent.  The  art  of  the  ventriloquist  depends  greatly  on 
the  correctness  of  ear  and  flexibility  of  organ,  through  which  common  tones 
are  modulated  to  the  position  and  character  in  which  the  imaginary  person  is 
supposed  to  speak  ;  other  means  often  being  used  to  heighten  the  deception,  as 
concealing  the  face  that  the  play  of  organs  may  not  be  observed ;  often  in 
speaking  with  expiratory  notes,  the  air  expelled  by  one  expiration  is  distributed 
over  a  large  space  of  time,  and  a  considerable  number  of  notes. 

In  stuttering,  the  several  organs  of  speech  do  not  play  in  their  normal  succes- 
sion, and  thus  are  continually  interfered  with  in  convulsive  impulses  and  ineffi- 
cient adjustments.  The  cause  of  this  result  lies  almost  wholly  in  the  nervous 
apparatus  which  rules  over  the  organs  of  speech.  Important  remedial  means 
are,  to  study  carefully  the  articulation  of  the  difficult  letters,  to  practice  their 
pronunciation  repeatedly  and  slowly,  and  to  speak  only  when  the  chest  is  well 
filled  with  air. 

In  deaf  and  dumb  persons  the  organs  of  speech  have  originally  no  essential 
defects.  The  true  cause  of  their  dumbness  lies  in  their  inability  to  perceive 
sound.  The  impossibility  of  appreciating  the  several  sounds,  and  thus  gradu- 
ally acquiring  the  power  of  properly  adjusting  the  organs  of  speech,  is  the 
chief  reason  why  the  second  infirmity  is  associated  with  the  first. 


ACOUSTICS.  285 

392.  Production  of  sounds  by  inferior  animals. — The  sounds 
which  the  different  animals  produce  are  peculiar  to  the  class  to  which 
they  belong ;  thus  the  horse  neighs,  the  dog  barks,  the  cat  mews,  &c. 
These  various  modifications  depend  on  the  peculiar  structure  of  the 
larynx,  but  more  upon  the  form  and  dimensions  of  the  nasal  and  other 
cavities,  through  which  the  vibrating  air  passes. 

The  cat  is  distinguished  from  other  mammifers  by  the  almost  equal  develop- 
ment of  the  inferior  and  superior  vocal  cords.  Many  of  its  notes  are  almost 
human.  The  horse  and  ass  are  supplied  with  only  two  vocal  cords.  Animals 
which  howl,  and  are  heard  at  great  distances,  have  generally  large  laryngeal 
ventricles. 

Birds  are  furnished  with  two  larynx,  a  superior  and  inferior,  which 
serve  at  the  same  time  for  the  entrance  and  exit  of  air,  and  for  the 
purposes  of  vocalization.  The  upper  larynx,  which  corresponds  to  the 
larynx  in  mammifers,  can  only  be  regarded  as  an  accessory  of  the 
voice.  The  lower  larynx  is  the  true  larynx  ;  it  is  placed  at  the  lower 
part  of  the  trachea,  where  it  branches.  Those  birds  in  which  it  is 
absent  are  voiceless.  The  voice  of  birds  is  produced,  like  that  of  mam- 
mifers, by  the  vibration  of  the  cords  of  the  glottis. 

Insects,  in  general,  produce  sounds  remarkable  for  their  acuteness. 
Their  sounds  are  produced  in  a  great  number  of  ways,  some  effecting 
it  by  percussion,  and  some  by  the  friction  of  exterior  horny  organs 
upon  each  other,  as,  for  example,  in  the  grasshopper.  In  others,  the 
swiftly  recurring  beatings  of  the  wings  produce  sounds,  as  with  the 
musquito.  Many  insects  produce  sound  by  the  action  of  some  of  their 
organs  on  the  bodies  around  them,  as,  for  example,  the  various  insects 
which  gnaw  wood.* 

II.     THE   EAR. HEARING. 

393.  Auditory  apparatus  of  man. — In  the  ear,  impressions  are  not 
at  once -made  upon  the  sensory  nerve,  by  the  body  which  originates  the 
sensation,  but  they  are  propagated  to  it  through  the  medium  of  the 
atmospheric  air. 

The  organ  of  hearing  in  man  is  composed  of  three  parts :  the  exter- 
nal ear,  the  middle  ear,  or  tympanum,  and  the  internal  ear,  or  laby- 
rinth. 

The  external  ear  consists  of  (1)  the  pinna,  or  pavilion,  a,  fig.  298, 
which  collects  the  soniferous  rays,  and  directs  them  into  (2)  the  audi- 
tory canal,  or  meatus  auditorius,  b. 

The  peculiar  form  of  the  pinna,  with  its  numerous  elevations  and  depressions, 
has  not  as  yet  been  satisfactorily  shown  to  be  related  to  the  principles  of 
acoustics. 

The  auditory  canal  proceeds   inwards  from  the  pinna,  to  the  tympanum,  cj 

*  See  Appendix,  p.  668. 

27 


286  THE    THREE    STATES    OF    MATTER. 

it  is  an  elliptical  tube,  about  an  inch  long.     Its  interior  is  protected  by  hairs, 
and  by  a  waxy  secretion. 

The  middle  ear,  tympanum,  or  tympanic  cavity. — The  middle 
ear  is  a  cavity  in  the  temporal  bone  filled  with  air,  and  somewhat  hemi- 


spherical in  form;  it  measures  about  half  an  inch  in  every  direction. 
It  extends  from  the  tympanum,  c,  fig.  298,  to  o  and/,  and  encloses  the 
chain  of  bones,  cdef,  called  the  ossicles,  or  little  bones,  of  the  ear. 

The  middle  ear  is  separated  from  the  auditory  canal  by  a  thin  oval 
membrane,  the  membrana  tympani,  which  is  placed  obliquely  across  the 
end  of  the  canal,  at  an  angle  of  about  45°,  its  outward  plane  looking 
downwards  and  forwards. 

The  Eustachian  tube  is  a  membranous  canal  leading  from  the  anterior 
portion  of  the  middle  ear  downwards  and  forwards  to  the  pharynx,  with 
which  it  communicates  by  a  valvular  opening  that  is  generally  closed. 

The  Eustachian  tube  gives  exit  to  the  mucus  which  forms  in  the  middle  ear, 
and  also  permits  the  entrance  of  air  to  preserve  equality  of  pressure  on  the 
external  and  internal  surfaces  of  the  membrana  tympani. 

The  discomfort  produced  by  unequal  pressure  on  the  two  surfaces  of  the 
membrana  tympani  may  easily  be  understood  by  closing  the  nose  and  perlorm- 
ing  the  act  of  swallowing,  when  the  air  will  be  partially  exhausted  from  the 
middle  ear.  The  external  pressure  on  the  membrana  tympani  then  becomes 
greater  than  the  internal,  an  unpleasant  sensation  is  produced,  and  the  sense 
of  hearing  is  obscured.  Forcible  distension  of  the  pharynx  in  blowing  a  horn 
or  trumpet  often  produces  a  disagreeable  fullness  in  the  ears,  by  forcing  air 


ACOUSTICS.  287 

through  the  Eustachian  tube  into  the  middle  ear.     A  cold  often  impairs  the 
sense  of  hearing  by  obstructing  the  Eustachian  tube. 

A  chain  of  three  small  bones,  the  ossicles  of  the  tympanum,  passes 
through  the  middle  ear  from  the  membrana  tympani  to  the  entrance 
of  the  internal  ear.  These  bones  are  shown  separated  from  each  other 
in  fig.  299. 

The  malleus,  or  hammer-bone,  m,  the  incus,  or  anvil,  o,  and  the  stapes,  or 
stirrup,  t.  They  are  connected  with  each  other  in  such  a  manner  299 

as  to  allow  of  slight  movements.  This  chain  of  bones  is  attached 
at  one  end,  as  is  shown  in  fig.  298,  by  the  handle  of  the  malleus, 
to  the  tympanic  membrane,  and  at  the  other  by  the  foot  of  the 
stirrup,  to  the  membrane  of  the  fenestra  ovalis. 

The  muscles  which  act  upon  these  small  bones  are  supposed  to 
have  the  power  of  giving  more  or  less  tension  to  the  membranes  /£, 

which  they  connect,  and  thus  rendering  them  more  or  less  sensi-  f^> 

tive  to  sonorous  undulations. 

The  internal  ear,  called,  from  its  complicated  structure,  the  laby- 
rinth, has  its  channels  curved  and  excavated  in  the  petrous  bone,  the 
hardest  of  any  in  the  body.  The  labyrinth  consists  of  three  parts ;  the 
vestibule,  the  semicircular  canals,  and  the  cochlea. 

The  vestibule,  g,  fig.  298,  is  a  central  chamber,  formed  in  the  petrous  bone ; 
in  it  are  a  number  of  openings,  for  branches  of  the  auditory  nerve,  small 
arteries,  &c.  In  its  external  wall,  the  fenestra  ovalis  is  found. 

The  semicircular  canals  are  three  in  number,  opening  into  the  vestibule  at  its 
posterior  and  upper  part,  and  placed  in  planes  at  right  angles  to  each  other. 
Within  these  canals  are  placed  flexible  tubes,  of  the  same  form,  called  membran- 
ous canals,  filled  with  fluid. 

The  cochlea,  i,  is  a  conical  tube,  wound  spirally,  making  two  and  a  half  turns. 
It  resembles  a  snail's  shell  in  appearance ;  whence  its  name.  Its  interior  is 
divided  by  a  spiral  lamina,  called  the  lamina  spiralis,  into  two  passages  which 
communicate  by  a  little  hole  in  the  upper  part  of  the  300 

helix.    Between  the  membranous  and  the  bony  labyrinths, 
a  peculiar  liquid  (the  perilymph)  intervenes,  which  also 
fills  the  cavities  and  cochlea  j  the  membranous  labyrinth 
is  distended  by  another  liquid  (the  endolympli).     Within 
the  labyrinth  thus  filled  with  liquid,  the  terminal  filaments 
of  the  auditory  nerve  are  placed. 
They  are  expanded  in  the  ves- 
tibule,   spread   out  upon    the 
lamina   spiralis,    and   also   in 
certain    enlargements,    called 
ampullae,  at  the   entrance   of 
the   semicircular   canals ;   but 
they  do  not  traverse  the  semi- 
circular canals. 

Fig.  300  is  a  magnified  view  of  the  labyrinth,  showing  the  form  and  relation 
of  the  vestibule,  semicircular  canals  and  cochlea,  partly  laid  open,  so  as  to  dis- 
play their  interior  construction. 


288  THE   THREE   STATES   OF   MATTER. 

394.  Functions  of  the  different  parts  of  the  ear. — 1.  The  wa\es 
of  sound  passing  into  the  external  ear,  are  collected  and  directed  into 
the  auditory  canal,  and  strike  upon  the  tympanic  membrane,  which  is 
thus  thrown  into  vibration. 

2.  The  chain  of  bones  connecting  the  membrana  tympani  with  the 
fenestra  ovalis,  receives  the  vibrations  and  transmits  them  to  the  vesti- 
bule through  the  membrane  which  covers  the  fenestra  ovalis. 

3.  Vibrations  thus  excited  in  the  fluid  which  fills  the  labyrinth,  are 
received  by  the  expanded  filaments  of  the  auditory  nerve,  and  the 
sensation  of  sound  is  thus  transmitted  to  the  brain. 

In  considering  the  uses  of  the  different  parts  of  the  middle  and  internal  ear, 
it  is  necessary  to  refer  to  the  following  principles,  which  have  been  fully 
demonstrated  by  experiment. 

1.  Atmospheric  vibrations  lose  much   of  their  intensity  when   transmitted 
directly  to  either  solids  or  liquids. 

2.  The  intervention  of  a  membrane  greatly  facilitates   the  transmission  of 
vibrations  from  air  to  liquids. 

3.  Vibrations  are  readily  transmitted  from  air  to  a  solid  body,  if  the  latter  is 
attached  to  a  vibrating  membrane,  so  placed  that  the  vibrations  of  the  air  act 
upon  it. 

4.  Sonorous  vibrations  are  communicated  from  air  to  water  without  any  per- 
ceptible loss  of  intensity,  when  to  the  membrane  forming  the  medium  of  com- 
munication there  is  attached  a  short  solid  body,  which  occupies  the  greater  part 
of  its  surface,  and  is  alone  in  contact  with  the  water. 

5.  A  solid  body  fixed  in  an  opening  by  means  of  a  border  membrane,  so  as  to 
be  movable,  communicates  sonorous  vibrations,  from  air  on  one  side  to  water 
or  the  fluid  on  the  other  side,  much  better  than  solid  media  not  so  constructed. 
But  the  propagation  of  sound  to  the  fluid  is  rendered  much  more  perfect  if  the 
solid  conductor  thus  occupying  the  opening  is  by  its   other  end  fixed  to  the 
middle  of  a  tense  membrane  which  has  atmospheric  air  on  both  sides. 

These  principles  enable  us  to  understand  that  vibrations  are  communicated  to 
the  internal  ear  with  greater  intensity,  by  means  of  the  membrana  tympani  and 
the  chain  of  tympanic  ossicles,  than  if  these  organs  did  not  intervene  between 
the  atmospheric  air  and  the  internal  ear.  We  find  that  in  the  lower  orders  of 
animals,  where  hearing  is  less  acute  than  in  man,  the  middle  ear  and  tympanic 
ossicles  are  wanting.  The  air  in  the  cavity  of  the  tympanum  serves  also  to 
insulate  the  chain  of  small  bones,  and  preserve  the  purity  and  intensity  of  the 
vibrations  which  are  transmitted.  The  communication  between  the  middle  ear 
and  the  external  air,  by  means  of  the  Eustachian  tube,  is  thought  to  prevent 
reverberation  and  echoes  in  that  cavity. 

The  sound  of  a  tuning-fork,  or  other  sonorous  solid  body,  applied  to  the  teeth, 
or  any  bone  of  the  head,  is  heard  more  distinctly  than  when  the  sound  is  trans- 
mitted to  the  ear  by  means  of  the  air ;  it  has  therefore  been  concluded  that  the 
cochlea,  and  especially  the  lamina  spiralis,  facilitates  the  appreciation  of  such 
sounds.  In  regard  to  the  use  of  the  semicircular  canals,  the  opinions  of  phy- 
siologists are  as  yet  divided. 

For  full  discussions  of  the  functions  of  different  parts  of  the  ear,  the  student 
is  referred  to  Carpenter's  Physiology  and  to  Todd  &  Bowman's  Physiology. 

395.  Natural   diapason.— Cagniard   de   Latour,   one   of  the   best 


ACOUSTICS.  289 

modern  authorities  in  acoustics,  satisfied  himself  that  he  heard  the 
Bound  la  (A  of  the  musical  scale)  sounding  within  his  head  when  he 
agitated  it  from  side  to  side.  Mr.  Jobard  suggests  that  this  natural  la 
is  caused  by  the  contact  of  the  malleus  against  the  incus  in  the  ear,  a 
contact  easily  made  by  a  rapid  movement  of  the  head,  the  neck  being 
disembarrassed  of  clothing.  (Am.  Jour.  Sci.  [2]  XXVI.  97.) 

396.  Organs  of  hearing  in  the  lower  animals. — The  zoophytes 
appear  to  be  wanting  in  the  sense  of  hearing,  and  no  special  auditory 
apparatus  has  been  discovered  in  insects,  although  they  do  not  appear 
to  be  altogether  insensible  to  sound.  In  the  mollusca,  the  organ  is  a 
sac,  filled  with  liquid,  in  which  the  last  fibrils  of  the  acoustic  nerve  are 
diffused,  or  a  nerve  fibril,  in  connection  with  a  little  stony  body  (an 
otolith),  included  in  a  sac  of  water.  These  animals  can  only  distinguish 
one  noise  from  another,  or  their  quality,  and  that  imperfectly,  and  have 
no  perception  of  musical  notes.  This  organ,  corresponding,  as  is  as- 
sumed, to  the  semicircular  canals,  increases  in  complexity  as  we  rise  in 
the  scale  of  being.  In  lizards  and  scaly  serpents,  the  ear  commences 
with  the  tympanic  membrane ;  and  there  is  added  a  conical  cochlea. 
As  we  pass  through  them,  the  plan  is  further  developed ;  the  tympanic 
cavity,  Eustachian  tube,  the  chain  of  bones,  &c.,  appear.  In  birds 
there  is  a  continued  improvement,  and  all  the  aerial  tribes  of  mammals 
have  external  ears,  while  a  full  development  of  all  the  auditory  parts  is 
reached  only  in  man. 


Problems  in  Acoustics. 

Velocity  of  Sound. 

153.  The  rumbling  of  thunder  was  heard  7£  seconds  .after  the  corresponding 
flash  of  lightning  was  seen  ;  what  was  the  distance  of  the  discharge  ? 

154.  Calculate  the  velocity  of  sound  in  air  at  a  temperature  of  90° ;  also  at 
40°  below  zero  of  Fahrenheit's  scale. 

155.  What  time  would  be  required  to  transmit  sound  ten  miles  in  the  waters 
of  a  quiet  lake  ? 

156.  In  what  time  would  sound  travel  a  distance  of  3£  miles  in  each  of  the 
following  substances :  iron,  wood,  carbonic  acid,  hydrogen  gas,  vapor  of  alcohol 
at  140°,  vapor  of  water  at  154°  ? 

157.  What  time  was  required  to  transmit  the  sound  of  the  explosion  of  the 
volcano  at  St.  Vincent's  to  Demerara  (see  page  260),  supposing  the  sound  to 
have  travelled  in  the  air  alone? 

158.  At  what  distance  from  the  source  of  sound  must  a  reflecting  surface  be 
placed  that  an  echo  may  be  heard  three  seconds  after  the  original  sound? 

159.  From  the  top  of  a  precipice  a  stone  was  let  fall,  and  after  5£  seconds  it 
was  heard  to  strike  the  bottom.     What  was  the  height  of  the  precipice  ? 

27* 


290  THE    THREE    STATES    OF    MATTER. 

160.  What  was  the  distance  of  the  meteor  which  was  heard  at  Windsor  Castle, 
in  1783,  ten  minutes  after  it  disappeared,  assuming  the  air  at  50°  F.  ? 

161.  An  observer  supposes  himself  in  the  range  of  a  distant  cannon,  the  repft-t 
of  which  he  hears  19  seconds  after  seeing  the  flash;  how  soon  may  he  appre- 
hend danger  from  the  hall,  supposing  it  to  fly  at  the  rate  of  a  mile  in  eight 
seconds  ? 

162.  The  flash  of  a  gun  throwing  shells  was  seen  due  east  from  the  observer; 
after  three  seconds  the  report  was  heard  ;  after  another  interval  of  three  seconds 
the  shell  was  seen  to  explode  40°  south  of  east,  and  the  explosion  of  the  shell 
was  heard  three  seconds  fater;  to  what  distance  was  the  shell  thrown  ?  and  what 
was  its  velocity  of  flight  ? 

Physical  Theory  of  Music. 

163.  A  metallic  wire,  placed  upon  the   sonometer,  vibrates  300  times  in   a 
second;    by  how  much  must  its  length  be  diminished  that  it  may  make  370 
vibrations  per  second  ? 

164.  What  number  of  vibrations  per  second  are  required  to  give  the  note  G  1 
of  the  Italian  opera? 

165.  What  is  the  length  of  a  wave  in' air  when  an  instrument  sounds  E  3  of 
the  Berlin  opera? 

166.  What  are  the  relative  numbers  of  vibrations  required  to  form  the  notes 
E  and  D  sharp  ? 

167.  What  is  the  interval  between  C  sharp  and  D  flat  when  both  notes  are 
correctly  sounded  ? 

168.  How  does  the  interval  of  four  perfect  fifths  differ  from  a  major  third  in 
the  scale  two  octaves  above  the  key  note? 

169.  What  is  the  fractional  expression  for  the  chromatic  semitone  ?    What  for 
the  grave  chromatic  semitone  ? 

170.  What  is  the  number  of  beats  in  a  minute  formed  by  two  tones  whose 
vibrations  are  as  24  to  25,  when  the  higher  note  makes  750  vibrations  per  second  ? 

171.  Calculate  the  number  of  vibrations  per  minute  at  the  Holyoke  Falls,  for 
1,  2,  and  4  nodes  respectively,  the  breadth  of  the  dam  1008  feet,  the  enclosed 
column  of  air  being  entirely  open  at  both  ends. 

172.  Estimating  the  velocity  of  sound  at  340  metres  per  second,  what  number 
of  vibrations  per  second  will  be  produced  in  a  square  organ  tube  whose  length 
is  1-13  metres  and  its  breadth  0-08  metres  ? 

173.  The  organ  of  the  church  of  Saint  Denis,  in  Paris,  is  tuned  to  the  normal 
la  (A  3)  of  880  simple  vibrations  per  second,  and  a  square  tube  9-566  metres 
long  and  0-48  metres  broad,  was  constructed  to  play  c£o_2  (C_2),  but  on  trial  it 
was  found  too  flat.     What  alteration  of  its  length  would  correct  its  tone  ? 

174.  Calculate  the  respective  lengths  of  a  series  of  square  organ  tubes  to  play 
the  scale  commencing  with  C  1,  the  longer  tube  having  a  breadth  of  4  inches, 
and  each  tube  in  the  ascending  scale  having  a  breadth  1  of  an  inch  less  than 
the  preceding ;  the  normal  la  being  reckoned  at  856  simple  vibrations. 

175.  Calculate  the  dimensions  of  a  series  of  cylindrical  organ  tubes  for  the 
scale  commencing  with  C  4,  the  longer  tube  having  a  diameter  of  1  inch,  and 
the  others  in  the  series  diminishing  regularly  in  diameter  by  2^  of  an  inch ;  the 
organ  to  be  tuned  as  in  the  last  example. 

176.  What  are  the  names  of  the  next  three  higher  notes  in  the  scale  v  hich 
the  tube  playing  G  4  in  the  last  example  would  give  by  sufficiently  increasing 
the  strength  of  the  blast  ? 


PART  THIRD. 

PHYSICS  OF  IMPONDERABLE  AGENTS. 

LIGHT,  HEAT,  AND  ELECTRICITY. 


CHAPTER  I. 

LIGHT,  OR  OPTICS. 

§  1.  General  Properties  of  Light. 

397.  Optics. — Light. — Optics  (from  the  Greek  verb  O7rro//a«,  to  see) 
is  that  branch  of  physical  science  which  treats  of  the  nature  and  pro- 
perties of  light. 

Light  is  a  mysterious  agent,  acting  upon  the  organs  of  vision,  and 
imparting  to  us  a  knowledge  of  external  things.  It  brings  us  into 
relation  with  surrounding  objects,  enlarging  the  sphere  of  our  habita- 
tion, in  a  measure  annihilating  distance,  unfolding  to  us  the  beauties 
of  nature,  and  acting  as  a  perpetual  source  of  enjoyment. 

398.  Nature  of  light. — Theories. — In   regard  to   the  nature  of 
light,  a  great  diversity  of  opinion  has  prevailed  among  philosophers. 

(a)  Corpuscular  theory. — Sir  Isaac  Newton  maintained  that  the 
phenomena  of  light  are  produced  by  luminous  corpuscles  thrown  off 
from  burning  bodies,  each  particle  producing,  in  its  flight,  vibrations 
in  the  surrounding  ether  similar  to  the  waves  produced  by  a  stone 
falling  into  the  water. 

(6)  Undulatory  theory. — Huyghens  maintained,  in  opposition  to 
Newton,  that  light  consisted  solely  of  vibrations  in  an  ethereal  medium, 
without  the  onward  progress  of  any  substance  whatever.  This  theory 

(291) 


PHYSICS    OP    IMPONDERABLE   AGENTS. 

has  been  investigated  and  defended  by  many  of  the  ablest  philosophers  : 
by  Young,  Malus,  Fresnel,  Brewster  and  others,  and  is  now  generally 
received. 

The  undulations  producing  the  phenomena  of  sound  take  place  in 
the  same  direction  that  the  sound  itself  moves ;  but  the  vibrations  of 
light  are  supposed  to  move  at  right  angles  to  the  direction  in  which 
light  is  propagated.  It  is  difficult  to  explain  all  the  phenomena  of  light 
even  on  this  theory. 

(c)  An  oscillatory  theory  of  light  has  been  proposed  by  Mr.  Rankine, 
of  Glasgow.*  In  this  theory,  the  particles  of  luminiferous  ether  are 
supposed  to  rotate  on  their  axes,  by  the  influence  of  a  species  of  mag- 
netic force,  which  is  wholly  destitute  of  effect  in  producing  resistance 
to  compression,  so  that  it  is  no  longer  necessary,  as  in  the  undulatory 
theory,  so  suppose  the  luminiferous  medium  to  have  the  properties  of 
an  elastic  body.  The  same  mathematical  formulae  are  employed,  with 
this  hypothesis,  as  for  the  undulatory  theory.  Whether  this^theory  can 
be  applied  to  explain  all  the  phenomena  of  physical  optics,  remains  to 
be  proved. 

399.  Sources  of  light. — Phosphorescence. — The  sources  of  light 
are  the  sun'  and  stars,  heat,  chemical  combinations,  phosphorescence, 
and  electricity. 

We  know  not  the  real  cause  of  the  light  emitted  by  the  sun  and 
stars,  but  we  know  that  bodies  become  luminous  at  a  high  temperature, 
and  shine  more  vividly  in  proportion  to  the  intensity  of  the  heat,  from 
which  we  arc  accustomed  to  suppose  that  heat  and  light  are  only  modi- 
fications of  one  and  the  same  cause.  Artificial  lights  depend,  in  general, 
upon  combustion,  or  the  union  of  the  oxygen  of  the  air  with  burning 
bodies.  This  chemical  action  is  attended  with  the  disengagement  of 
considerable  heat  as  the  burning  body  becomes  luminous.  Other  chemi- 
cal combinations  are  attended  with  light,  and  it  is  doubtful  whether  any 
bodies  become  luminous  without  chemical  action  of  some  kind. 

The  term  phosphorescence  is  given  to  a  pale  light  emitted  in  the  dark 
by  certain  substances  which  do  not  appear  to  emit  any  sensible  heat. 
Phosphorescence  has  been  observed  in  animals,  vegetables,  and  even  in 
minerals.  During  the  heat  of  summer  the  glow-worm  and  fire-fly  emit 
a  brilliant  light. 

In  tropical  regions  phosphorescent  insects  are  very  numerous.  The 
waters  of  the  ocean,  especially  in  warm  latitudes,  are  often  covered 
with  little  animalcules  which  become  luminous  at  night  when  the  water 
is  agitated,  shining  in  the  wake  of  a  vessel  like  a  track  of  living  fire. 

'*  See  transactions  of  the  British  Association  for  1853,  p.  9. 


OPTICS.  293 

In  certain  circumstances  also  rotten  wood  and  decaying  flesh  become 
phosphorescent.  By  friction,  or  by  long  exposure  to  the  rays  of  the 
sun,  certain  minerals,  as  the  diamond,  white  marble,  and  fluor  spar, 
acquire  the  property,  it  is  said,  of  shining,  for  a  brief  period,  in  the 
dark.  The  cause  of  phosphorescence  is  not  known,  but  in  some  cases 
it  appears  to  depend  upon  electricity. 

Electricity  is  a  source  of  light  so  intense  that  its  brightness  is  equal, 
in  some  cases,  to  one-fifth,  or  even  one- fourth  that  of  the  sun. 

400.  Relation  of  different  bodies  to  light. — All  bodies  are  either 
luminous,  transparent,  translucent,  or  opaque. 

(a)  Luminous  bodies  are  those  in  which  light  originates,  as  the  sun, 
and  burning  bodies, 

(b)  Transparent  bodies  allow  light  to  pass  freely  through  them,  thus 
permitting   the  form  of  other   bodies  to  be  distinctly  seen  through 
them.     Such  are  water,  air,  and  polished  glass.     Such  substances  are 
also  said  to  be  diaphanous  (from  8td,  through,  and  <patvaj,  to  shine). 

(c)  Translucent  bodies  permit  only  a  portion  of  light  to  pass,  and  in 
so  irregular  or  imperfect  a  manner,  that  the  outline  of  other  bodies 
cannot  be  clearly  seen,  as  rough  glass  and  oiled  paper. 

(d)  Opaque  bodies  are  those  which  do  not  ordinarily  allow  any  light 
to  pass  through  them,  as  wood  and  the  metals.     But  all  bodies,  even 
the  metals,  may  be  made  so  very  thin  as  to  become  partially  transparent 
or  translucent.     Opacity  is  not  absolute  in  metals,  as  is  proved  in  the 
case  of  gold-leaf  on  glass,  through  which  a  beautiful  violet-green  light 
is  seen.     This  light  is  found  by  optical  experiments  to  be  truly  trans- 
mitted light,  and  not  a  color  caused  by  the  minute  fissures  of  the  gold- 
leaf.     It  is  worthy  of  remark,  that  this  greenish  color  is  complementary 
to  the  red,  which  is  the  color  of  gold  when  seen  by  successive  reflections. 

401.  Rays,  pencils,  and  beams  of  light. — A  single  line  of  light 
is  called  a  ray.     A  pencil  of  light  is  a  collection  of  rays  diverging  from 
a  common  source,  or  converging  to  a  point.     A  beam  of  light  is  a 
collection  of  parallel  rays.     Diverging  rays  are  those  which  gradually 
separate  from  each  other.    Converging  rays  are  those  which  tend  to 
meet  in  a  common  point ;  hence  we  have  the  terms  301 
diverging  pencils,  and  converging  pencils  of  light. 

402.  Visible  bodies   emit   light  from   every 
point   and  in  every  direction,  the   rays   diverging 
from  each  point  in  right  lines. 

Let  ABC,  fig.  301,  be  three  points  in  any  visible  object; 
from  each  of  these  points,  light  is  emitted  in  diverging 
pencils,  as  partially  represented  in  the  figure. 

In  this  figure  certain  points  are  seen,  where  rays  from  ABC  cross  each  other, 


294 


PHYSICS  OF  IMPONDERABLE  AGENTS. 


and  between  them  are  vacant  spaces.  No  such  vacant  spaces  exist,  but  the 
rays  from  all  points  in  the  object  are  crossing  each  other  at  every  point  in  the 
space  where  the  object  is  visible. 

403.  Propagation  of  light  in  a  homogeneous  medium. — A  me- 
dium is  something  existing  in  space,  capable  of  producing  phenomena. 
A  medium  is  called  luminiferous,  which  is  capable  of  transmitting 
light;  and  it  is  said  to  be  homogeneous  when  the  composition  and  density 
of  all  its  parts  are  the  same.     All  space  is  supposed  to  be  pervaded  by 
a  luminiferous  medium,  called  luminiferous  ether,  and  yet  the  particles 
of  this  ether  may  act  upon  each  other  at  great  distances.     In  a  homo- 
geneous medium,  light  always  moves  in  straight  lines.     If  any  opaque 
body  is  placed  in  a  direct  line  between  the  eye  and  a  luminous  body, 
the  light  is  intercepted. 

When  light  enters  a  dark  chamber  by  a  very  small  opening,  the 
course  of  the  light  becomes  visible  by  illuminating  the  fine  particles  of 
dust  always  floating  in  the  air.  Rays  of  sun-light  are  thus  easily 
demonstrated  to  move  in  straight  lines. 

404.  Velocity  of  light. — Light  travels  with  such  amazing  velocity, 
that,  for  any  distances  on  the  surface  of  the  earth,  the  time  occupied  in 
its  passage  from   one   point  to   another   is   totally  inappreciable   by 
our  unaided  senses. 

In  1676,  Roemer,  a  Danish  astronomer,  observed  that  the  eclipses  of  the  first 
satellite  of  Jupiter,  which  occur  at  uniform  intervals  of  time  when  the  earth  is 
moving  in  that  part  of  her  orbit  nearest  to,  or  most  remote  from  Jupiter,  are 
constantly  retarded  when  the  earth  is  moving  from  that  planet,  and  as  regularly 
accelerated  when  the  distance  between  the  earth  and  Jupiter  is  diminishing. 
He  found  that  when  the  earth  was  in  that  part  of  her  orbit  most  distant  from 
Jupiter,  the  eclipses  of  the  first  satellite  take  place  16m.  36s.  later  than  when 
in  the  opposite  part  of  her  orbit. 

By  this  means  the  velocity  of  light  was  ascertained  to  be  about  192,000  miles 
in  a  second.  302 

Foucault's  apparatus 
for  measuring  the  velo- 
city of  light.— Notwith- 
standing the  prodigious 
velocity  of  light,  M.  Fou- 
cault  has  succeeded  in 
measuring  it,  by  employing 
a  revolving  mirror,  accord- 
ing to  the  method  devised  by 
Wheatstone  for  measuring 
the  velocity  of  electricity.  In  dt  scribing  this  apparatus,  we  shall  sup- 
pose the  properties  of  mirrors  and  lenses  to  be  already  understood. 

The  apparatus  of  M.  Foucault  is  represented  in  fig.  302.     The  shutter  of  a 


OPTICS.  295 

dark  chamber  is  pierced  with  a  square  opening,  K,  behind  which  a  fine  platinum 
wire,  o,  is  stretched  vertically.  By  means  of  a  mirror,  a  beam  of  solar  light  is 
made  to  enter  the  chamber,  and  being  divided  by  the  platinum  wire,  it  falls  upon 
an  achromatic  lens,  L,  of  long  focus,  placed  at  a  distance  from  the  platinum  wire 
less  than  double  the  distance  of  its  principal  focus.  The  image  of  the  platinum 
wire  would  be  formed  in  the  axis  of  the  lens,  somewhat  enlarged.  But  the 
beam  of  light,  after  passing  the  lens,  falls  upon  the  plane  mirror,  m,  which 
revolves  with  great  velocity,  and  being  reflected  by  it,  an  image  of  the  platinum 
wire  is  formed  in  space,  which  image  is  displaced  with  an  angular  velocity, 
double  the  velocity  of  the  mirror.*  This  image  is  received  by  a  concave  mirror, 
M,  so  fixed  that  its  centre  of  curvature  coincides  with  the  axis  of  rotation  of 
the  revolving  mirror,  m.  The  pencil  reflected  by  the  mirror,  M,  returns  back- 
ward and  is  again  reflected  by  the  mirror,  m,  and  passes  back  through  the  lens, 
L,  and  forms  an  image  of  the  platinum  wire,  coinciding  with  the  wire  itself,  if 
the  mirror,  m,  revolves  slowly.  In  order  to  view  this  image  without  obscuring 
the  pencil  of  light  which  enters  the  chamber  by  the  opening  K,  a  piece  of  plate 
glass,  V,  with  parallel  faces,  is  placed  between  the  lens  and  the  platinum  wire, 
inclined  in  such  a  manner  that  the  rays  reflected  fall  upon  a  powerful  eye-glass, 
P.  If  the  mirror,  m,  remains  stationary,  or  if  it  revolves  slowly,  the  returning 
ray,  M  m,  falls  upon  the  mirror,  m,  in  the  same  position  it  occupied  at  the  first 
reflection,  and  returning  in  the  direction  it  came,  it  meets  at  a  the  plate  glass, 
V,  and  is  partially  reflected,  and  forms  in  d,  at  a  distance  a  d,  equal  to  a  o,  an 
image  which  is  seen  by  the  eye  by  means  of  the  eye-piece,  P. 

The  revolving  mirror,  m,  causes  this  image  to  be  repeated  at  each  revolution, 
and  if  the  velocity  of  rotation  is  uniform,  the  image  does  not  change  its  position. 
When  the  velocity  does  not  exceed  thirty  revolutions  per  second,  the  successive 
appearances  of  the  image  are  distinct,  but  when  the  velocity  is  greater,  the 
impressions  upon  the  eye  are  continuous,  and  the  image  appears  constant. 

When  the  mirror,  m,  revolves  with  great  rapidity,  its  position  is  sensibly 
changed  during  the  interval  occupied  by  the  light  in  passing  from  m  to  M,  and 
back  again  from  M  to  m,  and  the  returning  ray,  after  reflection  by  the  mirror,  m, 
takes  the  direction  m  b,  and  forms  an  image  in  i  ;  thus  the  image  has  deviated 
from  d  to  ?'.  Strictly  speaking,  there  is  some  deviation  even  when  the  mirror 
turns  slowly,  but  it  is  appreciable  only  when  it  has  acquired  a  certain  magnitude, 
by  making  the  rotation  of  the  mirror  sufficiently  rapid,  or  by  taking  the  distance, 
M  m,  sufficiently  great.  By  means  of  the  deviation  in  the  position  of  the  image 
and  the  velocity  of  rotation,  the  time  required  for  the  light  to  pass  from  m  to  M, 
and  back  again,  becomes  known,  making  I  =  M  m,  V  =  L  m,  r  =  0  L,  n  =  the 
number  of  revolutions  per  second,  D  =  the  absolute  deviation  d  i,  and  V  = 
the  velocity  of  light  per  second.  M.  Foucault  obtained  the  following  formula 
for  the  velocity  of  light, 


*  To  demonstrate  this,  let  m  n,  fig.  303,  be  the  revolving  mirror,  0,  an  object 
placed  before  it,  and  forming  its  image  at  0'  ;  when  the  mirror  arrives  at  the 
position  m'  n',  the  image  will  be  formed  at  0".  But  the  angles,  0'  0  0'',  and 
m  c  m'  are  equal,  because  their  sides  are  perpendicular  to  each  other.  But  the 
inscribed  angle  0'  0  0"  is  measured  by  half  the  arc  0'  0",  and  the  angle  m  <;  m', 
is  measured  by  the  entire  arc  m  m'  •  hence  the  arc  0'  0",  is  double  m  m',  which 
thus  demonstrates  that  the  angular  velocity  of  the  image  is  double  the  angular 
velocity  of  the  mirror. 


296  PHYSIOS    OP   IMPONDERABLE    AGENTS. 

In  the  experiments  of  M.  Foucault,  m  M,  was  only  about  four  yards,  but  by 
giving  the  mirror,  m,  a  velocity  of  600  or  800  revolutions  per  second  he  obtained 
a  deviation  of  from  eight  one-hundredths  to  twelve  one-hundredths  of  an  inch. 
Owing  to  the  vibration  of  the  apparatus  revolving  with  such  great  rapidity,  the 
results  yet  obtained  by  this  method  for  the  absolute  velocity  of  light  are  not 
considered  as  entirely  correct,  although  of  the  highest  interest. 

Experiments  have  been  made  with  the  same  apparatus  to  determine  the  velo- 
city of  light  in  liquids  as  compared  with  the  velocity  in  air.  For  this  purpose 
a  tube,  A  B,  three  yards  long,  is  filled  with  distilled  water,  or  any  other  liquid, 
and  placed  between  the  revolving  mirror,  m,  and  the  concave  mirror,  M',  similar 
to  M.  The  rays  of  light  reflected  by  the  revolving  mirror  in  the  direction 
m  M',  pass  twice  through  the  column  of  fluid  in  the  tube,  A  B,  before  returning 
to  the  mirror,  V.  The  returning  ray  is  reflected  at  c,  and  forms  an  image  at  h. 
The  deviations  of  the  rays  which  traverse  the  liquid  are  greater  than  the  devia- 
tion of  the  rays  which  are  propagated  in  air  alone,  which  shows  that  the  velo- 
city of  light  in  fluids  is  less  than  in  air. 

Fizeau's  method. — Another  method  of  direct  determination  of  the  velo- 
city of  light  has  been  devised  by  M.  Fizeau,  of  Paris,  in  1849.  An  exposition 
of  this  method,  by  Prof.  A.  Caswell,  will  be  found  in  the  Smithsonian  Report 
for  1858,  p.  130. 

Results. — From  these  and  other  methods  the  velocity  of  light  has 
been  determined  to  be  in  air  192,000  miles  per  second ;  in  water 
144,000  miles ;  in  glass  128,000  miles  ;  and  in  diamond  77,000  miles. 

405.  No  theory  of  light  is  entirely  satisfactory. — In  the  cor- 
puscular theory  of  light,  advocated  by  Newton,  it  was  supposed  that 
fluids  and  solids  attracted  the  light,  and  refraction  was  explained  by 
supposing  that  light  moves  faster  in  dense  bodies  than  in  air,  as  ia 
known  to  be  the  case  in  regard  to  sound.    According  to  the  undulatory 
theory,  it  is  known  that  transverse  waves  or  undulations  must  move 
slower  in  dense  bodies  than  in  rarer  media. 

The  discovery  of  Foucault,  as  just  explained,  that  light  actually 
moves  slower  in  denser  media,  tends  to  confirm  the  undulatory  theory. 

The  immense  power  of  resisting  compression  which  a  medium  ought 
to  possess,  in  order  to  transmit  transverse  vibrations  with  a  velocity  so 
much  greater  than  the  motions  of  the  Swiftest  planets  or  comets,  is  an 
objection  against  the  undulatory  theory  that  has  not  yet  been  satisfac- 
torily answered. 

The  discussion  of  the  theories  of  light  belongs  to  the  higher  departments  of 
mathematics. 

406.  Properties  of  light. — (a)  Absorption. — Light  falling  upon  any 
substance  is  either  absorbed,  dispersed,  reflected,  or  refracted.    A  part 
of  the  light  disappears  and  is  said  to  be  absorbed;  as  when  light  falls  upon 
black  substances.     No  substances  absorb  all  the  light,  for  the  fact  that 
the  blackest  substance  is  still  visible,  shows  that  its  different  parts  emit 
some  of  the  light  which  they  receive. 


OPTICS. 


297 


(6)  Dispersion. — Light  falling  upon  opaque  bodies,  causes  them  to 
bocome  luminous,  or  to  emit  light  in  all  directions,  and  thus  become 
visible.  Such  bodies  are  said  to  disperse  light,  because  they  scatter  the 
light  in  all  directions  from  which  they  are  visible. 

Bodies  owe  the  property  of  dispersing  light  to  the  innumerable  little 
facets  of  the  particles  composing  their  rough  surfaces.  Only  part  of 
the  light  is  thus  irregularly  reflected  or  dispersed,  while  much  of  it  is 
probably  absorbed  or  destroyed. 

(c}  Reflection. — When  light  falls  upon  polished  surfaces,  or  on  bodies 
having  naturally  smooth  and  uniform  surfaces,  it  is  thrown  off  in  a 
regular  manner,  as  a  ball  rebounds  from  a  hard  floor. 

If  a  ray  of  light,  S  A,  fig.  304,  falls  upon  a  polished  surface,  B  C,  it  will  be 
reflected  in  the  direction  A  R.  If  N  A  is  drawn  perpendicular  to  B  C,  S  A  N 
will  be  the  angle  of  incidence,  and  N  A  R  will  be  304 

the  angle  of  reflection,  and  the  two  angles  will  be 
equal.  The  lines  S  A,  N  A,  and  A  R,  will  lie  in 
the  same  plane;  we  have  therefore  the  following 
rules : — 

1st.    The  incident  ray,  the  perpendicular    at    the 
point  of  incidence,  and  the  reflected  ray,  are  all  situated  in  the  same  plane. 

2d.   The  angle  of  incidence  and  the  angle  of  reflection  are  equal. 

(d}  Refraction. — If  a  straight  rod  is  placed  obliquely,  partly  iir- 
mersed  in  water,  it  appears  broken  or  bent  just  where  it  enters  the 


305 


water.  If  a  coin,  a,  fig.  305,  is  placed  in  a 
cup,  in  such  a  position  that  it  is  just  hidden 
from  view,  and  water  is  then  gently  poured 
into  the  cup,  the  coin  will  appear  to  be  lifted 
up  and  will  become  visible. 

Let  c  d  be  the  surface  of  the  water,  the  ray,  a  b, 
is  so  bent  or  refracted,  at  the  surface  of  the  water, 
that  the  coin  appears  as  if  placed  at  a'. 


This  bending  of  the  rays  at  the  surface  of  any  transparent  medium  is  called 


refraction. 

Let  C  B,  fig.  306,  be  the  surface  of  water  in  a  vessel, 
S  A  a  ray  of  light  incident  at  A,  and  NAN'  the  per- 
pendicular, A  R  the  reflected  ray,  and  A  T  the  direc- 
tion of  the  ray  which  enters  the  water  and  is  re- 
fracted ;  then  : — 

The  angle  S  A  N  is  called  the  angle  of  incidence  of 
the  ray  S  A.  The  angle  N  A  R  is  called  the  angle  of 
reflection,  which  is  in  all  cases  equal  to  the  angle  of 
incidence.  The  line  N  A  N',  is  called  the  normal. 
The  angle  T  A  N'  is  called  the  angle  of  refraction. 

If  we  take  A  a,  fig.  307,  equal  to  A  b,  and  draw 


306 


t  m  and  b  n,  each  perpendicular  to  N  A  N',  then  a  m  is  the  sine  of  the  angle  of 
mcidence,  and  b  n  is  the  sine  of  the  angle  of  refraction,  and  a  m  divided  by  6  n 

28 


298 


PHYSICS    OP    IMPONDERABLE    AGENTS. 


is  invariably  the  same  for  any  given  medium,  whether  the  angle  of  incidence  is 

increased   or  diminished.     The   quotient   obtained   by 

dividing  a  MI  by  b  n,  is  called  the  index  of  refraction, 

and  it  is  represented  by  n.     The  index  of  refraction 

varies  for  different  media ;  thus  for  light  passing  from 

air  into  water,  it  is  about  |,  for  light  passing  from  air 

into  glass,  about  f ,  and  about  f  when  light  passes  from 

air  into  diamond.     These  fractions  inverted  give   the 

index  of  refraction  for  light  passing  out  of  water,  glass, 

and  diamond,  into  air. 

When    light   passes  from  a  rare  to  a  denser 
medium,  it  is  refracted  towards  the  perpendicular 
or  normal,  and  when  it  passes  from  a  dense  to  a  rarer  medium,  it  is 
refracted  from  the  perpendicular  or  normal. 

The  general  law  of  the  refraction  of  light  is  thus  stated.  The  inci- 
dent ray,  the  refracted  ray,  and  the  perpendicular  to  the  refracting  surface 
at  the  point  of  incidence,  lie  in  the  same  plane  ;  and  the  sine  of  the  angle 
of  incidence  bears  a  constant  ratio,  in  the  same  medium,  to  the  sine  of  the 
angle  of  refraction  ; 

am 

or,     — -  =  n. 
on 

When  a  ray  of  ordinary  daylight  or  sunlight  is  refracted  by  a  dense  trans- 
parent medium,  the  refracted  light  is  not  confined  to  a  single  line,  but  it  is 


308 


spread  out  into  a  fan-like  form,  as  shown  in  fig.  308, 
between  A  r  and  A  v,  and  the  different  parts  of  the 
refracted  pencil  show  different  colors,  the  most 
strongly  refracted  part  being  violet,  and  the  least 
refracted  part  being  red.  The  index  of  refraction,  for 
a  single  color,  is  uniform  for  any  given  medium ;  but 
the  index  of  refraction  in  the  same  medium  varies  for 
differently  colored  light. 

407.  Amount  of  light  reflected  at  differ- 
ent angles  of  incidence. — When  light  falls 
upon  a  transparent  medium  perpendicular  to  its  surface,  nearly  all  the 
light  enters  the  medium,  and  only  a  small  portion  is  reflected.  As  the 
light  falls  more  and  more  obliquely  upon  the  medium,  the  amount,  of 
light  refracted  diminishes,  and  the  amount  reflected  increases. 

If  we  look  at  the  image  of  the  sun  in  water  at  midday,  and  again  near  sunset, 
we  shall  see  a  remarkable  difference.  Near  sunset  the  image  is  so  brilliant,  the 
eyes  can  scarcely  bear  to  look  at  it,  while  at  midday  we  observe  it  without  diffi- 
culty. The  image  of  objects  at  a  little  distance  are  seen  in  water  more  distinctly 
than  the  images  of  near  objects,  because  the  light  from  distant  objects  falls  more 
obliquely  upon  the  water  and  a  greater  amount  is  reflected. 

•  If  we  look  very  obliquely  at  a  sheet  of  white  paper,  placed  before  a  candle,  an 
imagje  of  the  flame  may  be  seen  reflected  from  the  surface  of  the  paper,  but  the 
image  disappears  when  the  rays  fall  upon  the  paper  nearer  to  the  perpendicular- 


OPTICS. 


299 


"When  light  falls  upon  any  polished  metallic  surface,  the  greatest 
amount  of  reflection  takes  place  when  the  incident  rays  are  perpen- 
dicular to  the  surface,  and  the  amount  of  light  reflected  diminishes  as 
the  angle  of  incidence  increases. 

Different  substances,  polished  with  equal  care,  differ  in  their  power  of  reflect 
ing  light.  The  amount  of  light  reflected  depends  also  upon  the  nature  of  the 
medium  in  which  the  reflecting  body  is  placed.  Bodies  immersed  in  water 
reflect  less  light  than  in  air. 

Table  showing  the  number  of  rays  of  light  reflected   out  of  100  rays  incident,  by 
different  kinds  of  glass  and  metals  used  for  optical  purposes.* 


Angle  of 
incidence. 

Crown  glass, 
Sp^avity, 

ra  =  1-524. 
Specific  heat, 
0-38. 

Plate  glass, 
Sp   gravity, 
2-511. 
n  =  1-517. 
Specific  heat, 
0-39. 

Flint  glass, 
Sp.  gravity,. 
3-2.5. 
7»=  1-570. 
Specific  heat, 
0-43. 

GHass  of 
Antimony. 

Speculum 
metal, 
Sp.  gravity, 
8-9. 
Specific  heat, 
0-67. 

Polished  steel, 
Sp.  gravity, 

Specific  heat, 
088. 

0° 

3452 

3-380 

3615 

8-20 

7230 

10° 

3-608 

3-546 

3-819 

8-36 

70  85 

60-52 

20° 

3-837 

3-790 

4117 

8-60 

69-43 

30° 

4189 

4-164 

4-574 

8'98 

68-11 

58-69 

40° 

4-767 

4-778 

5-320 

9-59 

66-91 

50° 

5810 

5-882 

6-656 

10-68 

65-87 

54-96 

60° 

7-964 

8.155 

•     9-369 

12-93 

65-03 

70° 

13-448 

13-891 

16-015 

18-52 

64-41 

80° 

32-396 

33  155 

36-422 

36-65 

64-04 

85° 

56-202 

•  56-204 

57-559 

57-07 

90° 
i 

75-776 

74-261 

72-074 

72-20 

6391 

53-60 

408.  Internal  reflection.  —  When  light  passes  through  a  transparent 
medium,  a  portion  of  the  light  is  reflected  at  each  surface. 

In  fig.  309,  S  A  is  a  ray  of  light  incident  upon  the  first  surface  of  a  trans- 
parent medium.     A  portion  is  reflected  in  A  R.     A  T  is  the  refracted  ray,  and 


309 


T  V  the  emergent  ray,  but  a  portion  of  the  light  is  re- 
fleeted  at  the  second  surface  in  the  direction  T  A',  of 
which  a  part  emerges  in  the  direction  A'  R',  a  part 
suffers  a  second  reflection  downward  from  A',  a  part 
emerges  from  the  second  surface,  and  another  portion 
suffers  successive  internal  reflections  before  it  is  either 
lost  by  absorption  or  finally  emerges  on  one  or  the  other 
side  of  the  medium.  In  general  only  the  rays  A  R, 
T  V,  and  A'  R',  have  sufficient  intensity  to  be  visible  to  the  naked  eye. 

409.  Total  reflection.  —  When  light  passes  from  a  dense  to  a  rarer 
medium,  the  angle  of  refraction  is  greater  than  the  angle  of  incidence, 
and  when  the  angle  of  refraction  is  90°,  the  angle  of  incidence  is  much 
less.  For  water  it  is  48°  35X,  for  ordinary  glass  it  is  41°  49X,  conse- 


*  From  Potter's  Physical  Optics. 


300          PHYSICS  OP  IMPONDERABLE  AGENTS. 

quently  a  ray  of  light  traversing  water  or  glass  at  greater  angles  cannot 
escape  into  the  air,  but  is  totally  reflected,  obeying  the  ordinary  law  of 
reflection.  The  proportion  of  light  suffering  internal  reflection  from  a 
surface  of  glass  or  water,  constantly  increases  from  the  perpendicular 
to  the  point  where  total  reflection  takes  place. 

Since  the  angle  of  incidence  for  a  dense  medium  is  always  greater  than  the 
angle  of  refraction,  when  the  angle  of  incidence  is  90°  the  angle  of  refraction 
must  be  considerably  less  than  90°.  If  the  angle  of  incidence  is  90°,  its  sine 
will  be  unity.  The  sine  of  the  angle  of  refraction  will  be  unity  divided  by  the 

index  of  refraction,  =  — ,  hence  the  angle  of  total  internal  reflection  for  any 
n 

1  310 

medium  is  the  angle  whose  sine  =  — •. 

n 

Fig.  310  shows  light  radiating  from  a  point  below 
the  surface  of  water  and  escaping  into  the  air,  the 
angle  of  emergence  increasing  much  faster  than  the 
angle  of  incidence,  until  the  light  emerges  parallel  to 
the  surface  of  the  water,  after  which  total  reflection 
takes  place. 

To  an  eye  placed  below  the  surface  of  the  water,  all 
objects  above  the  horizon  would  be  seen  within  an  angle  of  97°  10f,  or  double 
the  angle  of  total  reflection  for  water.  • 

410.  Irregular  reflection.— Diffused  light. — The  reflection  from 
polished  surfaces,  which  follows   the   two   laws   already   announced, 
is  called  regular  reflection;  but  only  a  part  of  the  light  is  reflected 
regularly  from  any  surface,  when  the  reflecting  body  is  more  dense 
than  the  surrounding  medium.     A  part  of  the  light  is  scattered  in 
all  directions,  and  is  said  to  be  irregularly  reflected  or  diffused.     This 
is   the   portion  of  light  which   renders  objects  visible.     Light  regu- 
larly reflected  gives   an   image  of  the   object  which  emits  the  light, 
while   light  irregularly  reflected   gives   only  an   image  of  the   body 
which  reflects  it.     When  a  mirror  becomes  dim  by  the  accumulation  of 
light  dust,  or  anything  which  tarnishes  its  surface,  the  amount  of 
regular  reflection  diminishes,  and  the  irregular  reflection  increasing, 
all  parts  of  the  mirror  become  distinctly  visible. 

411.  Umbra  and  penumbra. — When  an  opaque  object  is  held  in  a 
pencil  of  light  proceeding  from  a  luminous  311 

point,  as  s,  fig.  311,  a  dark  and  well-defined 

shadow  is  produced,  which  increases  in  size  s" 

as   it   becomes    more    distant.      The   dark 

shadow  is  called  an  umbra.     If  the  light  proceeds  from  a  luminous 

body  having  a  sensible  magnitude,  as  A,  fig.  312,  besides  the  dark 

shadow,  or  umbra,  where  no  part  of  the   luminous  body  is  visible, 

there   will   be   a  much   broader   partial   shadow,  called  the  penum- 


OPTICS. 


301 


bra,  where  a  part  only  of  the  luminous  body  is  visible.     The  breadth 
of  the  penumbra  increases  with  the  diameter  of  the  light,  and  with  the 
312  313 


distance  which  the  shadowr  extends  behind  the  opaque  object.  The 
darkness  of  the  penumbra  gradually  increases  from  the  extreme  border, 
which  is  too  faint  to  be  easily  seen,  to  the  umbra  or  full  shadow,  as  is 
shown  in  a  section  of  the  shadow,  at  fig.  313. 

412.  Images  produced   by  light   transmitted   through  small 
apertures. — If  a  white  screen  is  placed  near  a  small  opening  in  a  dark 
chamber,    the    rays   of    light   which   pass  314 

through  the  opening  will  form  on  the  screen 
inverted  images  of  external  objects. 

It  will  be  seen  in  fig.  314,  that  the  rays 
of  light  from  the  top  and  the  bottom  of  the 
object  cross  each  other  in  the  small  opening,  and  thus  invert  the  image. 
If  the  aperture  is  small,  the  image  will  be  formed  in  the  same  manner, 
whatever  be  the  form  of  the  aperture.  But  if  the  opening  is  large,  the 
image  is  indistinct,  or  entirely  disappears. 

413.  Intensity  of  light  at  different  distances.— The  intensity 
of  light  at  any  distance  from  a  luminous  body,  is  in 

an  inverse  proportion  to  the  square  of  the  distance. 

Let  0,  fig.  315,  be  a  luminous  point;  at  1  1,  place  a 
board  one  foot  square  ;  it  will  cast  a  shadow  that  will  cover 
a  space  two  feet  square  at  double  the  distance,  three  feet 
square  at  three  times  the  distance,  and  four  feet  square  at 
four  times  the  distance.  The  areas  will  therefore  be,  1,  4, 
9,  16,  and  the  intensity  of  the  light  at  the  distances  1,  2, 
3,  4,  will  therefore  be  in  the  proportions  of  1,  £,  £,  -fa. 

If  /  and  /'  represent  the  intensity  of  a  light  at  the 
^distances  D  and  D' ,  we  shall  have 

II          I         Z>'2 
/:/'  =  —:  — ,  or  — =  — . 

D1      D,1'          p  2)2 

Hence  the  intensity  of  a  light  at  different  distances  will  be  inversely  as  the 
squares  of  those  distances. 

414.  Photometers  are  instruments  employed  to  measure  the  com- 
parative intensity  of  different  lights.    .The  principle  on  which  they  are 
constructed  is,  to  so  place  the  lights  that  they  will  illuminate  a  single 
surface,  or  two  adjacent  surfaces,  with  equal  intensity.     The  relative 

28* 


302  PHYSICS    OF    IMPONDERABLE    AGENTS. 

intensities  of  the  two  lights  are  then  as  the  square  of  their  distances 
from  the  illuminated  surfaces. 

Buusen's  Photometer  is  the  simplest  and  most  convenient  photometer 
yet  invented.  A  disk  of  paper  four  or  five  inches  in  diameter,  is  rendered  trans- 
lucent by  washing  it  with  paraffine  or  stearine,  dissolved  in  oil  of  turpentine  or 
naphtha,  except  a  spot  about  an  inch  in  diameter  at  the  centre.  When  this  disk 
is  held  between  two  lights,  at  a  point  where  their  intensity  is  unequal,  the  trans- 
lucent part  of  the  paper  is  easily  distinguished  from  the  central  part,  but  when 
moved  to  a  point  where  the  two  lights  have  equal  intensity,  all  parts  of  the 
paper  have  a  uniform  appearance.  No  light  appears  to  shine  through,  because 
the  illumination  is  equal  on  both  sides.  By  means  of  a  graduated  bar,  on  which 
the  lights  and  disk  are  mounted,  the  distance  of  each  light  from  the  paper  is 
determined,  and  their  respective  intensities  are  calculated  on  the  principles 
above  mentioned. 

This  principle  may  be  applied  in  many  ways  to  determine  the  intensities  of 
lights;  as,  for  instance,  the  portion  which  is  transmitted  orxreflected  from  dif- 
ferent substances. 

Rumford's  Photometer. —  Rumford's  photometer  is  composed  of 
two  plates  of  ground  glass,  before  which  are  fixed  two  opaque  rods,  A 
and  B,  separated  by  a  screen,  fig.  316.  The  lights  to  be  compared,  as 
a  lamp  and  a  candle,  m  n,  are  so  placed  opposite  the  rods  that  each 

316 


plate  is  illuminated  by  only  one  of  the  lights,  and  a  shadow  of  the  cor- 
responding rod  falls  upon  each  plate,  as  shown  in  the  figure.  If  the 
two  shadows,  a  and  6,  are  of  unequal  intensity,  by  moving  one  of  the 
lights  backward  or  forward  a  position  is  obtained  where  the  shadows 
appear  equally  dark,  and  the  glass  plates  are  thus  known  to  be  equally 
illuminated.  The  relative  intensities  of  the  lights  are  determined  as  in 
the  preceding  case. 

Silliman's  Photometer. — Silliman's  photometer  is  the  reverse  of 
Rumford's,  comparing  two  discs  of  light  thrown  up  by  two  equal  trian- 
gular glass  prisms,  upon  a  disc  of  roughened  glass  in  the  body  of  a  dark 
moving  on  a  graduated  bar.  (Am.  Jour.  Sci.  [2]  XXII.  315.) 


OPTICS.  303 

$  2.  Catoptrics,  or  Reflection  by  Regular  Surfaces. 

I.     MIRRORS  AND  SPECULA. 

415.  Mirrors  are  solid  bodies  bounded  by  regular  surfaces,  highly 
polished,  aiid  capable  of  reflecting  a  considerable  portion  of  the  light 
which  falls  upon  them. 

The  term  mirror  is  generally  applied  to  reflectors  made  of  glass  and 
coated  with  an  amalgam  of  tin  and  quicksilver. 

416.  Specula  are  metallic  reflectors,  having  a  highly  polished 
surface.    The  best  speculum  metal  consists  of  32.  parts  of  copper,  and  15 
parts  of  the  purest  tin.   Specula  are  also  made  both  of  silver  and  of  steel. 

In  the  use  of  glass  mirrors,  a  portion  of  light  reflected  from  the  first  surface, 
interferes  with  the  perfection  of  the  image ;  hence,  where  the  most  perfect  instru- 
ments are  required,  metallic  reflectors  are  employed.  In  treating  of  reflectors, 
we  shall  notice  only  the  action  of  the  principal  reflecting  surface,  and  use  the 
term  mirror  to  comprehend  all  regular  reflectors. 

417.  Forms  of  mirrors. — Mirrors  are  either  plane  or  curved.  Curved 
mirrors  may  be  spherical,  elliptical,  or  paraboloid.     The  properties  of 
elliptical  and  paraboloid  reflectors  have  been  mentioned  in  sections  324 
and  325.     A  concave  spherical  mirror  is  a  portion  of  the  surface  of  a 
sphere,  reflecting  from  the  internal  side.     A  convex  spherical  mirror  is 
a  portion  of  the  surface  of  a  sphere,  reflecting  from  the  outside.   Curved 
mirrors,  whether  concave  or  convex,  may  be  regarded  as  made  up  of  an 
infinite  number  of  plane  mirrors,  each  per-  317 
pendicular  to  a  radius  drawn  through  it  from 

the  centre  of  the  mirror. 

Fig.  317  shows  a  plane  mirror,  M  A  N,  a  concave 
mirror,  m  A  n,  and  a  convex  mirror,  m'  A  n' ,  having 
a  common  point,  A,  and  the  line,  P  A  C,  perpen- 
dicular to  each  at  the  point  A.  If  a  ray  of  light, 
I  A,  is  incident  upon  either  mirror  at  the  point  A, 
the  reflected  ray,  A  R,  will  make  the  same  angle 
with  the  perpendicular  as  is  made  by  the  incident 

ray.     At  any  other  points,  as  t  or  t' ',  the  curved  mirrors  will  act  like  little  plane 
mirrors,  perpendicular  to  the  radii  P  t  and  Ct'. 

II.  REFLECTION  AT  PLANE  SURFACES. 

418.  Reflection  by  plane  mirrors.— Parallel  rays  of  light,  falling 
upon  a  plane  mirror,  will  be  parallel  after  reflection. 

If  parallel  rays  of  light,  A  D,  A'  D',  fig.  318,  fall  upon  the  plane  mirror,  M  N, 
they  will  each  make  equal  angles  with  the  perpendicu-  318 

lars,  E  D,  E'  D',  and  as  the  angles  of  incidence  and  ~ 
reflection  will  be  equal,  the  reflected  rays,  D  B,  D'  B', 
will  make  equal  angles  with  the  perpendiculars,  and 
will  consequently  be  parallel  after  reflection. 

If  A  D  represent  the  upper  side  of  the  beam  of  light  before  reflection,  it  will 


304  PHYSICS    OF    IMPONDERABLE    AGENTS. 

become,  after  reflection  in  D  B,  the  lower  side  of  the  beam.     Hence  a  beam  of 
parallel  light  .is  inverted  in  one  direction  by  reflection  from  a  plane  mirror. 

Diverging  rays  of  light,  falling  upon  a  plane  mirror,  will  continue  to 
diverge  after  reflection,  and  will  appear  to  emanate  from  a  point  as 
much  behind  the  mirror  as  the  luminous  point  is  319 

before  it.  N-'  ;E<^  & 

•***   ^^    •      \: 

Let  A  be  a  radiant  point  in  front  of  the  plane  mirror 
M  N,  fig.  319.  If  the  perpendiculars,  E  D,  E'  D',  E"  D", 
be  drawn,  the  reflected  rays  will  make  the  same  angles 
with  the  perpendiculars  as  the  incident  rays,  and  hence  ''•••C-X 

the  reflected  rays  will  make  the  same  angles  with  each  '''-^ 

other  as  they  did  before  reflection,  but  they  will  appear  to  diverge  from  the 
point  A',  behind  the  mirror. 

Converging  rays  continue  to  converge  after  reflection  from  a  plane 
mirror.  After  reflection  they  will  converge  towards  a  point  as  much  in 
front  of  the  mirror  as  the  distance  of  the  point  behind  the  mirror, 
towards  which  they  converged  before  reflection. 

This  is  easily  seen  by  tracing  the  rays  of  light  backward  in  the  preceding 
figure. 

Reflection  from  a  plane  mirror  changes  the  direction  of  the  rays  of 
light,  and  removes  the  point  of  apparent  convergence  or  divergence  to 
the  opposite  side  of  the  mirror. 

419.  Images  formed  by  plane  mirrors. — Let  M  N  be  an  object 
placed  in  front  of  the  plane  mirror,  A  B,  fig.  320,  and  E  the  place  of 
the  eye.  From  the  great  number  of  rays  emitted  in 
every  direction  from  M  N,  and  reflected  from  the 
mirror,  a  few  only  can  enter  the  eye  at  E.  These 
will  be  reflected  from  those  portions,  D  F,  G  H,  of 
the  mirror,  so  situated  with  respect  to  the  eye  and  A 
the  points,  M  N,  that  the  angles  of  incidence  and 
reflection  will  be  equal.  If  the  rays,  D  E,  F  E,  are 
continued  backward,  they  will  meet  at  m,  and  they 
will  appear  to  the  eye  to  radiate  from  that  point.  In 
the  same  manner  the  rays  G  E,  H  E,  will  appear  to  radiate  from  n  ;  a 
virtual  image  of  the  object  will  therefore  be  formed  between  m  and  n. 

This  is  called  a  virtual  image,  because  it  is  not  formed  of  rays  of  light 
actually  coming  from  the  position  of  the  image,  but  by  rays  so  changed 
in  their  direction,  that  they  appear  to  the  eye  as  though  originating 
from  an  object  situated  at  m  n,  behind  the  mirror. 

If  the  eye  is  moved  about,  the  image  remains  stationary,  hence  it  is 
seen  by  means  of  rays  reflected  from  other  parts  of  the  mirror.  Two 
or  more  persons  may  see  the  image  at  the  same  time  and  in  the  same 
position,  but  by  different  rays  of  light. 


OPTICS. 


305 


The  position  of  the  image  behind  the  mirror  may  be  found  by  draw- 
ing lines  from  prominent  points  in  the  object,  perpendicular  to  the 
mirror,  extending  them  as  far  behind  the  mirror  as  the  points  from 
which  they  are  drawn  are  situated  before  it,  then  uniting  the  extremi- 
ties of  the  lines,  the  outlines  of  the  image  will  be  delineated.  The 
images  of  all  objects  seen  in  a  plane  mirror  have  the  same  form  and 
distance  from  the  mirror  as  the  objects  themselves. 

420.  Images  multiplied  by  two  surfaces  of  a  glass  mirror. — 
Glass  mirrors  produce  several  images.     This  may  be  readily  demon- 
strated by  looking  very  obliquely  at  the  image  of  a  candle  in  a  glass 
mirror.    The  first  image,  caused  by  partial  reflection  from  the  first  sur- 
face of  the  glass,  is  comparatively  faint.    The  second 

image  is  formed  by  reflection  from  the  quicksilver, 
which  covers  the  second  surface,  and  is  very  clear  and 
distinct. 

When  rays  of  light  from  any  object  fall  upon  the  first 
surface  of  a  plate  of  glass,  M  N,  fig.  321,  a  portion  of  the 
light  being  reflected,  forms  the  first  image,  a.  The  principal 
part  of  the  light  penetrates  the  glass,  and  is  reflected  at  c,  by 
the  silvering  which  covers  the  back  of  the  mirror,  and  coming  to  the  eye  in  the 
direction  d  H,  produces  the  image,  a',  at  a  distance  from  the  first  image  equal 
to  about  once  and  a  third  the  thickness  of  the  glass.  This  image  is  much 
brighter  than  the  first,  because  the  metallic  coating  of  the  mirror  reflects  a 
greater  amount  of  light  than  the  first  surface  of  the  glass. 

Other  images,  more  and  more  obscure,  are  formed  by  rays  which 
emerge  from  the  glass  after  successive  interior  reflections  from  the  two 
surfaces  of  the  glass.  As  this  multiplicity  of  images  diminishes  the 
distinctness  of  vision,  metallic  reflectors  are  often  employed  in  optical 
instruments.  322 

421.  Images  formed  by  light  reflected 
by  two  plane  mirrors. — Let  AB,  fig.  322, 
be  an  object,  and  G  D,  E  F,  two  plane  mir- 
rors, making  an  angle  with  each  other  less 
than   180°.     The   light   falling  upon   the 
mirror  C  D  will  form  an  image  at  a  &,  the 
position  of  which  may  be  determined  by 
the  method  explained  at  section  419.     A 
portion  of  this  light,  after  reflection,  will 
fall  upon  the  mirror  E  F,  and  be  reflected 

as  if  coming  from  an  image  a'  b',  which  will  be  seen  by  the  eye  at  e. 

To  trace  the  course  of  the  rays  which  enter  the  eye  from  any  point,  Q,  in  the 
object  A  B  ;  let  q  be  the  corresponding  point  in  a  b,  and  q'  a  similar  point  in 
a'  b'  i  the  light  will  enter  the  eye  as  if  it  came  from  q',  therefore  draw  the  lines 


306 


PHYSICS    OF    IMPONDERABLE   AGENTS. 


323 


or 


q'  e,  and  they  will  show  the  final  course  of  the  pencil  by  which  the  point  Q  ia 
seen.  From  the  points  where  these  lines  meet  the  mirror,  E  F,  draw  lines  to  q, 
and  they  will  represent  the  course  after  reflection  by  C  D  ;  from  the  points  where 
these  lines  meet  the  mirror  C  D,  draw  lines  to  the  point  Q,  and  they  will  show 
the  course  of  the  rays  which,  after  reflection  by  each  of  the  mirrors  C  D,  E  F, 
form  the  pencil  by  which  the  eye  at  e  sees  the  point  q'  in  the  secondary  image 
a'  V. 

The  inversion  of  parts  by  the  two  mirrors  are  now  seen  to  correct  each  other, 
and  all  the  parts  of  the  image,  a'  b',  have  the  same  relation  to  each  other  as  in 
the  object  A  B.  The  peculiar  excellence  of  "Wollaston's  Camera  lucida  (^18) 
depends  upon  the  fact  that  by  means  of  two  reflections  all  parts  of  the  image 
preserve  their  natural  relations. 

422.  Multiplicity  of  images  seen  by  means  of  inclined  mir- 
rors.— When  an  object  is  placed  between  two  mirrors,  which  make 
with  each  other  an  angle  of  90°  or  less,  several 

images  are  produced,  varying  in  numbers  accord- 
ing to  the  inclination  of  the  mirrors.     If  they  are 
placed  perpendicular  to  each  other,  three  images  °f 
will  be  seen,  situated  as  in  fig.  323. 

The  rays  0  C  and  0  D,  from  the  point  0,  form,  after  a 
single  reflection,  one  the  image  0',  the  other,  the  image 
0"  ;  and  the  ray  0  A,  which  undergoes  two  reflections  at 
A  and  B,  gives  a  third  image,  0'".  When  the  inclination  jt  /  ]• '  f 

of  the  mirrors  is  60°,  five  images  are  formed;  and  when  *~ 
they  are  placed  at  an  angle  of  45°,  seven  images  are  produced.  The  number 
of  images  continues  to  increase  as  the  inclination  of  the  mirrors  diminishes,  and 
when  the  mirrors  become  parallel,  the  number  of  images  is  theoretically  infinite, 
but  as  some  of  the  light  is  lost  at  every  reflection,  and  the  successive  images 
appear  more  and  more  distant,  only  a  moderate  number  of  images  are  visible. 

423.  Deviation  of  light  reflected  by  two  mirrors. — When  a  ray 
of  light  reflected  by  a  mirror  is  again  reflected  by  a  second  mirror,  in 
a  plane  perpendicular  to  the  intersection  of  the  two 

mirrors,  the  deviation  of  the  ray  from  its  original 
direction  is  equal  to  twice  the  angle  formed  by 
the  two  mirrors. 

Let  two  mirrors,  A  and  B,  fig.  324,  be  inclined  to 
each  other,  so  that  their  directions  shall  meet  at  some 
point,  C,  forming  an  angle  A  C  B  =  a.  Let  the  ray 
of  light,  S  A,  be  reflected  by  the  first  mirror  in  the 
line  A  B,  and  falling  upon  the  second  mirror  be  again 
reflected  in  the  direction  B  D,  meeting  the  original  direc- 
*ion  S  A  D  in  D.  Let  the  angle  of  deviation  A  D  B  =  d. 
Draw  N  A  n  perpendicular  to  the  mirror  A,  and  B  n  per- 
pendicular to  the  mirror  B.  The  angle  between  these 
perpendiculars  will  be  equal  to  the  angle  formed  by  the  inclinations  of  the 
m'rrors,  orAnB  =  ACB  =  a. 


ff 

\C 


OPTICS.  307 

Let  S  A  N  =  N  A  B  =  i,  and  A  B  n  =  i' ;  then  since  N  A  B  =  A  B  n  +  A  n  B, 
we  have : — 

i  =  i'  -(-  a    •'.     a  =  i  —  i' ; 

also     BAD-|-ABD-j-ADB  =  180°, 

or  2(90°  —  i)  +  2t'  +  d=  180°    .-.    d  =  2(t  — t')  =  2o  j 

Or  the  deviation  of  any  ray  after  two  reflections  is  equal  to  twice  the  angle  be- 
tween the  mirrors. 

424.  Kaleidoscope. — This  beautiful  toy  depends  upon  the  multi- 
plication of  images  by  inclined  mirrors.  Two  mirrors,  inclined  at 
angles  of  30°,  45°,  or  60°,  are  placed  in  a  paper  tube,  one  end  of  which 
is  closed  by  plain  and  the  other  by  ground  glass.  Various  objects,  as 
fragments  of  colored  glass,  tinsel,  twisted  glass,  &c.,  are  placed  in  a 
narrow  cell,  at  the  end  of  the  tube,  closed  with  ground  glass,  just  room 
enough  being  left  to  allow  the  objects  to  tumble  around  as  the  tube  is 
moved.  On  looking  through  this  instrument  towards  the  light,  multi- 
plied images  of  every  object  are  seen,  beyond  all  description  splendid 
and  beautiful ;  an  endless  variety  of  symmetrical  combinations  appear- 
ing to  the  view  as  the  instrument  is  moved,  but  never  recurring  with 
the  same  form  and  color. 

Let  A  C  and  B  C,  fig.  325,  be  the  two  mirrors  of  the  kaleidoscope,  and  let  the 
dotted  circle,  described  about  C  as  a  centre,  represent  the  tube  in  which  they 
are  placed ;  let  Q  be  the  position  of  an  object  325 

within  the  angle  formed  by  the  mirrors.  If  Q  is 
in  the  circumference  of  the  circle  described  about 
C,  the  two  series  of  images  of  Q  will  be  formed  in 
the  circumference  of  the  same  circle,  qi  qz  qs  q4  be- 
ing  formed  by  the  mirror  A  C,  and  q'  q"  q'"  q"" 
being  formed  by  the  mirror  B  C.  Since  q1  is  in  a 
line  perpendicular  to  A  C,  and  at  the  same  dis- 
tance  from  A  C  behind  it  as  Q  is  before  it,  that 
perpendicular  is  the  chord  of  the  arc  Q  qv  and  q1  ^2  \ 
is  in  the  circumference  of  the  circle  drawn  about 
C  as  a  centre.  For  the  same  reason  q'  is  also  in 
the  same  circumference  ;  so  also  q"  being  the  image 
of  qv  is  as  far  behind  B  C  as  q1  is  before  it,  and  as  the  line  joining  q1  and  q"  is 
perpendicular  to  B  C,  it  must  be  the  chord  of  the  circle,  and  hence  q"  is  in  the 
circumference.  In  the  same  manner  it  may  be  shown  that  every  image,  formed 
by  repeated  reflections  from  A  B  and  B  C,  is  also  in  the  circumference  of  the 
circle  described  about  C.  When  we  arrive  at  any  image,  qt  or  q"",  falling,  as 
in  the  figure,  between  the  directions  of  the  mirrors  produced,  such  an  image 
being  situated  at  the  back  of  both  the  mirrors  must  be  the  last  of  its  series,  as 
no  light  from  such  an  image  can  fall  upon  either  mirror. 

According  to  g  423,  the  distance  between  any  two  images,  formed  by 
an  even  number  of  reflections,  will  be  equal  to  twice  the  angle  between 
the  mirrors.  It  is  evident  that  images  formed  by  an  odd  number  of 
reflections  will  be  situated  between  each  two  of  the  former  series; 


308 


PHYSICS    OP    IMPONDERABLE    AGENTS. 


326 


hence  the  entire  number  of  images  seen  in  the  kaleidoscope,  including 
the  object  itself,  will  be  equal  to  360°  divided  by  the  angle  contained 
between  the  mirrors.  If  the  inclination  of  the  mirrors  is  60°,  the  num- 
ber of  images,  including  the  object,  will  be  six  ;  if  the  inclination  is  45°, 
the  number  will  be  eight;  and  for  30°  every  object  will  appear  as 
twelve.  If  the  inclination  of  the  mirrors  is  small,  the  images  formed 
by  many  successive  reflections  become  too  faint  to  be  distinctly  seen. 

425.  Hadley's  sextant  is  an  instrument  depending  on  reflection 
from  two  mirrors,  and  used  chiefly  by  seamen  for  measuring  the  alti- 
tudes and  angular  distances  of  the  heavenly  bodies. 

Two  mirrors,  a  and  &,  fig.  326,  are  so  mounted  that  the  angle  of  inclination 

can  be  varied  at  pleasure.     The  mirror  a  is  attached  to  a  movable  arm,  a  C, 

yhich  turns  about  the  centre  of  the  graduated 

arc  A  B.     This  arm  carries  at  C  a  vernier  by 

which  minute  divisions  of  the  graduated  arc 

are   easily    distinguished.     The   mirror  b  is 

firmly  attached  to  the  frame  of  the  instru- 
ment, and  the  outer  portion  has  the  silvering 

removed,  so  that  an  eye  placed  at  e  sees  the 

distant  horizon,  or  any  other  object  to  which 

it   is   directed,    in   its    true    position.      The 

mirror  a  is  turned  with  the  index  arm  a  C, 

until  any  other  object,  as  the  sun,  moon,  or  a 

star,  whose  light  is  twice  reflected  in  the 
^directions  S  a  b  e,  appears  to  coincide  in 
direction  with  the  horizon  or  other  object,  H, 

seen  by  direct  light,  from  which  its  angular 

distance  is  to  be  measured.     The  telescope  at 

e  is  used  to   facilitate  accurate  observation. 

The  divisions  of  the  graduated  arc  and  vernier  are  also  read  by  the  aid  of  a 

magnifying  lens,  not  shown  in  the  figure.     The  deviation  of  the  ray  S  a,  after. 

being   twice   reflected,  is,  by   §    423,   twice   the   angle  contained  between   the 

mirrors,  or   twice   the  degrees  contained   between  A  C  ;    half  degrees    on   the 

scale  are  therefore  marked  as  whole  degrees.     The  reading  by  the  vernier  gives 

the  altitude  or  angular  distance  of  the  observed  object. 

III.  REFLECTION  AT  CURVED  SURFACES. 

426.  Concave  and  convex  spherical  mirrors. — If  an  arc  of  a 

circle,  M  N,  fig.  327,  is  made  to  revolve  around  a  line,  ACL,  drawn 

through  its  centre  of  figure  A,  and  327 

its   centre  of  curvature   C,  it  will 

generate   a   curved  surface,  which 

will  be  a- segment  of  the  surface  of    — — 

a  sphere.  Internally,  such  a  polished   ~_ 

surface  is  called  a  concave  mirror, 

and  externally  a  convex  mirror.     The  line,  A  C,  is  called  the  principal 

axis  of  the  mirror,  and  any  other  line  drawn  through  the  centre  of 


JL 


OPTICS.  309 

curvature,  C,  is  called  a  secondary  axis.  The  angle  M  C  N  is  called 
the  angular  aperture  of  the  mirror.  A  section  made  by  a  plane  pass- 
ing through  the  principal  axis,  A  C,  is  called  the  principal  section,  or 
a  meridional  section. 

The  theory  of  reflection  from  curved  mirrors  is  easily  deduced  from  the  laws 
of  reflection  by  plane  mirrors.  Every  point  in  the  curved  mirror  may  be 
regarded  as  a  point  in  a  plane  mirror  so  situated  that  its  perpendicular,  where 
the  ray  of  light  falls  upon  it,  coincides  with  the  radius  of  the  curved  mirror  at 
that  point. 

A  line  drawn  from  any  point  in  a  spherical  mirror  to  the  centre  of 
curvature,  will  be  perpendicular  to  the  mirror  at  that  point,  and  also 
perpendicular  to  any  plane  mirror  touching  the  curved  mirror  at  that 
point. 

427.  Foci  of  concave  mirrors  for  parallel  rays. — The  focus  of 
a  concave  mirror  is  the  point  towards  which  the  reflected  rays  con- 
verge. 

(a]  Parallel  rays  falling  near  the  axis  of  a  concave  mirror,  fig.  327, 
converge,  after  reflection,  to  a  point  equidistant  between  the  mirror 
and  the  centre  of  the  sphere,  of  which  the  mirror  forms  a  part.  This 
point  is  called  the  principal  focus. 

Rays  of  light  emanating  from  the  principal  focus  of  a  concave  mirror, 
will  be  reflected  parallel  to  each  other. 

Demonstration.— The  lines  C  M,  C  B,  C  D,  fig.  327,  drawn  from  the  centre  of 
curvature  of  the  mirror,  M  N,  are  perpendicular  to  the  mirror  at  those  points. 
The  parallel  rays,  H  B,  G  D,  will  converge,  after  reflection,  to  the  point  F.  It 
is  evident  that  the  angle  of  reflection,  CDF,  for  any  ray,  will  be  equal  to  the 
angle  of  incidence,  GDC;  but  G  D  C  is  equal  to  D  C  F,  which  is  the  alternate 
angle  formed  by  a  line  D  C,  meeting  two  parallel  lines,  G  D,  LA;  hence  in  the 
triangle,  C  F  D,  the  angles,  F  C  D  and  F  D  C,  are  equal,  and  therefore  the  sides, 
C  F  and  F  D,  are  equal.  If  the  point,  D,  gradually  approaches  the  point,  A, 
C  F  -)-  F  D  will  differ  less  and  less  from  C  A,  until  their  sum  will  be  sensibly  equal 
to  C  A,  and  F  A  will  be  sensibly  equal  to  one-half  of  C  A  ;  or  the  focus  of  parallel 
rays,  after  reflection  from  a  concave  mirror,  will  be  equal  to  one-half  the  radius 
of  curvature.  If  the  point  of  incidence,  D,  recedes  from  A  towards  M,  or  N,  the 
point,  F,  will  gradually  approach  A,  or  the  focal  distance  will  diminish.  A 
concave  spherical  mirror  will  therefore  reflect  parallel  rays  to  a  single  focal 
point  only  when  the  diameter  of  the  mirror  is  small.  Practically  it  is  found  that 
the  diameter  of  the  mirror,  or  the  angular  aperture,  M  C  N,  should  not  exceed  8 
or  10  degrees. 

428.  Foci  of  diverging  rays. — If  rays  of  light  falling  upon  a  con- 
cave mirror  diverge  from  a  point  beyond  the  centre  of  curvature,  they 
will  converge,  after  reflection,  to  a  point  between  the  principal  focus 
and  the  centre  of  curvature.  This  point  of  convergence  is  called  the 
conjugate  focus,  because  the  distance  of  the  radiant  point  and  the  focus 
29 


310  PHYSICS    OP    IMPONDERABLE    AGENTS. 

to  which  the  rays  converge,  after  reflection,  have  a  mutual  relation  to 
each  other.  328 

Let  rays  diverging  from  a  point,  It, 
fig.  328,  fall  upon  a  concave  mirror,  the 
angle  of  incidence,  L  K  C,  will  be  smaller  A| 
than  S  K  C,  which  is  the  angle  of  incidence 
for  parallel  rays  falling  upon  the  mirror  at 
the  same  point.  The  angle  of  reflection, 

C  K  I,  will  also  be  smaller  than  C  K  F ;  hence  the  ray,  L  K,  will  be  so  reflected 
as  to  cross  the  principal  axis  at  a  point,  I,  between  F,  the  principal  focus,  and 
C,  the  centre  of  curvature  of  the  mirror. 

The  relation  between  the  radiant  point  and  point  of  convergence  is  easily 
determined.  In  the  triangle  L  K I  the  radius  K  C  bisects  the  angle  L  K  I,  hence 
by  a  well  known  principle  of  geometry  : — 

CL        1C 
CL:*C  =  LK:,K    ,.    —  =  -- 

When  the  incident  pencil  is  very  small,  L  K  =  LA,  and  I K  =  I  A,  very 
nearly,  hence  we  have, 

CL       1C 

—  =  -nearly. 

Let  LA  =  «,  lA  =  v,  C  A  =  radius  of  the  mirror  =  r,  and  A  F  =  the 

r 
principal  focal  length  =f.     Theny  =  — ,  and  by  substituting  these  values,  the 

above  equation  becomes 

tt_r       r__w  1         1         1         I 

= •   Dividing  by  r  we  have •  = : 

«  v  r        u        v        r 


„_/       2«—  r 

From  this  formula  we  may  deduce  the  value  of  v,  or  the  focus  of  reflected 
rays,  whatever  may  be  the  point  of  divergence  of  the  incident  rays. 

If  the  luminous  point  is  removed  to  Z,  the  reflected  rays  will  meet  at 
L.  If  the  luminous  point  is  placed  at  the  centre  of  curvature,  C,  all 
the  rays  will  fall  perpendicularly  upon  the  mirror,  and  be  reflected  back 
to  the  point  C,  from  whence  they  came. 

If  the  luminous  point  is  situated  between  the  centre  of  curvature  and 
the  principal  focus,  the  conjugate  focus  will  be  removed  beyond  the 
centre  of  curvature,  and  become  more  and  more  distant  as  the  luminous 


OPTICS.  311 

point  approaches  the  principal  focus.  When  the  luminous  point  arrives 
at  the  principal  focus,  the  conjugate  focus  will  be  removed  to  an  infinite 
distance,  or,  in  other  words,  the  reflected  rays  will  become  parallel. 
While  the  radiant  point  has  removed  from  C  to  F,  the  conjugate  focus 
has  removed  from  C,  to  an  infinite  distance. 

429.  Converging   rays. — Virtual   focus. — If   the    radiant  point 
passes  from  the  principal  focus,  F,  towards  the  mirror,  as  in  fig.  329, 
it  is  evident  that  the  reflected  rays  will  diverge,  as 

though  emanating  from  a  point  Z,  behind  the  mirror, 
sailed  the  virtual  focus. 

When  the  radiant  point  is  near  the  principal 
focus,  between  it  and  the  mirror,  the  virtual  focus 
of  the  divergent  reflected  rays  will  be  at  a  very 
great  distance.  As  the  radiant  point  continues  to  approach  the  mirror, 
the  virtual  focus  also  approaches  it.  While  the  radiant  point  passes 
from  the  principal  focus  to  the  mirror,  the  conjugate  virtual  focus,  or 
point  from  which  the  reflected  rays  appear  to  diverge,  passes  from  an 
infinite  distance  behind  the  mirror,  to  the  surface  of  the  mirror,  or  to 
the  radiant  point  itself. 

These  propositions  may  be  easily  proved  by  giving  to  u  appropriate 
values  in  the  formula. 

430.  Secondary  axes. — Oblique  pencils. — If  the  luminous  point, 
L,  fig.  330,  is  not  situated  in  the  principal  axis  of  the  mirror,,  a  line 
drawn  from  the  radiant  point  through  the  centre  330 

of  curvature,  as  L  C  B,  will  constitute  a  second- 
ary axis,  and  the  focus  of  the  oblique  pencil  of 
rays  diverging  from  L,  will  be  found  in  this 
secondary  axis.  In  the  same  manner  we  may 
draw  secondary  axes,  and  determine  the  foci, 
whether  real  or  virtual,  for  any  number  of  points  in  a  luminous  object. 

431.  Rule  for  conjugate  foci  of  concave  mirrors. — Multiply  tlie 
distance  of  the  radiant  point  from,  the  mirror,  by  the  radius  of  curvature, 
and  divide  this  product  by  twice  the  distance  of  the  radiant  point,  minus 
the  radius  of  curvature  oftlie  mirror,  and  tlie  quotient  will  be  the  distance 
of  the  conjugate  focus  from  the  mirror. 

If  the  quotient  given  by  this  rule  is  negative,  or  if  twice  the  distance  of  the 
radiant  point  is  less  than  the  radius  of  curvature,  the  conjugate  focus  will  be  a 
virtual  focus  behind  the  mirror,  and  the  reflected  rays  will  diverge. 

432.  Convex  spherical  mirrors. — The  effects  attending  the  reflec- 
tion of  diverging,  converging,   or  parallel   rays  of  light   by  convex 
reflectors,  are,  in  general,  the  opposite  of  tlie  effects  produced  by  con- 
cave  reflectors.     The   foci  of  parallel    and   diverging   rays  of  light, 


312 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


reflected  by  a  convex  reflector,  are  at  the  same  distance  as  for  concave 
mirrors,  but  they  are  situated  behind  the  reflector,  and  are,  hence,  only 
virtual  foci.  Light  converging  towards  any  point  behind  a  convex 
mirror,  more  distant  than  the  centre  of  curvature,  will  diverge,  after 
reflection,  from  a  virtual  focus  between  the  centre  of  curvature  and  the 
principal  focus.  Rays  converging  toward  the  principal,  virtual  focus, 
will  be  reflected  parallel ;  but  rays  converging  towards  a  point  nearer 
to  the  mirror  than  the  principal  focus,  will  be  reflected  to  a  real  focua 
in  front  of  the  convex  reflector.  331 

These  phenomena  will  be  readi-  H  ^\ 

ly  understood  by  an  examina- 
tion  of  fig.  331.  ffhe  ray  S  I  is 
reflected  in  the  direction  F I  M ; 
LE  is  reflected  in  the  direc- 
tion I  E  G,  and  reciprocally, 
G  E  is  reflected  in  the  direction  E  L,  and  M  I  in  the  direction  I  S. 

The  formula  for  the  convex  mirror  may  be  determined  in  the  same  manner  as 
for  the  concave  mirror,  or  we  may  deduce  it  at  once  from  the  formula  for  the 
concave  mirror.  Since  the  focus  of  parallel  rays  is  behind  the  convex  mirror, 
if  we  call  the  value  of  /  for  the  concave  mirror  positive,  it  must  be  negative  for 
the  convex  mirror.  If  therefore  we  insert  — f  instead  of  f  in  the  formula  for 
the  concave  mirror,  it  will  become  for  the  convex  mirror : — 


from  which  it  appears  that  the  value  of  v  must  also  be  negative  when  u  is  posi- 
tive, that  is,  u  and  v  are  on  opposite  sides  of  the  mirror.  Now  by  putting  —  v 
instead  of  v  in  the  above  formula,  it  will  represent  the  absolute  value  of  the 
focus  of  reflected  rays  reckoned  on  the  back  side  of  the  convex  mirror,  and  we 

111  /« 

have  for  the  convex  mirror,       -  = (--     .'.     v  = . 

v      f        u  /-fit 

433.  Images  formed  by  concave  mirrors. — The  principles  already 
explained  enable  us  to  understand  the  formation  of  images  by  concave 
mirrors.  Let  A  B,  fig.  332,  represent  an  object  placed  before  a  concave 
mirror,  beyond  its  centre  of  333 

curvature.  The  lines,  A  C 
and  B  C,  drawn  through  the 
centre  of  curvature  from  the 
extremities  of  the  object,  are 
the  secondary  axes  in  which 
the  extremities  of  the  image,  a  b,  will  be  formed,  at  a  distance  from  the 
Miirror  equal  to  the  conjugate  foci  for  the  extreme  points  of  the  object. 


OPTICS.  313 

This  image  is  real,  inverted,  smaller  than  the  object,  and  placed  between 
the  centre  of  curvature  and  the  principal  focus. 

If  a  b  is  regarded  as  the  object,  placed  between  the  centre  of  curva- 
ture and  the  principal  focus,  an  enlarged  image  will  be  formed  at  A  B. 
If  the  object  is  placed  at  the  principal  focus,  no  image  will  be  formed, 
because  the  rays  from  each  point  of  the  object  will  be  reflected  parallel 
to  an  axis  drawn  through  the  centre  of  333 

curvature   from    the  points  where  they 
vriginate. 

If  the  object,  A  B,  is  placed  entirely  on 
one  side  of  the  principal  axis,  as  in  tig. 
333,  it  is  evident  that  its  image,  a  6,  will  be  formed  on  the  opposite  side 
of  the  principal  axis. 

434.  Virtual  images. — If  the  object,  A  B,  fig.  334,  is  placed  between 
the  mirror  and  the  principal  focus,  the  incident  rays,  A  D,  A  K,  take, 
after  reflection,  the  directions,  D  I,  K  H,  and 

their  prolongations  backward,  form  at  a,  a 
virtual  image  of  the  point  A.     In  the  same  «., 
manner  the  image  of  B  is  formed  at  b,  so 
that  the  image  of  A  B  is  seen  at  a  b.     The 
image,  in  this  case,  is  a  virtual  image,  erect,   |~ 
and  larger  than  the  object. 

From  the  preceding  illustrations,  it  is  evident,  that,  when  an  object 
is  placed  before  a  concave  mirror,  more  distant  than  the  centre  of 
curvature,  the  image  is  real,  but  inverted,  and  smaller  than  the  object; 
as  the  object  approaches  the  centre  of  curvature,  the  image  enlarges 
and  becomes  equal  to  the  object  and  coincides  with  it ;  when  the  object 
approaches  nearer  to  the  mirror  than  the  centre  of  curvature,  the  image 
becomes  larger  than  the  object,  and  more  distant  from  the  mirror. 
When  the  object  arrives  at  the  principal  focus,  the  image  becomes 
infinitely  distant,  and  disappears  entirely:  wrhen  the  object  approaches 
nearer  to  the  mirror  than  the  principal  focus,  an  erect  virtual  image, 
larger  than  the  object,  appears  behind  the  mirror. 

435.  Formation  of  images  by  convex  mirrors. — Let  A  B,  fig. 
335,  be   an   object  placed   before   a  convex  335 

ziiirror,  at  any  distance  whatever.  If  we 
draw  the  secondary  axes,  AC,  B C,  it  fol- 
lows,  from  what  has  been  said  (433)  concern- 
ing  the  construction  of  foci  of  convex  mirrors, 
that  all  the  rays  emitted  from  the  point  A,  diverge  after  reflection,  and 
that  their  prolongations  backward  converge  to  a  point,  a,  which  is  a 
29* 


314  PHYSICS    OF    IMPONDERABLE    AGENTS. 

virtual  image  of  the  point  A.     In  the  same  manner,  rays  emitted  from 
the  point  B,  form  a  virtual  image  of  that  point  in  6. 

Whatever  may  be  the  position  of  an  object  before  a  convex  mirror, 
the  image  is  always  formed  behind  the  mirror,  erect  and  smaller  than 
the  object. 

436.  General  rule  for  constructing  images  formed  by  minors. 
— To  construct  the  image  of  a  point ;  1.  Draw  a  secondary  axis  front 
that  point ;   2.   Take  from  the  given  point  any  incident  ray  whatever ; 
join  the  point  of  incidence  and  the  centre  of  curvature  of  the  mirror  by  a 
right  line;  this  will  be  the  perpendicular  at  that  point,  and  will  show  the 
angle  of  incidence;  3.  Draw  from  the  point  of  incidence,  on  the  other 
side  of  the  perpendicular,  a  right  line,  which  shall  make  with  it  an  angle 
equal  to  the  angle  of  incidence.    This  last  line  represents  the  reflected  ray, 
which,  being  prolonged  until  it  crosses  the  secondary  axis,  determines  the 
place  where  the  image  of  the  given  point  is  formed.     4.  Determine  the 
position  of  any  other  point  in  the  object  in  the  same  manner. 

437.  Spherical   aberration    of    mirrors. — Caustics. — The   rays 
from  any  point  of  an  object,  placed  before  a  spherical  mirror,  concave 
or  convex,  do  not  converge  sensibly  to  a  single  point,  unless  the  aperture 
of  the  mirror  is  limited  to  8°  or  10°.     If  the  aperture  of  the  mirror  is 
larger  than  this,  the  rays  reflected  from  the  borders  of  the  mirror  meet 
the  axis  nearer  to  the  mirror  than  those  which  are   reflected   from 
portions  of  the  mirror  very  near   to   the   centre.  336 
There  results,  therefore,  a  want  of  clearness  or  dis- , 

tinctness  in  the  image,  which  is  designated  spherical 
aberration  by  reflection. 

The  reflected  rays  cross  each  other  successively, 
two  and  two,  and  their  points  of  intersection  form  in 
space  a  brilliant  surface,  called  a  caustic  by  reflec- 1 
tion,  curving  towards  the  axis,  as  shown  in  fig.  336, ' 
where  C  is  the  centre  of  curvature,  F  the  principal  focus,  and  d  the 
centre  of  figure. 

§  3.    Dioptrics,  or  Refraction  at  Regular  Surfaces. 

I.     DEFINITIONS. 

438.  Prisms  and  lenses,  are  bodies  having  certain  regular  forms, 
sections  of  which  are  shown  in  fig.  337 

337. 

A  prism  is  a  solid  having  three 
or  more  plane  faces,  variously  in- 
clined to  each  other,  as  shown  at  A,  fig.  337.  The  angle  formed  by 


OPTICS.  315 

the  faces,  A  R,  A  S,  is  the  refracting  angle  of  the  prism.     For  some 
purposes  prisms  are  used  having  more  than  three  plane  faces. 

A  lens  is  a  portion  of  some  transparent  substance,  as  glass  or  crystal, 
of  which  the  surfaces  are  generally  either  both  spherical,  or  one  plane 
and  the  other  spherical.  The  axis  of  a  lens  is  the  line  joining  the 
centres  of  the  spherical  surfaces  when  both  are  curved,  and  the  line 
perpendicular  to  the  plane  surface  which  passes  through  the  centre  of 
the  other  surface  when  one  side  is  plane.  When  the  surfaces  of  lenses 
are  of  different  kinds,  they  are  named  in  reference  to  the  side  on  which 
the  light  first  falls. 

If  the  figures  C,  D,  E,  F,  G,  II,  I,  were  revolved  around  the  axis, 
M  N,  they  would  severally  describe  the  solid  lenses  they  are  intended 
to  represent. 

In  explaining  the  properties  of  lenses,  and  showing  the  progress  of 
light  through  them,  we  make  use  of  such  sections  as  are  shown  in  the 
figure,  for  every  plane  passing  through  the  axis  has  the  same  form,  and 
what  is  true  of  one  section  is  true  of  all. 

A  plane  glass,  B,  is  a  plate  of  glass  having  two  plane  surfaces,  a  b, 
c  d,  parallel  to  each  other. 

A  sphere,  shown  in  section  at  C,  has  all  parts  of  its  surface  equally 
distant  from  a  certain  point  within,  called  the  centre. 

A  double  convex  lens,  D,  is  a  solid  bounded  by  two  convex  surfaces, 
which  are  generally  spherical. 

A  plano-convex  lens,  E,  has  its  first  surface  plane,  and  the  other 
convex. 

A  double  concave  lens,  F,  has  two  concave  surfaces  opposite  to  each 
other. 

A  plano-concave  lens,  G,  has  its  first  surface  plane,  and  the  other 
concave. 

A  meniscus,  shown  at  H,  has  one  surface  convex,  and  the  other  con- 
cave, their  curvatures  being  such  that  the  two  surfaces  meet,  if  con- 
tinued. As  this  lens  is  thicker  in  the  centre  than  at  its  edges,  it  may 
be  regarded  as  a  convex  lens. 

A  concavo-convex  lens,  shown  at  I,  has  its  first  surface  concave,  and 
the  other  convex,  but  the  curvatures  are  such  that  the  surfaces,  if  con- 
tinued,  would  never  meet.  As  therefore  the  concavity  exceeds  the 
convexity,  it  may  be  regarded  as  a  concave  lens. 

II.  REFRACTION  AT  PLANE  SURFACES. 

439.  Refraction  by  prisms.— If  a  ray  of  light,  In,  fig.  338,  falls 
obliquely  upon  a  transparent  medium,  whose  opposite  plane  faces  are 
not  parallel,  the  ray  will  be  refracted  at  the  first  surface,  and  take 


316 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


338 


a  direction  nearer  to  the  perpendicular.  Now  if  the  position  of  the 
incident  ray,  and  the  inclination  of  the  faces  of  the  medium,  are  as 
shown  in  the  figure,  it  is  obvious  that  the  emergent 
ray,  n'  I' ',  will  be  turned  still  further  from  its  original 
direction.  It  is  evident  that  any  other  position  of  the 
second  refracting  surface  would  cause  a  correspond- 
ing alteration  in  the  direction  of  the  emergent  ray. 

Let  a  b  c,  fig.  339,  be  a  section  of  a  triangular  prism,  I  n  a 
ray  of  light  incident  at  n,  One  the  perpendicular  at  that 
point,  n  n'  will  be  the  course  of  the  ray  of  light  through  the 
prism,  and  n'  I'  the  emergent  ray.  V 

If  the  prisrn  is  more  dense  than  the  surrounding  medium,  the  light  will  enter 
the  prism,  whatever  may  be  the  angle  of  incidence,  but  if  the  angle  of  incidence, 


will  fall  more  obliquely  upon  the  second  sur- 
339  340 


I  n  0,  diminishes,  then  the  ray,  n  n', 
face  of  the  prism,  until  it  may  arrive 
at  an  inclination  where  it  will  suf- 
fer total  internal  reflection. 

If  the  incident  ray,  I  n,  fig.  340, 
falls  upon  the  prism  at  such  an 
angle,  that,  after  refraction,  it  takes 
the  direction,  n  n',  parallel  to  a  c, 
the  base  of  the  prism,  the  angles  at  which  it  enters  and  leaves  the  prism  will  bo 
equal,  and  the  deviation  of  the  emergent  ray  from  the  course  of  the  incident 
ray,  will  be  the  least  possible.  The  ray,  I'  n,  will  emerge  in  the  direction  mp', 
and  I"  n  will  emerge  in  the  direction  op",  each  deviating  more  from  the  direc- 
tion of  the  incident  ray  than  n'  p  deviates. 

If  a  candle  is  viewed  through  a  triangular  prism,  on  slowly  turning 
the  prism  about  its  axis,  a  certain  position  will  be  found  where  the 
apparent  position  of  the  candle  differs  least  from  its  real  position.  In 
whichever  direction  the  prism  is  now  turned,  the  difference  between  the 
real  and  apparent  position  of  the  candle  increases. 

440.  Method  of  determining   the    index   of  refraction. — Let 

I  n  n'  p,  fig.  341,  be  the  direction  of  the  ray  of  light  when  the  deviation  caused 
by  the  prism  is  a  minimum.  Draw  h  I  parallel  to  the 
incident  ray,  In,  and  r  b  o  parallel  to  the  emergent' ray, 
n'  p.  Let  D  =  h  b  r,  the  entire  deviation  caused  by  the 
prism ;  d  =  h  b  n,  the  complement  of  the  angle  of  inci- 
dence ;  g  —  a  b  c,  the  refracting  angle  of  the  prism  ; 
q  =  n'  b  o  =  c  n'  p,  the  complement  of  the  angle  of  emer- 
gence. In  this  case  the  angles  of  incidence  and  emer- 
gence are  equal,  hence  d  =  q  =  90°  —  i,  i  being  the  ajam' 
angle  of  incidence,  D  =  180°  —  d  —  g  —  q ;  substituting  in  this  equation  the 
values  of  d  and  q,  we  have  D  =  2  i  —  g,  and  i  =  i  (D  -f-  g).  Let  x  and  y,  as 
in  fig.  339,  represent  the  angles  formed  with  the  perpendiculars  by  the  ray 
traversing  the  prism,  x  -f-  y  =  g,  and  when  the  angles  of  incidence  and  emer- 
gence are  equal,  x  =  y.  If  n  equals  the  index  of  refraction,  we  shall  have: — 

sin.  i  sin.  J  (D  -\-  g) 

n  =  _ f      or,      n  =  :  — . 

sin.  x  sin.  £  y 


OPTICS. 


317 


Now  when  the  angle  of  minimum  deviation  and  the  refracting  angle  of  the 
prism  are  measured,  this  formula  enables  us  at  once  to  determine  the  index  of 
refraction.  In  this  manner  the  index  of  refraction  of  any  substance  is  easily 
determined. 

441.  Plane  glass. — A  ray  of  light  passing  through  a  plane  glass,  or 
any  other  medium  of  uniform  density  bounded  by  parallel  faces,  will 
have  the  emergent  ray  parallel  to  the  incident  ray.  Parallel  rays  of 
light  passing  through  plane  glass  are  parallel  after  emergence,  and  the 
emergent  rays  are  parallel  to  the  incident  rays. 

If  the  two  surfaces  of  the  transparent  medium  are  parallel,  it  is  evident  that 
the  ray  of  light  traversing  the  medium  will  make  equal  angles  with  the  perpen- 
dicular at  both  surfaces.  Let  7  be  the  angle  of  incidence,  K  the  angle  of  refrac- 
tion at  the  first  surface,  and  also  the  internal  angle  of  incidence  on  the  second 
surface,  and  E  the  angle  of  emergence.  Then,  if  n  represents  the  index  of 
refraction,  we  shall  have : — 


Sin.  7  =  n  sin.  R  =  sin.  E 


=  E: 


Or  the  angles  of  incidence  and  emergence  are  equal,  and  the  incident  ray  is 
parallel  to  the  emergent  ray.  The  same  is  true  for  any  number  of  rays ;  hence 
also  parallel  incident  rays  will,  after  passing  through  the  glass,  emerge  parallel. 

Let   M  N,    fig.   342,    be   a   plane    glass,    or   any  medium  342 

bounded  by  parallel  surfaces,  the  rays  A  B,  A'  B',  will  be 
refracted  towards  the  perpendicular,  on  entering  the  medium, 
and  emerging  at  C,  C,'  they  will  be  refracted  from  the  per- 
pendicular, and  take  the  directions,  C  D,  C'  D',  parallel  to 
each  other,  and  parallel  to  their  directions  before  entering 
the  medium.  The  displacement,  A  a,  A'  a',  is  the  lateral 
aberration  produced  by  transmission  through  a  homogeneous  medium  bounded 
by  parallel  surfaces.  The  amount  of  lateral  aberration  increases  with  the  thick- 
ness of  the  medium,  and  it  also  increases  with  the  obliquity  of  the  incident  rays. 

442.  Light  passing  through  parallel  strata  of  different  media. 

— It  is  found  by  experiment  that  if  a  ray  of  light  passes  through  a 
series  of  plates  of  dense  media,  all  the  refracting  surfaces  being  parallel 
planes,  that  the  emergent  ray  is  parallel  to  343 

the  incident  ray.  It  therefore  follows,  that 
the  direction  of  the  ray  in  passing  through 
any  one  of  the  plates  is  parallel  to  the  course 
it  would  have  taken  if  it  had  entered  the 
plate  directly,  or  if  that  plate  had  been  the 

first  in  the  series. 

/'*>  A 

/  V 
SQ 

dense  media,  the  second  medium  being  more  dense 

than  the  first,  and  P'  D  E  Q'  the  course  of  a  ray  passing  through  the  second 
medium  without  entering  the  first ;  if  P  A  is  parallel  to  P'  D,  C  Q  will  be  parallel 
to  E  Q',  and  also  B  C  will  be  parallel  to  D  E.  We  may  consider  the  ray  of 


318  PHYSICS    OF   IMPONDERABLE    AGENTS. 

light  as  passing  in  the  opposite  direction,  and  make  n"  the  index  of  refraction 
for  the  medium  traversed  by  the  ray  C  B,  then  sin.  Q  C  p'  =  n"  sin.  B  C  p, 
hence  the  angle  B  C  p  depends  only  on  the  direction  of  the  emergent  ray  C  Q, 
parallel  to  the  incident  ray  PA,  and  upon  the  index  of  refraction,  n",  of  the 
lower  medium.  Let  m  Am',  nB  n',  p  C  p',  be  perpendicular  to  the  refracting 
surfaces  at  A,  B,  and  C,  and  let  n  be  the  absolute  index  of  refraction  for  the 
first  medium,  n"  that  of  the  second  medium,  and  n'  the  index  of  refraction  for 
light  passing  from  the  first  medium  to  the  second  :  — 

sin.  PAm  sin.  QCV 

Then,  n  =  -  j  n"  =  -  —  ; 

sin.  BAm/  sin.  BCp 

sin.  AB>i         sin.  BAw*'        sin.  BAm'        sin.  QCy        n" 
~~  sin.  CB;t'          sin.  BCp          sin.  PAm  ^  sin.  ECp          n  ' 

Hence:  The  index  of  refraction  for  light  passing  from  one  medium  to 
another,  is  equal  to  the  index  of  refraction  of  the  second  medium  divided 
by  the  index  of  refraction  of  the  first  medium. 

443.  Pencils  of  light  refracted  at  plane  surfaces.  —  When  a 
pencil  of  light  falls  upon  a  plane  surface  of  any  dense  medium,  it  is  so 
changed  by  refraction  that  a  diverging  pencil  is  made  to  diverge  from 
a  focus  without  the  medium  more  distant  from  the  dense  medium  than 
before  it  entered  it;  and  a  converging  pencil  is  made  to  converge  to  a 
focus  within  the  dense  medium  more  distant  from  its  surface  than  before. 

Let  Q,  fig.  344,  be  the  focus   of  incident  344 

rays,  and  Q  A  B    the   ray  which   enters  the 
medium  perpendicularly  to  its  surface,  suffer-  /• 
ing  no  deviation.     Let  Q  P  be   any  oblique  \ 
ray  meeting  the  surface  at  P  ;  let  N  P  N'  be  / 
drawn  perpendicular  to  the  refracting  surface  I 
at  P,  it  will  also  be  parallel  to  Q  A  B  ;  let  \ 
P  R  be  the  refracted  ray  which  being  extended 
backward  meets  the  line  A  Q  at  q'.     The  angle  of  incidence  QPN  =  PQA,  and 
the  angle  of  refraction  RPN'  =  Pq'A. 

sin.  QPN         sin.  PQA 


Also  the  index  of  refraction,  n  = 


- 
sin.  RPN'        sin. 


PA  PA  Pq' 

Sin.  PQA  =  —  j  sin.  Pq'A  =  -    .-.     n  =  —  . 
PQ  Pq'  PQ 

If  the  pencil  is  very  small,  PQ  =  AQ,  and  Pqr  =  Aq'  nearly,  hence 
A^'  =  n.AQ.  If  we  let  AQ  =  u,  and  Aq'  =  «',  then  u'  ==  nv,  which  determines 
the  point  q',  from  which  the  pencil  diverges  after  refraction. 

When  the  pencil  is  large,  and  P  is  so  far  from  A  that  we  cannot  consider 
QP  =  QA,  let  i  =  the  angle  of  incidence,  i'  =  angle  of  refraction  :  — 

We  have  QP  =  -^—  .;  *2'P  = 


cos.  ^  cos.  i' 

cos.  i' 
And  since  q'P  =  n.QP    .'.   u'  =  n. u. 


OPTICS. 


319 


Since  the  cosine  of  V  is  greater  than  cosine  of  i,  this  last  value  of  u'  is  greater 
than  nu,  the  first  value ;  this  shows  that  a  pencil  of  light  suffers  aberration 
when  refracted  at  a  plane  surface.  The  formula  also  shows  that  u'  is  greater 
than  u,  or  that  the  focus  of  the  pencil  after  refraction  is  more  distant  than  the 
focus  of  the  incident  rays.  If  the  pencil  of  345 

incident  rays  converges  to  a  point,  Q,  within  ^^ 

the  dense  medium,  as  in  fig.  345,  the  pencil  of 
the  refracted  rays  will  converge  to  point  qr. 
Solving  the  triangle  Q  P  q',  we  should  find  the 
same  result  as  before;  or  Aq'  =  n.AQ. 

Therefore :  When  a  pencil  of  light  is 
refracted  at  a  plane  surface,  the  focus  of 
the  refracted  rays  is  on  the  same  side  of  the  refracting  surface  as  the 
focus  of  incident  rays,  and  at  a  distance  equal  to  the  distance  of  the 
focus  of  incident  rays  multiplied  by  the  index  of  refraction. 

If  the  rays  had  been  proceeding  from  the  dense  medium  to  a  rarer 
medium,  as  from  g',  fig.  345,  or  towards  q',  fig.  344,  then  the  focus  of 
refracted  rays  would  be  at  Q,  or  nearer  to  the  refracting  surface  than 
the  focus  of  incident  rays. 

If  the  rays  proceed  from  a  dense  to  a  rarer  medium,  and  if  n  still 
represent  the  index  of  refraction  for  light  entering  the  dense  medium, 
the  index  of  refraction  for  light  passing  from  the  dense  to  the  rare 

medium  will  be  n'  =  -. 
n 

The  index  of  refraction  for  light  passing  from  air  into  water  is  n  =  f, 
and  hence  n'  =  -  =  f ,  for  light  passing  from  water  into  air. 

If  therefore  u  represents  the  actual  distance  of  an  object  below  the 
surface  of  water,  and  «'  its  apparent  distance,  u'  =  n' .u  =  f  u,  that  is, 
the  apparent  distance  below  the  surface  of  the  water  is  only  three-fourths 
of  the  real  distance ;  or  water  is  a  third  deeper  than  it  appears  to  be. 
As  every  point  in  an  object  appears  elevated  one-fourth  as  much  as  its 
distance  below  the  surface  of  the  water,  a  pole  or  cane  thrust  obliquely 
into  the  water  appears  bent,  or  broken  (406),  just  at  the  surface  of  the 
water. 

It  follows  also,  from  the  preceding  considerations,  that  an  object  im- 
mersed in  water,  or  any  other  transparent  dense  fluid,  appears  larger 
than  when  seen  in  the  air. 

As  the  atmosphere  diminishes  in  density  very  rapidly  above  the 
earth's  surface,  a  man  upon  the  top  of  a  steeple  or  tower  looks  much 
smaller  than  when  seen  at  an  equal  distance  on  level  ground ;  and  an 
object  at  the  foot  of  the  tower,  will,  for  the  same  reason,  appear  larger 
when  viewed  from  the  top  than  if  placed  at  the  top  of  the  tower  and 
viewed  from  below. 


320 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


346 


444.  Pencils  of  light  transmitted  through  plane  glass.—  When 
a  pencil  of  light  is  transmitted  through  a  plane  glass,  the  focus  of  the 
emergent  rays  is  removed  from  the  focus  of  the  incident  rays,  in  the 
direction  that  the  light  is  moving,  a  distance  equal  to  the  quotient 
arising  from  dividing  the  thickness  of  the  glass  by  the  index  of  refrac- 
tion, and  multiplying  the  quotient  by  the 
index  of  refraction  diminished  by  unity. 

Let  a  pencil  of  light  fall  upon  a  plane 
glass,  fig.  346,  so  that  Q  A  shall  be  perpen- 
dicular to  the  surface  of  the  glass,  and  Q  P  ^ 
an  oblique  ray,  Q  A  will  be  transmitted  in  the 
line  Q  A  B  without  deviation,  and  Q  P  will 
be  refracted  in  the  direction  q'  P  R,  and 
emerge  in  the  direction  q  R,  q  being  the  focus 
of  the  emergent  rays.  Let  Q  A  =  u,  q'  A  =  u'  B  q  —  v,  and  A  B  =  t  . 

By  the  formula  already  demonstrated  (443),  if  the  pencil  is  small  u'  =  nu  ; 
and  if  the  pencil  had  entered  the  other  side  of  the  plate,  converging  to  q,  we  should 
have, 

B  q'  =  n.B  q  ;    or,  t  -f-  «'  =  nv  =  t  -f-  nu, 


Hence  «  =  «  -f-  -,  by  which  the  position  of  q  is  determined.     The  displacement 

n 


of  the  focus 


=  BQ  — 


/  1    \  71  —  1 

v=  tl  I  --      =  - 
\          n  n 


Or  the  rays  diverge,  after  emerging  from  the  glass,  from  a  point  nearer  to  the 
glass  than  the  focus  of  the  incident  rays. 

If  we  suppose  the  rays  to  proceed  in  the  opposite  direction,  we  shall  have  the 
case  of  a  converging  pencil,  and  the  focus  of  the  rays  after  emergence  will  be 
more  distant  from  the  first  surface  of  the  glass  than  before.  In  both  cases  the 
focus  of  the  rays  is  removed  in  the  same  direction  that  the  light  is  proceeding. 
If  we  take  the  case  of  plate  glass,  for  which  n  =  |,  the  distance  to  which  tbe 
focus  is  removed  is  equal  to  ^  the  thickness  of  the  glass. 

III.  REFRACTION  AT  CURVED  SURFACES. 

445.  Principles  determining  the  foci  of  lenses. — A  double 
convex  lens  may  be  regarded  as  composed  of  a  number  of  segments  of 
prisms,  the  faces  of  each  347 

prism  more  inclined  as 
we  proceed  from  the 
centre  to  the  borders  of 
the  lens,  as  shown  in  fig. 
347.  The  central  por- 
tion, abed,  may  be  re- 
garded as  a  plane  glass,  having  its  faces,  a  c,  b  d,  parallel,  a  gfb  haa 
its  face,  a  g,  inclined  towards  fb,  and  the  triangular  prism,  g  hf,  has 


OPTICS.  321 

its  sides  still  more  inclined.  Now  since  the  deviation  of  any  ray  pass- 
ing through  a  prism  increases  as  the  inclination  of  the  two  faces  of  the 
prism  increases,  s  I  will  deviate  more  than  s  i,  and  if  the  form  of  each 
prism  is  properly  adjusted  to  its  distance  from  the  axis,  M  N,  the  rays, 
si  and  s  i,  or  any  number  of  rays,  may  be  made  to  meet  at  a  common 
point,  R,  in  the  axis  M  N. 

If  the  segments  of  prisms,  of  which  we  suppose  such  a  lens  to  be 
composed,  are  made  sufficiently  small,  so  that  each  face  shall  receive 
but  a  single  ray  of  light,  the  sides  of  the  successive  prisms  will  form  a 
regular  curve,  which,  if  the  lens  be  of  small  diameter,  will  correspond 
almost  exactly  with  a  segment  of  a  sphere. 

On  account  of  the  great  difficulty  of  grinding  lenses  with  any  other 
than  spherical  or  plane  surfaces,  other  forms  are  seldom  employed,  and 
require  no  discussion  in  an  elementary  work. 

446.  Small  pencils  of  light  refracted  at  a  spherical  surface 
have  the  position  of  their  348 

foci  changed. 

Let  PAP',  fig.  348,  be  a 
convex  spherical  surface  of  a 
dense  medium,  0  being  the 
centre  of  curvature  of  the 
dense  medium,  Q  the  focus  of 
the  incident  rays,  and  q'  the  focus  of  the  refracted  rays.  Let  Q  A  q'  be  the  ray 
which  enters  the  medium  perpendicular  to  its  surface,  and  Q  P  another  ray  which 
is  refracted  in  P  qf,  so  as  to  meet  Q  A  continued  in  q'.  Draw  0  P  N  perpendicular 
to  the  curved  surface  through  the  centre  of  curvature  and  point  of  incidence. 

We  shall  then  have  the  angle  of  incidence  i  ==  Q  P  N,  the  angle  of  refraction 
{'  =  q'  P  0.  Let  P  0  A  =  o,  then  from  the  triangle,  Q  0  P,  we  have  :— 

Sin.  i  :  sin.  o  =  Q  0  :  Q  P, 
and  from  the  triangle,  q'  0  P,  we  have  :  — 

Sin.  o  :  sin.  i'  =  q'  P  :  q1  0. 
By  compounding  these  proportions  we  have  :  —  • 

sin.  i  Q  0        q'  P  Q  0  q'  0 

sln77'=        -QPXfo5    °r'QP  =  >Vp' 

Since  the  pencil  of  rays  is  very  small,  we  may  consider  Q  P  =  Q  A,  and 
q'  P  =  q'  A  nearly.  Let  Q  A  =  «,  q'  A  =  u',  A  0  =  r,  then  the  last  formula 

u  -\-  r  u'  —  r  n         n  —  11 

becomes  -  =  n.  -  ,  which  may  be  reduced  to  —  =  ---  . 
u  n'  u'  r  u 

If  we  suppose  Q  to  be  situated  at  an  infinite  distance  from  A,  the  incident 
rays  will  be  parallel,  and  we  shall  have  n  =  infinity,  and  :  — 
n          n  —  1  nr 


n  n          1 

Making  this  value  of  u'  —  f,  the  general  formula  will  be  -  =  -  --  . 

u'  r         u 
30 


322          PHYSICS  OP  IMPONDERABLE  AGENTS. 

Refraction  at  a  concave  surface.  —  If  the  surface  of  the  dense  medium 
is  concave,  as  shown  in  fig.  349,  let  Q,  as 
before,  be  the  focus  of  the  incident  rays,  qr 
the  virtual  focus  of  the  refracted  rays,  and  0 
the  centre  of  curvature.  Then  the  angle  of 
incidence  i  =  Q  P  0  ;  the  angle  of  refraction 
i'  =  R  P  N  =  q'  P  0  ;  let  the  angle  P  0  A  =  o. 
In  the  triangle  Q  P  0  we  have  :— 

Sin.  t  :  sin.  o  =  Q  0  :  Q  P, 
and  from  the  triangle  qf  P  0  we  have  :  — 

*  Sin.  o  :  sin.  i'  =  q'  P  :  q'  0. 
Combining  these  proportions  we  have  :  — 

sin.*  QO       q'P  QO          $'0 

ti^i>=     "QPX^O;   °r'  QP=nyp* 

The  pencil  being  small,  we  may  put  Q  A  =  Q  P,  and  q'  A  =  q'  P  nearly,  and 
putting  Q  A  =  u,  qr  A  =  u'  ,  and  0  A  =  r,  we  have  :  — 

QO  9'0  u  —  r          «'  —  r 


^      n         n—1        I         n         I 

From  this  we  obtain    -  =  --  h  -  =  --  h  "  >  in  iW6b  /'  represents  the 
«  r  u       /'        u 

value  u'  when  u  =  infinity,  or  the  incident  rays  are  parallel. 

We  may  take  the  general  formula  for  refraction  at  a  convex  surface 
of  a  dense  medium,  and,  by  applying  proper  values  to  the  letters,  deduce 
formulae  for  all  other  cases,  whether  the  medium  be  dense  or  rare,  and 
the  refracting  surface  convex  or  concave. 

n       n—l       1 

In  the  formula  —  -.  =  ---  , 
u'  r          u 

we  have  supposed  the  value  of  u  measured  from  the  convex  surface  of 
the  dense  medium,  in  the  direction  A  Q  in  the  rarer  medium.  Calling 
this  direction  positive,  if  the  focus  of  incident  rays  were  taken  in  the 
dense  medium  u  should  be  considered  negative  ;  u'  has  been  reckoned 
positive  when  measured  in  the  dense  medium,  therefore  if  it  is  measured 
in  the  rare  medium,  as  in  the  example  of  the  concave  dense  surface,  it 
should  be  reckoned  negative  ;  we  also  reckon  r  positive  when  it  lies  in 
the  dense  medium,  and  negative  when  it  lies  in  the  rare  medium. 

Therefore,  to  apply  the  general  formula  for  a  convex  surface  of  a  dense  medium 
to  the  case  where  the  incident  rays  converge  to  a  focus  in  the  dense  medium, 

n         n  —  l         1 

we  make  u  negative,  and  the  formula  becomes    —  =  --  1  --  . 

u'  r  u 

To  adapt  the  formula  to  the  case  of  diverging  rays  refracted  at  the  concave 


OPTICS.  323 

epherical  surface  of  a  dense  medium,  we  make  r  negative,  and  the  formula  becomes 

—  =  -----  ,  which  shows  that  «'  is  essentially  negative,  or  that  it  lies 
u'  r  u 

on  the  same  side  of  the  refracting  surface  as  the  centre  of  curvature. 

71         n  —  1        1 

If  then  we  change  the  sign  of  u'  in  the  formula,  it  becomes  —  =  -  -  -  —  , 

u'  r  u 

in  which  u'  represents  the  distance  of  the  focus  of  refracted  rays  measured  in  the 
direction  of  the  rarer  medium.  This  formula  is  the  same  as  was  deduced  from 
fig.  349,  where  the  same  conditions  were  applied  to  the  analysis  of  the  diagram. 

To  apply  the  formula  to  the  case  of  rays  of  light  proceeding  from  a  dense  to 
a  rarer  medium,  we  have  but  to  let  «  and  u'  change  places  in  the  formula,  and 
change  the  sign  of  r.  Making  these  changes  in  the  general  formula  for  a  convex 
surface  of  a  dense  medium,  the  formula  for  diverging  rays  refracted  at  a  convex 
surface  of  a  rare  medium  will  become  :  — 

n  n  —  1        1          ]  n        n  —  1 

u  r  »'         u'  u  r     ' 

The  formula  for  diverging  rays,  refracted  at  a  concave   surface   of  a  rare 

medium  (by  similar  changes),  will  become  —  =  ---  . 

u'         u  r 

The  formula  for  converging  rays  issuing  from  a  convex  surface  of  a  dense 
medium,  or,  which  is  the  same  thing,  entering  a  concave  surface  of  a  rare  medium, 

n         7i  —  l        1 

will  become  --  =  ----  ;  u'  being  the  focus  of  rays  traversing  the  dense 
u'  r  v 

medium,  and  v  the  focus  of  rays  issuin^from  a  dense  medium  or  entering  a  rare 
medium. 

447.  Action  of  a  double  convex  lens  upon  small  pencils  of 
light.  —  Let  P  A  P'  B,  fig.  350,  be  a  double  convex  lens,  of  which  r  is  the  radius 
of  the  first  surface,  and  a  the  359 

radius  of  the  second  surface. 
Let  Q  be  the  focus  of  the  inci- 
dent rays,  q'  the  focus  of  the 
rays  after  refraction  at  the 
first  surface  of  the  lens,  and 
q  the  focus  of  the  rays  as  they 
emerge  from  the  second  sur- 
face of  the  lens.  Also,  let  Q  A  =  v,  A  q'  =  u',  B  q  =  r,  and  the  thickness  of 
the  lens  A  B  =  t. 

n          n  —  l        1 

After  refraction  at  the  first  surface,  we  shall  have  (446)  —  =  ---  . 

u'  r  u 

n  n  —  l        1 

By  refraction  at  the  second  surface,  we  have  (446)  —  -  —  -  =  ----  . 

B  q'  s  v 

If  the  thickness  of  the  lens  is  so  small  that  when  compared  with  B  q'  it  may  be 

neglected,  we  make  B  q'  =  A  q'  =  u'  nearly  ;  adding  the  two  preceding  equations; 

n  —  l       n  — 


I       I  I  /11\1 

•      °r  -    =(«_!)-  +  -_-. 
u        v  v  \r         s  J        u 


324          PHYSICS  OP  IMPONDERABLE  AGENTS. 

1  1  /I         1\ 

For  parallel  rays,  «=  infinity,  -  =  0,  and  -  =  (n  —  1)  I  -  -f      ) . 
«  v  \r         «/ 

Let  /=  this  value  of  v  when  the  incident  rays  are  parallel,  and  the  general 

111 

formula  for  a  double  convex  lens  becomes  —  =  — . 

v        f        u 

If  t  is  small,  but  not  small  enough  to  be  neglected,  we  shall  have  :— 
n  n  n          nt          f  nt*  \ 

-5?  =  -,^=-;?-  i-  +  (&  -  (-'  -  •>)' 

but  as  t2  must  be  very  small  compared  with  u'2,  the  quantity  contained  in  the 
brackets  may  be  neglected ;  hence, 


1                          / 1         1  \         1         nt 
Adding  and  transposing,  —  =  (n  —  1)  I   -  -| —  I (-  — ; 

V  \  1°  8    I  U  U 


And 

v 


1          1        i          t     /n  —  1        1  \2 

i_  _  [ J 

v        f        u         n    \      r  u  J 


Conclusions  deduced. — Analysis. — 1.  Parallel  rays  of  light  fall- 
ing upon  a  convex  lens,  A  B,  fig.  351,  will  be  refracted  to  some  point, 
as  F,  on  the  other  side  of  p  351 

the  lens.     The    distance  of  A 

the  focus,  F,  from  the  lens, 
will  depend  upon  the  amount 
of  curvature,  and  also  upon 
the  refractive  power  of  the  substance,  of  which  the  lens  is  composed. 
If  the  two  surfaces  of  the  lens  have  the  same  curvature,  and  the  index 
of  refraction,  as  for  ordinary  glass,  is  one  and  a  half,  the  focus  of 
parallel  rays,  called  the  principal  focus,  will  be  at  a  distance  from  the 
lens  equal  to  the  radius  of  curvature  of  either  surface  of  the  lens. 

1  /I        1  \       1  3 

In  the  formula  —  =  (n  —  1)  [  -  -j —  1 ,  let  n  =  -,  the  index  of  refrac- 

r  \r        e  /        u 

tion  for  ordinary  glass,  then  since  the  incident  rays  are  supposed  to  be  parallel, 

«  =  oo,  and  -  =  0,  and  if  the  two  surfaces  of  the  lens  have  the  same  curvature, 
u 

r  =  «,  and  the  formula  becomes  —  =  —  ( j ]          -    .*.    v  =  r,  or   F   the 


1         1/1         1\         1 

—  =  —  I  --  1  --  I      ;  —    .*.    v  = 
v         2\r^rJ         r 


focus  of  parallel  rays  is  at  a  distance  from  the  lens  equal  to  the  radius  of 
curvature. 


OPTICS.  325 

2.  Diverging  rays. — If  the  rays  falling  upon  the  lens  come  from  a 
point,  R,  at  a  distance  from  the  lens  equal  to  twice  the  principal  focus, 
they  will  converge  to  a  point,  S,  at  an  equal  distance  on  the  other  side 
of  the  lens. 

It  will  be  easily  seen  from  fig.  351,  that  the  angles,  X  and  Z,  are  equal  to 
each  other  (being  the  alternate  angles  formed  by  the  straight  line,  R  A,  meeting 
two  parallel  lines),  and  also  that  the  angles,  X  and  0,  are  equal.  In  the 
triangle,  ASF,  the  sides,  F  A  and  F  S,  are  equal,  hence  the  angles,  0  and  Y, 
are  equal,  and  Y  equals  Z,  therefore  if  the  incident  ray  is  bent  inward  to  a  dis- 
tance represented  by  the  angle,  Z,  the  refracted  ray  must  be  bent  outward  by  an 
equal  angle,  Y,  by  which  means  the  radiant  point  is  removed  from  F,  the  princi- 
pal focus  of  parallel  rays,  to  S,  which  is  at  double  the  distance  of  F. 

The  formula  shows  the  same  thing.  Making  u  =  2r,  we  find  v  =  2r. 
If  the  radiant  point  is  taken  more  distant  than  R,  as  at  V,  fig.  352,  the 

352 


conjugate  focus  will  be  removed  from  S,  to  some  point,  T,  between  S 
and  the  principal  focus. 

The  formula  will  then  give  —  =  -  —     ,     ,.   ;  —  ]>  n— ;   or  v  <  2r. 
v       r       t*  >  2r '  »       2r ' 

3.  Converging  rays. — If  rays  of**light  falling  upon  the  lens,  A  B,  fig. 
353,  converge  towards  a  point,  V,  be-  353 

fore  refraction,  they  will  converge, 
after  refraction,  towards  a  point,  T, 
between  the  principal  focus,  F,  and  the 
lens.  Conversely,  if  rays  of  light 
diverge  from  a  point,  T,  between  the 
lens  and  its  principal  focus,  they  will  diverge  after  passing  through 
the  lens,  from  a  virtual  focus,  V,  more  distant  than  the  principal  focus. 
In  the  first  case  u  becomes  essentially  negative,  and  with  the  same 

values  of  n,  r,  and  s  the  formula  becomes  -  =  — I — :  and  as  -   is 

v       r       u  v 

greater  than  -,  v  must  be  less  than  /,  hence  T  lies  between  the  princi- 
pal focus  and  the  lens. 

4.  Plano-convex  lenses. — The   action  of  a  plano-convex   lens   is  in 
general  the  same  as  that  of  the  double  convex  lens,  but  its  foci  are  at 
double  the  distance,  the  principal  focus  being  at  a  distance  equal  to 
twice  the  radius  of  the  curved  surface. 

30* 


326  PHYSICS    OF    IMPONDERABLE    AGENTS. 

/ 

To  adopt  the  formula  to  this  case,  we  make  n  —  f  ,  and  r  =  oo,  hence 

-  =  ---  .     If  the  rays  are  parallel,  -  =  0,  and  v,  or/=  2s. 
v        2s       u  u 

448.  Action  of  a  double  concave  lens  upon  small  pencils  of 
light.—  Let  P  A  P>'  B  p,  fig.  354 

354>  be  a  double  concave  lens 
of  a  dense  medium,  r  being  the 
radius  of  the  first  surface  and  « 
the  radius  of  the  second  surface. 
Let  Q  be  the  focus  of  the  inci- 
dent rays,  q'  the  focus  of  the  „/ 
rays  after  refraction  at  the  first 
surface,  and  q  the  focus  of  the 

emergent  rays  p  R,  p'  R'.     Let  Q  A  =  u,  A  q'  =  «',  B  q  =  v,  and  A  B  =  t. 
According  to  the  formula  for  refraction  at  a  concave  dense  surface  (446)  :  — 

n          n  —  1        I 

u'  r  u' 

and  by  the  formula  for  rays  emerging  from  a  concave  dense  surface, 
n  n  —  I        1 


If  the  thickness  of  the  lens  is  so  small  that  when  compared  with  B  q'  it  may 
be  neglected,  and  that  we  may  consider  B  q'  =  A  q'  =  «',  combining  these  two 

1  /I        1  \        1  111 

equations  we  have  -  =  (  n  —  1)   I  —  I-   —  I  -\  --  .     Or,   —=      -4-  —  . 
v  '   \r         s  ]        u  v        f        it 

If  the  thickness  of  the  lens  is  too  great  to  be  neglected,  we  find  by  the  same 

1        1        1         t    I    n    \2 

method  as  for  a  convex  lens  —  =  —  I  ----  I  -7-  I 
v       f       u        n  \u'2  /• 

This  formula  for  the  double  concave  lens  may  be  deduced  directly  from  the 
formula  for  the  double  convex  lens,  by  substituting  in  that  formula  for  r  and 
s,  —  r  and  —  s,  and  as  the  value  of  v  would  then  be  negative,  changing  that 
sign  also  when  its  positive  value  is  reckoned  on  the  same  side  as  u. 

Conclusions  deduced  from  analysis.  —  A  concave  lens  produces, 
upon  rays  of  light  transmitted  through  it,  an  355 

effect  the  opposite  of  that  produced  by  a  con- 
vex lens. 

1.  Parallelrays  of  light,  transmitted  through 
a  double  concave  lens,  diverge  from  a  virtual 
focus  in  front  of  the  lens,  as  shown  in  fig. 

355  ;  the  virtual  focus  being  at  the  centre  of  the  sphere  of  which  the 
first  surface  forms  a  part.     This  is  its  principal  focus. 

2.  Diverging  rays.  —  If  the  radiant  point  is  more  distant  than  the  prin- 
cipal focus,  as  at  B,  fig.  356,  the  virtual  355 
conjugate  focus,  A,  will  be  between  the 

principal  focus,  F,  and  the  surface  of  the 
lens,  and  the  rays  will  diverge  after  re- 
fraction. 

3.  Converging  rays,  transmitted  through  a  concave  lens,  will  be  reu- 


OPTICS.  327 

dered  less  convergent,  parallel,  or  divergent,  depending  upon  the 
distance  of  the  point  towards  which  they  converge  before  entering 
the  lens. 

The  above  propositions  are  easily  proved  by  reference  to  the  formula  for  a 

1  /I         1   \        1 

double  concave  lens,  —  =  (n  —  1)   {  -j • 

v  \r          s  I        u 

449.  Rules  for  determining  the  foci  of  lenses. — When  lenses 
are  made  of  glass  whose  refractive  index  is  one  and  a  half,  their  foci 
may  be  determined  by  the  following  rules  : — 

Rule  for  the  Principal  Focus. 

Divide  twice  the  product  of  the  radii  by  their  difference,  for  the 
meniscus  and  concavo-convex  lenses,  and  by  their  sum,  for  the  double 
convex  and  double  concave  lenses.  The  quotient  will  give  the  focus  for 
parallel  rays.  The  focus  of  parallel  rays,  or  principal  focus,  of  the 
plano-convex  or  plano-concave  lens,  is  double  the  radius  of  curvature. 

Rule  for  the  Conjugate  Focus,  when  the  Focus  of  the  Incident  Raijs  is 

given. 

Multiply  the  length  of  the  principal  focus,  with  its  proper  sign,  by 
the  focus  of  the  incident  rays,  and  divide  the  product  by  the  difference 
between  the  principal  focus  and  the  focus  of  incident  rays,  and  the 
quotient  will  be  equal  to  the  conjugate  focus. 

If  the  distance  of  the  focus  of  incident  rays  is  less  than  the  principal  focus, 
the  value  of  the  conjugate  focus  will  be  positive,  and  it  will  lie  on  the  same  side 
of  the  lens  as  the  focus  of  incident  rays;  but  if  the  value  of  the  focus  of  inci- 
dent rays  is  greater  than  the  principal  focus,  the  value  of  the  conjugate  focus 
will  be  negative,  and  the  focus  of  refracted  rays  will  lie  on  the  other  side  of  the 
lens. 

450.  Combined  lenses. — If  two  convex  lenses,  A  A,  B  B,  are  placed 
near  together,  as  in  fig.  357,  their  com-  357 

bined  focus  will  be  shorter  than  that 
of  either  lens  used  alone. 


Let  parallel  rays  be  refracted  by  the  first ' 
lens,  A  A,  to  a  focus  at  N ;  represent  the  distance  of  this  point  from  the  first  lens 
by/',  and  let  the  distance  between  the  lenses  be  represented  by  a,  let/"  repre- 
sent the  corresponding  focal  length  of  the  second  lens  for  parallel  rays,  and 
/  the  distance  of  the  focus  L  from  the  second  lens.  In  the  general  formula 
111 

-  = ,  considered  with  reference  to  the  second  lens,  u  =  —  (/'  —  a},  and 

v       f        u 

/becomes/",  v  =  /,  and  we  have: — 

*  ./"X  (/'-«) 


328  PHYSICS   OF   IMPONDERABLE    AGENTS. 

If  the  distance  between  the  lenses  is  nothing,  then  for  the  focus  of  parallel 

fn  \C  f 
rays,  /=  — -•         For  rays  not  parallel,  the  formula  will  be: — 

1  =  I  4-       l        a  1  •  4  U~ff 

v        f><^~  v'  —  a        f"  ~  f'u  —  a(u  — /')' 

When  the  lenses  are  in  contact,  —  =  -  -| •     For  any  number  of  lenses 

v        f       f"        u 

11111,  1  /1\1 

in  contact,  -  =  -  -f -f  Ac., —  1  I  -   I  —  — 

v        f       f"       /'"       /"  «  \f  J        u 

451.  Oblique  pencils,  when  transmitted  through  lenses,  have  their 
foci  in  secondary  axes,  and  their  foci  are  determined  by  the  same  rules 
as  the  foci  of  direct  pencils  in  the  principal  axis. 

It  has  been  shown,  in  §  439,  that  a  ray  of  light  transmitted  through  a 
prism  in  a  direction  parallel  to  its  base,  suffers  the  least  deviation  possible ; 
hence  in  every  other  position  the  deviation  is  increased.  From  this  principle  it 
follows  that  the  foci  of  oblique  pencils  transmitted  through  lenses  will  be  some- 
what shorter  than  the  foci  of  direct  pencils.  This  fact  requires  consideration  in 
the  formation  of  the  images  of  large  objects.  (See  $  455.) 

452.  The  optical  centre  of  a  lens  is  a  point  so  situated  that  every 
ray  of  light  passing  through  it  will  358 

undergo  equal  and  opposite  refrac-  \ 

tion  on  entering  and  leaving  the 
lens.  It  will,  therefore,  be  found 
where  a  line  joining  the  extremi- 
ties of  two  parallel  radii  of  the 
opposite  surfaces  cuts  the  axis  of 
the  lens. 

Let  S  P  R  Q,  fig.  358,  be  a  ray  of  light  passing  through  a  double  convex  lena 
so  that  the  radii  0'  P,  0  R,  drawn  from  the  points  of  incidence  and  emergence 
are  parallel.  Let  C  be  the  point  where  this  ray  intersects  the  axis  of  the  lens. 
The  triangles  0'  C  P,  0  C  R,  are  similar,  hence  :— 

O'P  :  O'C  =  OR  :  OC; 
O'P  —  0'  C  :  0  R  —  0  C  =  0'  P  :  0  R ; 

AC  :I3C  -=  O'P:  OR; 

AC    |-  B  C  :  0'  P  -f  0  R  =  A  C  :  0'  P. 

Putting  0'  P  =  r,  0  R  =  «,  and  A  B  =  t. 

AC:f  =  r:r-fs     .-.     AC=r — — ,    BC= 

r  -f  «  »•-{-• 

If  the  lens  were  double  concave,  r  and  «  both  become  negative,  but  the  values 
of  A  C  and  B  C  remain  unchanged.  Since  these  values  are  both  positive  and 
constant,  whatever  may  be  the  positions  of  the  points  P  and  R,  the  optical 
centre  of  a  double  convex  or  double  concave  lens  will  be  a  fixed  point  in  the 
lens.  For  a  plano-convex  or  piano -con-jave  lens,  r  =  oo,  A  C  —  t,  BC  =  0. 


OPTICS.  329 

The  optical  centre  will  be  at  the  intersection  of  the  axis  with  the  curved  surface. 
For  a  meniscus,  either  r  or  «  will  be  negative,  and  the  formulae  show  that  in 
that  case  the  optical  centre  will  be  situated  without  the  lens  at  a  point  depend- 
ing upon  the  relative  values  of  the  tw^o  radii. 

All  rays  of  light  passing  through  the  optical  centre  emerge  from  the 
lens  parallel  to  the  incident  rays.  The  position,  form,  and  foci  of  all 
pencils  of  light  passing  through  a  lens  are  determined  by  their  relation 
to  some  line,  or  secondary  axis,  passing  through  the  optical  centre  of 
the  lens,  whether  any  ray  of  light  from  the  radiant  point  actually 
passes  through  that  centre  or  not. 

453.  Images  formed  by  lenses. — If  an  object  is  placed  before  a 
convex  lens  at  a  greater  distance  than  the  principal  focus,  an  image  of 
the  object  will  be  formed  on  the  other  side  of  the  lens. 

If  from  the  extremities  of  the  object  A  B,  fig.  359,  the  secondary  axes,  A  a, 
B  6,  are  drawn  through  the  optical  centre  of  the 
lens,  the  image  will  be  formed  between  these 
axes  prolonged,  at  a  distance  equal  to  the  con- 
jugate focus  of  the  lens,  estimated  separately  for 
every  point  of  the  object.  If  the  object  is  placed 
beyond  the  principal  focus,  and  at  less  than 
twice  this  distance,  the  image  will  be  more  distant  and  larger  than  the  object. 
If  the  object  recedes  from  the  lens,  the  image  will  approach  it.  When  the 
object  is  removed  from  the  lens,  more  than  twice  the  principal  focus,  the  imago 
will  be  smaller  than  the  object,  and  it  will  gradually  approach  the  lens,  and 
diminish  in  size  as  the  object  recedes.  The  image  can  never  approach  nearer  to 
the  lens  than  the  principal  focus.  The  linear  magnitude  of  the  image  as  com- 
pared with  the  object  will  be  proportional  to  their  respective  distances  from  the 
lens.  360 

If  the  object  is  placed  nearer  to  the  lens  than  the 
principal  focus,  as  A  B,  fig.  360,  the  rays  will 
diverge  after  passing  the  lens,  and  a  virtual  image, 
a  6,  will  be  formed  on  the  same  side  of  the  lens  as 
the  object.  The  virtual  image  formed  by  a  convex 
lens  is  always  larger  than  the  object. 

If  an  object,  A  B,  fig.  361,  is  placed  before  a  concave  lens,  the  rays  from 
every  point  of  the  object  will  diverge  after  refraction  more  than  they  did 
before  entering  the  lens ;  consequently  a  virtual  361 

image,  smaller  than  the  object,  will  be  formed  on 
the  same  side  of  the  lens.  The  size  of  the  virtual 
inia^e  will  be  in  proportion  to  its  distance  from 
the  lens. 

454.  Spherical  aberration  of  lenses. — It  has  been  assumed  that 
spherical  lenses  bring  rays  of  light  issuing  from  a  point  to  a  sensible 
focus.     For  many  purposes,  however,  greater   accuracy   is   required, 
and  it  becomes  necessary  to  consider  the  imperfections  of  spherical 
lenses. 


330  PHYSICS    OF    IMPONDERABLE    AGENTS. 

If  the  diameter  of  the  lens  V  W,  fig.  362,  is  large  in  proportion  to  its 
radius  of  curvature,  rays  of  parallel  light  362 

will  not  be  brought  to  an  accurate  focus, 
but  while  the  central  rays  cross  the  axis  at 
F,  the  extreme  rays  will  intersect  the  axis 
at  G,  and  intermediate  rays  will  intersect 
the  axis  at  every  possible  point  between 
F  and  G.  The  distance,  F  G,  is  called  the  longitudinal  spherical  aberra- 
tion of  the  lens. 

For  lenses  of  small  aperture,  the  aberration  is  neai'ly  in  proportion  to  the  square 
of  the  angular  aperture  of  the  lens  ;  but  for  lenses  of  larger  aperture,  the  aberra- 
tion increases  more  rapidly  than  would  be  required  by  this  proportion.     If  the 
length  of  the  principal  focus  be  taken  as  unity,  the  longitudinal  aberration  for 
lenses  of  different  angular  apertures  will  be  as  follows  : — 
For  15°  the  aberration  will  be  0-025, 
«    22°    "          "  "     "  0-062, 

«    30°    "          "  "     "  0-150, 

«    450    «          «  «     «  0-375. 

This  effect  of  spherical  lenses  causes  images  to  be  formed  at  every  point 
between  F  and  Gr,  the  rays  going  from  each  image,  more  or  less  interfering  with 
the  distinctness  of  all  the  others. 

The  amount  of  spherical  aberration  depends  also  on  the  form  and  position  of 
lenses.     If  n  =  index  of  refraction,  r  =  the  radius  of  the  anterior  surface,  and 
R  =  the  radius  of  the  posterior  surface,  then  for  parallel  rays,  the  form  of  least 
aberration  will  be  expressed  by  the  following  equation  : — 
r         4  -j_  n  _  2n2 

Jt=       2«2  -f  n 

If  n  =  l^,  the  form  of  least  aberration  will  be  a  lens  whose  surfaces  have 
their  radii  in  the  proportion  of  1  to  6,  the  side  of  deeper  curvature  being  towards 
parallel  rays.  If  the  spherical  aberration  of  such  a  lens,  in  its  best  position,  is 
taken  as  unity,  the  aberration  of  other  lenses  will  be  as  follows  : — 

Plano-convex  with  plane  surface  towards  distant  objects,  4-2. 

Plano-convex  with  convex  surface  towards  distant  objects,  1-081. 

Plano-concave  the  same  as  plano-convex. 

Double  convex  or  double  concave  with  both  faces  of  the  same  curvature,  the 
aberration  will  be  1-567. 

The  spherical  aberration  of  a  convex  lens  is  called  positive,  and  the 
aberration  of  a  concave  lens  is  called  negative  because  it  is  in  an 
opposite  direction  from  that  produced  by  a  convex  lens. 

Accurate  estimate  of  spherical  aberration.* — To  estimate  with 
accuracy  the  amount  of  spherical  aberration  in  any  given  case,  it  is 
necessary  to  calculate  the  exact  course  of  a  ray  which  falls  upon  the 
border  of  the  lens. 

*  Microscopical  Journal,  Vol.  VIII.  p.  21. 


OPTICS. 


331 


Let  A  C,  fig.  363,  be  a  section  of  a  curved  refracting  surface  in  the  plane  of 
refraction,  Q  C  q  being  its  axis.     The  refractive  index  =  n.     Here  the  distance 

363 


Q  C  of  the  radiant  point  from  the  refracting  surface  is  given.     Also  C  D  and 

D  A  co-ordinates  of  the  point  A.     Hence,  also  the  normal  A  E  and  sub-normal 

D  E  may  be  found.     Let  A  q  be  the  refracted  ray  required,  cutting  Q  C  q  in  q. 

Now  sin.  incidence  is  to  sin.  AEC  =  QE:QA. 

Sin.  E  is  to  sin.  refraction  =  q  A  :  q  E. 

qA     QA 

.•.  Sin.  incidence  :  sin.  refraction  =  m  :  1  =  —  :  — — ' 

jE     Q  E 

q  A        m.Q,  A 

.-.  —  =  — -—  =  c,     (a  known  quantity). 
q  &        y  .hi 

.-.  q  A2  =  C2.q  E2. 

i.  e.,       q  E2  -f  E  A2  -f  2  q  E.E  D  =  c2.?  E2. 
...  (C2  _  i)  q  E2  —  2  E  D.q  E  ==  E  A2. 

2  E  D  E  A2 

•'•9'E   ~"7z       i'3E  =  ^      7' 


ED2 


(  ED    ]2          ED 

...     |    q  E   _  c.2_1   I       ==  (c2_ 


2   H 


(c2  —  1)EA2 


1          (  _  ) 

...  q  E  =  -  -  j  E  D  ±  j/E  D  2  -f  (c2  —  1)  E  A2  [•  . 

From  this  formula  the  accurate  value  of  q  E  for  any  surface  may  be  calculated. 

455.  Aberration  of  sphericity  ;  distortion  of  images.  —  When  a 
straight  object  is  placed  before  a  lens,  the  extremities  of  the  object  not 
being  in  the  principal  axis,  if  the  images  of  the  extreme  points  are 
formed  in  the  secondary  axes  at  the  same  distance  from  the  optical 
centre  of  the  lens,  as  the  central  portions  of  the  image,  the  image  will 
not  be  straight,  but  formed  on  a  curve,  the  centre  of  which  is  at  the 
optical  centre  of  the  lens,  as  a'  V,  fig.  364.  But  as  an  object  recedes 
from  the  lens,  the  image  will  364 

approach  it,  therefore  as  A  and 
B  are  more  distant  from  the 
lens  than  the  centre  of  the 
object,  the  extremities  of  the 
image  must  be  nearer  than  the 
centre,  and  instead  of  a'  C  b',  we 
shall  have  the  image  a"  C  b" 
described  around  a  centre,  somewhere  between  the  lens  and  the  centre 


332  PHYSICS    OF    IMPONDERABLE    AGENTS. 

of  the  image.  Oblique  pencils  are  also  more  strongly  refracted  than 
pencils  which  belong  to  the  principal  axis ;  hence  this  cause  must  tend 
to  curve  the  image  still  more.  This  curvature,  or  distortion  of  images, 
is  called  aberration  of  sphericity.  For  ordinary  purposes  this  imperfec- 
tion of  lenses  may  be  disregarded.  The  practical  method  of  overcoming 
these  difficulties  will  be  best  explained  in  connection  with  the  descrip- 
tion of  achromatic  lenses. 

\  4.  Chromatics. 

456.  Analysis  of  light. — Spectrum. — Primary  colors. — A  beam 
of  sunlight,  S  H,  fig.  365,  admitted  into  a  dark  chamber,  through  a 
small  opening  in  the  shutter,  E,  forms  365 

a  round  white  spot,  P,  upon  a  screen  or 
any  other  object  upon  which  it  falls. 
If  a  triangular  prism,  B  A  C,  is  inter- 
posed in  its  path,  as  shown  in  the  figure, 
the  light  will  be  refracted  both  on  enter- 
ing and  leaving  the  prism,  but  instead 
of  forming  only  a  circular  white  spot  on  ^'' 

the  screen,  M  N,  it  will  be  spread  over 

a  considerable  space  from  S  to  K,  called  the  solar  spectrum,  in  which 
will  be  seen  all  the  colors  of  the  rainbow.  Beginning  with  the  color 
most  refracted,  they  are  violet,  indigo,  blue,  green,  yellow,  orange,  and 
red. 

If  an  opening  is  made  in  the  screen  so  as  to  permit  only  the  rays  of 
a  single  color  to  pass,  and  we  attempt  to  analyze  this  color  by  passing 
it  through  a  second  prism,  we  find  it  cannot  be  further  decomposed  by 
refraction ;  hence  the  colors  of  the  solar  spectrum  produced  by  the 
refraction  of  a  triangular  prism  are  generally  called  primary  colors. 

457.  Recomposition  of  white  light. — If  a  second  prism,  A  B  a, 
exactly  similar  to  BAG,  is  placed  behind  the  first,  but  in  a  reversed 
position,  as  shown  in  the  figure,  the  differently  colored  rays  will  be  re- 
united and  form  white  light  at  P,  as  though  no  prism  had  been  used. 

Moreover,  if,  instead  of  the  second  prism,  a  double  convex  lens  is  so 
placed  as  to  receive  the  colored  rays  and  converge  them  to  a  focus,  a 
round  spot  of  white  light  will  be  again  formed  in  the  focus  of  the  lens. 

If  colored  powders  are  mixed  in  the  proportions  that  the  several  colors  occupy 
in  the  solar  spectrum,  the  color  of  the  compound  will  be  a  grayish  white.  That 
the  resulting  color  is  not  pure  white  is  probably  owing  to  the  fact  that  we  cannot 
procure  artificial  colors  that  will  accurately  represent  the  colors  of  the  solar 
spectrum. 

458.  Analysis  of  colors  by  absorption. —Although  the  colors  of 
the  prismatic  spectrum  cannot  be  further  divided  by  refraction,  Brewster 


OPTICS.  333 

has  shown,  that  any  of  the  colors  may  be  still  further  decomposed  bj 
transmission  through  variously  colored  glass.  He  thus  ascertained  that 
red,  yellow,  and  blue  light  are  found  in  various  proportions  in  all  parts 
of  the  spectrum,  and  that  any  other  color  whatever  may  be  formed  by 
suitable  combinations  of  these  three.  Brewster  and  other  eminent 
philosophers  have  hence  inferred  that  there  are  really  only  three  pri- 
mary colors,  red,  yellow,  and  blue. 

Dr.  Young  considered  red,  green,  and  violet,  primary  colors.  According  to 
Herschel,  any  three  colors  of  the  spectrum  may  be  taken  as  primary,  and  all 
other  colors  may  be  compounded  from  them,  with  the  addition  of  a  certain 
amount  of  white.  The  distinction  of  colors  into  primary  and  secondary,  should 
therefore  be  considered  to  a  certain  extent  as  arbitrary,  and  as  adopted  princi- 
pally for  convenience  of  illustration. 

459.  Complementary  colors. — Any   two   colors  which   by   their 
union  would  produce  white  light,  are  said  to  be  complementary  to  eac£ 
other.     If  we  take  away  from  the  solar  spectrum  any  color  whatever, 
we  may  reunite  all  the  remaining  colors,  by  means  of  a  double  convex 
lens,  or  by  a  second  prism,  and  the  resulting  color  will  obviously  be 
complementary  to  the  first,  because  it  is  just  what  the  first  wants  to 
make  white  light.     In  this  manner  it  is  found  that, 

Red  is  complementary  to Green. 

Violet  red  " Yellowish  green. 

Violet                "  " Yellow. 

Violet  blue       "  " Orange  yellow. 

Blue                   "  " Orange. 

Greenish  blue  "  " Reddish  orange. 

Black                "  .         " White. 

The  subject  of  harmony  and  contrast  of  colors,  will  be  treated  in  connection 
with  the  phenomena  of  vision. 

460.  Properties  of  the  solar  spectrum. — In  the  solar  spectrum 
there  are  found  three  distinct  properties  which  exist  in  various  degrees 
of  intensity  in  the  differently  colored  rays.     See  fig.  368. 

(a)  Luminous  rays. — According  to  Herschel,  Fraunhofer,  and  others, 
it  is  found  that  the  maximum  illuminating  power  resides  in  the  yellow 
rays,  and  the  minimum  in  the  violet. 

(b)  Calorific,  or  heating  rays. — The  position  of  greatest  intensity  for 
the  calorific  rays  varies  with  the  nature  of  the  material  of  the  prism 
with  which  the  spectrum  has  been  produced.     In  the  spectrum  pro- 
duced by  a  prism  of  crown  glass,  the  greatest  heating  power  is  found 
in  the  pale  red.     If  a  prism  filled  with  water  is  used,  the  greatest 
heating  power  is  found  connected  with  the  yellow  rays.     If  the  prism 
is  filled  with  alcohol,  the  greatest  heat  is  connected  with  the  orange 

31 


834  PHYSICS    OF   IMPONDERABLE    AGENTS. 

yellow.  "With  prisms,  formed  of  highly  refracting  gems,  the  maximum 
heating  power  is  found  beyond  the  red  ray.  Flint  glass  resembles  the 
gems  in  this  respect. 

(c)  Chemical  rays. — In  a  great  variety  of  phenomena,  solar  light  acts 
as  a  chemical  agent.  Under  the  influence  of  solar  light,  plants  decom- 
pose carbonic  acid,  evolving  pure  oxygen,  and  most  vegetable  colors  are 
destroyed ;  phosphorus  is  changed  to  its  red  or  amorphous  state,  and 
loses  its  power  of  emitting  light ;  chlorine  and  hydrogen  may  be  safely 
mixed  in  the  dark,  but  combine  with  an  explosion  when  exposed  to 
the  sun's  light ;  the  green  color  of  plants  disappears  in  the  dark,  and 
the  nature  of  the  vegetable  juices  is  changed  when  withdrawn  from 
the  chemical  action  of  light ;  and  the  wonderful  phenomena  of  pho- 
tography depend  upon  the  action  of  light  upon  sensitive  chemical 
substances. 

The  maximum  chemical  effect,  produced  by  solar  light,  appears  to 
be  connected  with  the  violet  rays,  or  with  rays  between  the  violet  and 
the  blue.  Some  chemical  effect  is  produced  by  rays  refracted  entirely 
beyond  the  extreme  border  of  the  visible  violet  rays.  The  lavender 
light  of  Herschel  results  from  the  concentration  of  the  so-called  invisi- 
ble rays,  beyond  the  border  of  the  violet.  A  large  convex  lens  gathers 
these  otherwise  invisible  rays  into  a  faint  beam  of  lavender  colored 
light. 

461.  Fraunhofer's  dark  lines  in  the  solar  spectrum. — In  1802, 
Dr.  Wollaston  first  discovered  the  existence  of  dark  lines  in  the  solar 
spectrum,  but  the  discovery  excited  no  special  attention,  and  was 
applied  to  no  practical  purpose. 

Unacquainted  with  Wollaston's  observations,  the  late  celebrated 
Fraunhofer,  of  Munich,  rediscovered  the  dark  lines  of  the  spectrum, 
now  distinguished  as  Fraunhofer's  dark  lines.  Viewing  through  a 
telescope  the  spectrum  formed  from  a  narrow  line  of  solar  light,  by 
the  finest  prisms  of  flint  glass,  he  noticed  that  its  surface  was  crossed 
by  dark  lines  of  various  breadths.  None  of  these  lines  coincide  with 
the  boundaries  of  the  colored  spaces. 

From  the  distinctness  and  ease  with  which  they  may  be  found  and 
identified,  seven  of  these  lines  have  been  distinguished  by  Fraunhofer 
by  the  letters  B,  C,  D,  E,  F,  G,  H.  Numerous  other  lines — varying 
from  600  to  2000  in  number,  according  to  the  power  of  the  telescope 
with  which  they  are  viewed — have  since  been  counted  in  the  solar 
spectrum. 

To  view  these  lines  with  the  naked  eye,  a  ray  of  sunlight  is  admitted  into  a 
dark  chamber  through  narrow  openings  in  two  screens,  one  placed  behind  the 
other,  as  shown  in  fig.  366,  and  is  then  refracted  by  a  prism  of  the  purest  flint 


OPTICS. 


335 


glass.    The  lines,  or  some  of  them,  will  then  be  seen  on  the  screen.    The  positions 
of  these  lines  in  the  colored  spaces  of  the  spectrum  is  perfectly  definite,  but  their 
366  367 


F 

9 

''•!) 

'•T* 

\  ii  i 

1       1 

!        Ill 

BC          0) 

<E             ff 

ft                ^i 

FLINT  GLASS 
UJVN  GLASS 

III   1    1 

\      Hi™ 

ifC     D     E    J 

?.         G          11 

I.!!,!.  11 

Hi*™. 

J 

distances  from  each  other  vary  with  the  substance  of  which  the  prism  is  formed. 

Prof.  0.  N.  Rood  states  (Am.  Jour.  Sci.  [2]  XVII.  429),  that  fine  flint  glass 
prisms  are  by  no  means  indispensable  for  viewing  the  fixed  lines,  as  he  found  no 
prism  among  twelve  in  a  candelabrum  which  did  not  show  several  of  them. 

Fig.  367  shows  the  arrangement  of  the  dark  lines  in  the  spectrum,  formed  by 
prisms  of  flint  and  crown  glass,  and  also  by  a  prism  filled  with  water.  These 
dark  lines  answer  the  important  purpose  of  landmarks  for  determining  the 
indices  of  refraction  for  various  substances.  The  exact  limits  of  the  several 
colors  in  the  spectrum  are  not  well  defined,  but  the  dark  lines  establish  definite 
points  from  which  the  practical  optician  estimates  the  refractive  power  of  any 
medium,  and  also  the  comparative  refrangibility  of  the  differently  colored  rays 
in  which  the  dark  lines  occupy  fixed  positions. 

Lines  in  light  from  different  sources. — In  the  spectrum  produced 
by  the  light  of  the  sun,  whether  reflected  by  the  moon  or  planets,  or  from  the 
clouds  or  any  terrestrial  object,  the  position  of  the  dark  lines  is  invariable.  But 
the  light  of  the  stars  differs  from  that  of  the  sun,  and  the  light  of  one  star  dif- 
fers from  other  stars  in  regard  to  the  number  and  position  of"  the  dark  lines  in 
the  spectrum.  Electrical  light,  and  the  light  of  flames  produced  by  any  burn- 
ing body  whatever,  give  bright  lines  instead  of  the  dark  lines  in  the  spectrum 
formed  by  solar  or  stellar  light. 

The  relation  of  the  dark  lines  to  the  colors  of  the  spectrum  is  shown 
in  fig.  368.  B  lies  in  the  red  portion  near  the  end ;  C  is  farther 
advanced  in  the  red ;  D  in  the  orange  is  a  strong  double  line  easily 

368 


Red.  Orange.    Yellow.  Green.     Bl 


recognised  ;  E  in  the  green  ;  F  in  the  blue ;  G  in  the  indigo  ;  and  II  in 
the  violet.  Besides  these,  there  are  also  others  very  remarkable  ;  thus 
6  is  a  triple  line  in  the  green,  between  E  and  F,  consisting  of  three 
strong  lines,  of  which  two  are  nearer  each  other  than  the  third  ;  A  is 
in  the  extreme  border  of  the  red,  and  a  is  a  band  of  delicate  linos 
between  A  and  B. 


336  PHYSICS    OF    IMPONDERABLE    AGENTS. 

462.  Fixed  lines  in  the  spectra  from  various  colored  flames. 
— It  is  well  known  to  chemists  that  characteristic  colors  are  imparted 
to  the  flame  of  alcohol  by  the  salts  of  various  metals.     It  has  been 
lately  observed   that  the   spectra   from   flames   thus  colored   possess 
characteristic  fixed  lines.    Thus  the  spectrum  of  a  soda  flame  is  charac- 
terized by  two  bright  lines  in  the  position  of  the  two  dark  lines  at  D  in 
the  solar  spectrum.    Lithium  gives  a  brilliant  red  line  between  B  and 
C,   and   potash   salts  give    bright   lines   corresponding   to    the    dark 
lines  A  a  B   shown   in  fig.  368.     The   spectrum   from   lime   (in   the 
Drummond  light)  gives  at  first  two  bright  lines  like  salts  of  sodium, 
which  however  soon  disappear  as  the  heat  is  continued;    but  if  an 
alcohol-sodium  flame  is  held  in  the  path  of  the  rays,  two  dark  lines 
assume  the  place  of  the  original  bright  lines  in  this  spectrum,  corres- 
ponding exactly  in  position  to  the  two  dark  lines  D  of  the  solar  spectrum. 

These  variously-colored  flames  held  in  the  path  of  the  rays  producing 
the  solar  spectrum  render  the  dark  lines  more  distinct  although  these 
flames  alone  would  produce  bright  lines. 

From  similar  observations  Kirchoff  deduces  the  inference  that  the 
sun's  atmosphere  contains  compounds  of  sodium  and  potassium  but  no 
lithium.* 

463.  Intensity  of  luminous,  calorific,  and  chemical  rays. — 
Fig.  368  also  shows  how  the  intensity  of  the  luminous,  calorific,  and 
chemical  rays,  varies  in  different  parts  of  the  spectrum.     The  greatest 
illuminating  power  resides  in  the  yellow  part  of  the  spectrum.     The 
heating  power  is  almost  entirely  absent  in  the  violet  and  the  blue,  where 
the  chemical  agency  is  at  its  maximum,  and  it  is  greatest  beyond  the  red, 
and  extends  a  considerable  distance,  where  no  illumii.ann         chemical 
power  is  ordinarily  manifest.     The  relative  positions  of  the  maximum 
illuminating,  chemical,  and  heating  powers  of  the  solar  spectrum,  vary 
somewhat  with  the  nature  of  the  substance  composing  the  prism  with 
which  the  spectrum  has  been  produced. 

464.  Refraction  and  dispersion  of  the  solar  spectrum. — Kaly- 
chromatics. — If  a  glass  tube,  retort  neck,  drinking  glass,  or  any 
similar  instrument  of  glass,  be  held  in  the  path  of  the  colored  rays 
from  a  triangular  prism  in  a  dark  chamber,  a  beautiful  system  of 
colored  rings  will  be  formed,  varying  their  form,  position,  and  color, 
with  every  change  in  the  position  or  form  of  the  glass  interposed. 

This  experiment  exhibits,  in  a  surprising  and  agreeable  manner, 
the  wonderful  resources  of  color  contained  in  the  solar  beam.  Lan- 
guage fails  to  express  the  exquisite  and  wonderful  beauty  of  this 
simple  experiment,  involving  only  the  refraction  and  dispersion  of  the 

*  Monthly  notices  of  the  Berlin  Academy,  1859,  p.  662. 


OPTICS.  337 

solar  spectrum.  Kali/chromatics  (from  the  Greek  for  beautiful  colors) 
has  been  suggested  as  a  word  to  distinguish  these  phenomena. 

465.  Chromatic  aberration. — When  rays  of  ordinary  white  light 
are  refracted  by  a  lens  of  any  form,  consisting  of  a  single  transparent 
substance  like  glass,  or  a  transparent  gem,  the  rays  are  each  acted  upon 
as  by  a  prism,  and  dispersed  into  all  the  colors  of  the  solar  spectrum. 

This  effect  is  shown  by  fig.  369,  where  V  is  the  focus  of  the  violet  rays  which 
are  most  refracted,  and  R  is  the  focus  of  red 
rays  which  are  least  refracted.  A  violet  image 
is  formed  at  V,  and  a  red  image  at  R,  and  as 
the  other  colors  are  situated  between  the  violet 
and  the  red,  all  the  space  between  V  and  R  is 
occupied  by  images  of  intermediate  colors. 
If  an  image  of  a  point  or  line  is  formed  at  V, 

its  color  will  be  violet,  but  it  will  be  surrounded  by  fringes  composed  of  all  the 
colors  of  the  spectrum,  the  outer  border  of  the  fringe  being  red.  This  defect  of 
all  single  lenses,  formed  of  whatever  substance,  is  called  chromatic  aberration. 

466.  Achromatism.— We  have  seen,  $  461,  fig.  367,  that  the  spec- 
trum formed  by  flint  glass  is  nearly  twice  as  long  as  that  370 
formed  by  crown  glass.     If  therefore  we  take  a  prism  of 

crown  glass,  A,  fig.  370,.  and  another  prism  of  flint  glass, 
B,  having  a  refractive  angle  so  much  smaller  than  the 
refractive  angle  of  A,  that  the  solar  spectrum  formed  by 
it  will  exactly  equal  in  extent  the  spectrum  formed  by 
the  first  prism,  we  may  place  the  two  prisms  in  opposition, 
as  shown  in  the  figure,  and  the  colored  rays  separated  by  transmis- 
sion through  one  prism,  will  be  exactly  reunited  by  the  other.  The 
light  transmitted  through  the  two  prisms,  thus  placed,  will  therefore 
be  of  the  same  color  as  before  transmission.  But  while  the  color  of  the 
transmitted  light  is  unaltered,  its  direction  will  be  changed  by  about 
one-half  the  refractive  power  of  the  prism  A^  for  while  the  prism,  B, 
has  neutralized  all  the  dispersion  of  color  produced  by  A,  it  has  neu- 
tralized only  about  half  of  its  refractive  power. 

Applying  these  principles  to  lenses,  a  double  convex  lens  of  crown 
glass,  A  A,  fig.  371,  may  be  united  with  a  plano-concave  lens  of  flint 
glass,  B  B,  having  a  focus  about  double  the  focus  of  the  convex     371 
lens.    These  two  lenses  will  act  like  the  prisms  in  the  preceding 
figure.     The  concave  lens  of  flint  glass  will  correct  the  chro- 
matic aberration  of  the  double  convex  lens  of  crown  glass,  and 
leave  about  one-half  of  the  refractive  power  of  the  convex  lens 
as  the  effective  refracting  power  of  the  compound  lens. 

An  achromatic  lens,  formed  of  a  double  convex  lens  of  crown 
glass,  equally  convex  on  both  sides,  joined  with  a  plano-concave  lens 
31* 


338          PHYSICS  OF  IMPONDERABLE  AGENTS. 

of  flint  glass,  having  its  concave  side  ground  to  fit  one  side  of  the  double 
convex  lens,  will  have  the  focus  of  a  simple  plano-convex  lens,  with  ita 
convexity  equal  to  one  side  of  the  double  convex  lens. 

467.  Formulae  for  achromatism.  —  Let  it  be  required  to  determine 
the  forms  of  two  thin  lenses  composed  of  different  media,  which  will 
together  form  a  compound  lens  free  from  chromatic  aberration.  In 
this  problem  we  will  consider  only  two  colors  of  the  spectrum,  as  red 
and  violet.  » 

Let  m  and  n  be  the  indices  of  refraction  for  the  mean  ray  in  the  two  media  ; 
m'  and  n1  the  indices  for  one  of  the  colored  rays,  and  m"  and  n"  the  refractive 
indices  for  the  other  ray. 

Let  /and/7  be  the  mean  focal  lengths  of  the  two  lenses,  of  which  r  and  «  and 
»•'  and  «'  are  the  radii  of  the  surfaces.  By  the  principles  already  established  we 
shall  have  :  — 

1  /I         1  \  /I         1  \        1 

-     —  O'-D  (-  +  -)  +  K-O  (?  +  ?;-;» 


Subtracting  the  first  equation  from  the  second, 
0  =  (m"  —  m 


This  equation  may  be  put  under  the  form, 

m"  —  m'  1         n"  —  n'  1 
0  =  ---  1  --  .  —  . 
m  —  1  '/          n  —  If 

m"  _  m>  n"  _  „' 

The  coefficients  -  and  -  ,  are  called  the  dispersive  powers  of  the 
m  —  1  n  —  1 

IP        *P* 
two  media,  and  may  be  represented  by  p  and  p'f  hence  0  =  -  -|  —  -,  and  as  p 

and  p'  are  either  both  positive  or  both  negative,  under  any  supposition  this  equa- 
tion can  only  be  satisfied  byVmaking  either  /  or  /'  negative,  that  is,  one  of  the 

/        P 
lenses  must  be  concave.     We  shall  then  havej       --  =  —  ,       Or/:/'  =  p  :  p'. 

We  therefore  obtain  the  following  conclusions  :  — 

1st.  An  achromatic  combination  must  be  composed  of  two  or  more 
lenses  formed  of  media  having  different  dispersive  powers. 

2d.   One  of  the  lenses  must  be  concave  and  the  other  convex. 

3d.  The  two  lenses  forming  an  achromatic  combination  must  have 
focal  lengths  directly  proportional  to  the  dispersive  powers  of  the  media 
of  which  they  are  respectively  composed. 

As  it  was  stated  in  g  454  that  the  spherical  aberration  of  a  concave 
lens  is  the  opposite  of  the  aberration  of  a  convex  lens,  it  is  easy  to  see 
that  the  combination  of  such  lenses  as  are  required  to  produce  achro- 
matism will  also  wholly,  or  in  part,  correct  the  spherical  aberration. 


OPTICS.  339 

g  5.  Vision. 

468.  Structure  of  the  human  eye. — The  human  eye  is  the  most 
perfect  of  all  optical  instruments.  By  means  of  this  organ,  stimulated 
by  the  light  reflected  or  refracted  from  external  objects,  we  recognise 
their  presence,  nearness,  color,  and  form.  Some  knowledge  of  the 
structure  and  action  of  the  eye  is  essential  to  a  proper  understanding 
of  the  uses  of  other  optical  instruments. 

The  eye,  situated  in  its  bony  cavity  called  the  orbit,  is  maintained  in 
its  position  by  the  optic  nerve  and  its  sheath,  by  muscles  which  serve 
to  move  it  or  hold  it  steady  in  any  required  position,  and  by  the  delicate 
membrane  called  the  conjunctiva,  which  covers  its  anterior  surface  and 
lines  the  eyelids.  The  eyelids  serve  to  protect  the  organ  from  external 
injuries,  and  also  to  shut  out  light  which  might  otherwise  be  trouble- 
some or  injurious  by  its  excess,  or  too  long-continued  action. 

Fig.  372  shows  a  horizontal  section  of  the  eye,  the  lower  part  of  the 
figure  representing  the  side  of  the  eye  towards  the  nose.  The  globe,  or 
ball  of  the  eye,  is  nearly  spherical, 
though  the  anterior  portion  is  more 
convex  than  the  other  portions,  as 
shown  in  the  figure. 

The  principal  portions  of  the  eye 
which  require  consideration,  are  the  a-\ 
sclerotic  coat,  the  cornea,  the  choroid 
coat,  the  retina  and  optic  nerve,  the 
iris,  the  pupil,  the  crystalline  lens, 
the  aqueous  humor,  the  vitreous 
humor,  and  the  hyaloid  membrane. 

The  sclerotic  coat,  i,  is  a  strong  opaque  structure,  composed  of  bundles  of 
strong  white  fibres,  interlacing  each  other  in  all  directions.  This  membrane 
covers  about  four-fifths  of  the  eyeball,  and  more  than  any  other  structure,  serves 
to  preserve  the  globular  form  of  the  eye.  It  has  a  posterior  sieve-like  opening,  for 
the  transmission  of  the  fibres  of  the  optic  nerve,  n ;  anteriorly,  a  transparent 
membrane  .called  the  cornea,  a,  is  set  into  a  groove  in  the  sclerotic  coat,  as  a 
watch  crystal  is  set  in  the  case,  but  these  two  membranes  are  so  firmly  united 
that  they  are  separated  only  with  considerable  difficulty.  The  cornea  is  more 
convex  than  the  sclerotic  coat. 

The  choroid  coat,  k,  is  a  strong  vascular  membrane,  lining  the  sclerotic  coat, 
and  covered  internally  by  a  dark  pigment,  the  piymentum  nigrum,  which  pre- 
vents any  reflection  of  light  from  the  internal  parts  of  the  eye. 

The  third,  or  inner  membrane  of  the  eye,  is  the  retina,  m,  which  is  merely  an 
expansion  of  the  optic  nerve,  n,  uniting  it  to  the  brain.  It  is  on  this  delicate 
lining  membrane  (the  retina)  that  the  images  of  external  objects  are  formed. 

The  iris,  d,  which  forms  the  colored  part  of  the  eye,  is  a  dark  annular  curtain 
or  diaphragm,  adherent  at  its  outer  margin,  with  a  central  opening  which,  in 


340  PHYSICS    OF    IMPONDERABLE    AGENTS. 

man,  is  circular;  in  cats  and  the  feline  tribe  generally  it  is  elongated  vertically; 
in  the  ox  and  other  ruminating  animals,  in  a  horizontal  direction.  The  central 
opening  of  the  iris,  e,  which  allows  light  to  penetrate  the  eye,  is  called  the  pupil. 
It  varies  from  one- eighth  to  one-quarter  of  an  inch  in  diameter.  In  a  strong 
light  the  pupil  contracts,  but  where  the  light  i<s  diminished  it  expands. 

Every  one  knows  the  sensation  produced  by  entering  a  house  after  spending, 
hours  in  the  open  air  exposed  to  the  light  of  the  sun  reflected  from  snow.  In 
this  case  the  pupil  becomes  so  contracted,  and  the  eye  so  accustomed  to  a  strong 
light,  that  objects  within  doors  are  almost  invisible  until  the  pupil  expands  and 
the  eye  recovers  its  sensitiveness  in  ordinary  light.  The  movements  of  the  iris 
are  involuntary. 

The  pupil  of  the  owl  is  so  very  large  that  it  sees  distinctly  at  night,  while  in 
the  day-time  the  pupil  cannot  contract  enough  to  protect  the  eye  from  the  blind- 
ing effect  of  the  solar  rays,  and  hence  the  owl  is  nearly  blind  by  day. 

The  crystalline  lens,  f,  is  a  transparent  body,  placed  behind  the  iris  and  very 
near  to  it;  it  is  enveloped  in  a  transparent  membrane  or  capsule,  which  adheres 
by  its  borders  to  the  ciliary  process,  </.  The  posterior  surface  of  the  crystalline 
lens,  is  more  convex  than  the  anterior.  The  crystalline  lens  is  made  up  of 
serrated  fibres,  arranged  in  layers  which  increase  in  density  from  the  circum- 
ference to  the  centre  of  the  lens. 

Aqueous  humor. — The  space  between  the  cornea  and  the  crystalline  lens  is 
filled  with  a  transparent  liquid  called  the  aqueous  humor.  The  iris  divides  this 
space  into  two  chambers,  the  anterior  chamber,  6,  between  the  cornea  and  the  iris, 
and  the  posterior  chamber,  c,  between  the  iris  and  the  crystalline  lens.  These 
two  chambers  communicate  freely  with  each  other  through  the  pupil,  e.  The 
free  edge  of  the  iris  floats  in  the  aqueous  humor. 

Vitreous  humor. — The  posterior  compartment  of  the  eye,  h,  behind  the  crystal- 
line lens,  constitutes  by  far  the  larger  part  of  the  internal  cavity  of  this  organ, 
and  is  filled  with  a  transparent  gelatinous  fluid,  enclosed  in  exceedingly  delicate 
cellular  tissue,  which  is  condensed  externally,  and  forms  a  delicate  hyaloid 
membrane,  everywhere  covering  the  retina  and  the  posterior  surface  of  the 
crystalline  lens.  The  vitreous  humor,  enclosed  in  its  cellular  tissue,  and 
enveloped  by  the  hyaloid  membrane,  is  called  the  vitreous  body. 

469.  Action  of  the  eye  upon  light. — The  eye  may  be  compared 
to  a  dark  chamber,  the  pupil  being  the  opening  to  admit  the  light,  the 
crystalline  lens  being  a  converging  lens  to  collect  the  light,  and  the 
retina  a  screen  upon  which  is  spread  out  the  image  of  external  objects. 
The  effect  is  the  same  as  when  a  double  convex  lens  forms,  at  its  con- 
jugate focus,  an  image  of  any  object  placed  in  the  other  focus. 

Let  A  B,  fig.  373,  be  an  object  placed  before  the  eye,  and  consider  that  rays 
are  emitted  from  any  point,  as  373 

A,  in  all  directions ;  only  those 
rays  which  are  directed  towards 
the  pupil  can  penetrate  the  eye, 
or  contribute  to  the  phenomena 
of  vision.  The  rays,  on  enter- 
ing the  aqueous  humor,  'are 
refracted  towards  the  axis,  0  o,  drawn  through  the  optical  centre  of  the  crystal- 
line lens  ;  but  on  entering  the  lens,  which  is  more  dense  than  the  aqueous 
humor,  they  are  still  further  refracted,  and  undergoing  yet  another  refraction 
on  leaving  the  crystalline  lens,  they  converge  towards  a  point,  a,  where  they 


OPTICS.  341 

form  an  image  of  the  point  A  The  rays  of  light  emitted  from  B  form  its 
image  in  the  point  b,  and  in  the  same  manner  every  part  of  the  object,  A  B,  is 
delineated  in  the  very  small  image  a  b,  which  is  a  real  image,  inverted,  and 
formed  exactly  upon  the  retina. 

470.  Inversion  of  the  image  formed  in  the  eye. — To  prove  that 
the  image  formed  in  the  eye  is  really  inverted,  take  the  eye  of  an  ox, 
cut  away  the  posterior  part  of  the  sclerotic  and  choroid  coats  ;  fix  the 
eye  thus  prepared  in  an  opening  in  the  shutter  of  a  dark  chamber,  and 
look  at  it  with  the  aid  of  a  magnifying  glass,  when  external  objects 
will  be  seen  beautifully  delineated  in  an  inverted  position,  on  the  retina 
at  the  posterior  part  of  the  eye. 

Philosophers  and  physiologists  have  proposed  various  theories  to  explain  how 
we  come  to  perceive  objects  erect,  when  their  images  in  the  eye  are  actually 
inverted.  The  most  rational  of  these  theories  are  the  two  following  :  1st.  That 
we  judge  of  the  relative  position  of  objects,  or  of  different  parts  of  the  same 
object,  by  the  direction  in  which  the  rays  come  to  the  eye,  the  mind  tracing 
them  back  from  the  eye  towards  the  object.  2d.  That  the  image  formed  on  the 
retina,  gives  correct  ideas  of  the  relation  of  external  objects  to  each  other;  up 
and  down  being,  in  reference  to  impressions  on  the  retina  or  brain,  merely  the 
relative  directions  of  the  sky  and  earth ;  and  we  see  all  bodies,  including  our 
own  persons,  occupying  the  same  relations  to  these  fixed  directions  as  our  other 
senses  demonstrate  that  they  really  occupy. 

471.  Optic  axis. — Optic  angle. — The  principal  axis  of  the  eye, 
called  the  optic  axis,  is  its  axis  of  figure,  or  th'e  right  line  passing 
through  the  eye  in  such  a  position  that  the  eye  is  symmetrical  on  all 
sides,  of  it.     In  a  well  formed  eye  this  is  a  right  line,  passing  through 
the  centre  of  the  cornea,  the  centre  of  the  pupil,  and  the  centre  of  the 
crystalline  lens,  as  0  o,  fig.  373.     The  lines  A  a,  B  6,  which  are  sensi- 
bly right  lines,  are  secondary  axes.     Objects  are  seen  most  distinctly 
in  the  principal  optic  axis. 

When  both  eyes  are  directed  towards  the  same  object,  the  angle 
formed  by  lines  drawn  from  the  two  eyes  to  the  object,  is  called  the 
optic  angle,  or  the  binocular  parallax. 

To  appreciate  this  difference  of  direction,  look  at  two  objects  that  are  situated 
in  a  line  with  one  eye,  the  other  being  closed ;  then,  without  moving  the  head, 
look  at  the  same  objects  with  the  other  eye,  and  the  objects  will  not  both  appear 
in  the  same  line,  but  will  seem,  suddenly  to  change  their  positions.  By  such 
experiments  it  will  readily  be  found  that  some  persons  see  principally  with  the 
right,  and  others  chiefly  with  tl*e  left  eye,  when  both  eyes  are  open.  Others 
will  find  that  a  part  of  the  time  the  direction  of  objects  is  determined  by  one 
eye,  and  part  of  the  time  by  the  other.  374 

472.  Visual    angle. — The    angle 
formed  between  two  lines  drawn  from 
the  eye  to  the  two  extremities  of  an 

object,  is  called  the  visual  angle,  as  A  0  B,  fig.  374.     If  the  object  is 


842  PHYSICS    OF   IMPONDERABLE   AGENTS. 

removed  to  twice  the  distance,  the  visual  angle  A'  0  W  will  be  only 
one-half  as  great  as  A  0  B,  and  the  breadth  of  the  image  formed  on 
the  retina  will  be  proportionally  decreased. 

The  apparent  linear  magnitude  of  an  object  is  in  inverse  proportion  to  its 
distance  from  the  eye,  or  in  direct  proportion  to  the  visual  angle.  The  apparent 
superficial  magnitude  is  always  the  square  of  the  apparent  linear  magnitude,  and 
is  in  inverse  proportion  to  the  square  of  the  distance. 

473.  The  brightness  of  the  ocular  image  of  any  object  will  be 
in  direct  proportion  to  the  intensity  of  the  light  emanating  from  each 
point  in  the  object. 

The  amount  of  light  received  by  the  eye  from  any  point  in  the  object, 
or  from  the  entire  object,  will  be  inversely  as  the  square  of  the  distance, 
and  directly  as  the  intensity  of  the  light  from  each  point  (413).  But 
the  superficial  magnitude  of  the  image  will  diminish  as  the  square  of 
the  distance  increases :  Hence,  the  apparent  brightness  of  the  image  will 
remain  constant,  whatever  may  be  the  distance  of  the  object. 

As  the  object  recedes  from  the  eye,  the  size  of  the  image  formed  on  the  retina 
diminishes,  the  details  of  the  various  parts  become  crowded  together,  and  only 
the  bolder  outlines  occupy  sufficient  space  to  make  a  sensible  impression,  or  to 
be  clearly  discerned. 

475.  Conditions  of  distinct  vision. — Ittaay  be  stated  in  general, 
that  two  conditions  are  essential  to  distinct  vision.    1st.  That  an  object 
should  be  situated  at  such  a  distance  as  to  form  on  the  retina  an  image 
of  some  appreciable  magnitude.     2d.  That  the  object  shall   be  suffi- 
ciently illuminated  to  produce  a  distinct  impression  upon  the  retina. 

The  distance  at  tchich  an  object  can  be  seen  varies  with  the  color  of  the  object, 
and  the  amount  of  illumination.  A  white  object  illuminated  by  the  light  of  the 
sun  can  be  seen  at  a  distance  of  17,250  times  its  own  diameter.  A  red  object 
illuminated  by  the  direct  light  of  the  sun  can  be  seen  only  about  half  as  far  as 
though  it  were  white,  and  blue  at  a  distance  somewhat  less.  Objects  illuminated 
by  ordinary  day-light  can  be  seen  only  about  half  as  great  a  distance  as  when 
illuminated  by  the  direct  rays  of  the  sun.  The  smallest  visual  angle  under 
which  an  object  can  be  seen  with  the  naked  eye,  is  estimated  at  twelve  seconds. 
All  these  calculations  will  vary  for  different  eyes. 

Persons  having  dark-colored  eyes  can  generally  see  much  farther  than  those 
who  have  light-colored  eyes.  Those  whose  eyes  are  trained  to  view  distant 
objects,  as  sailors  and  surveyors,  will  see  objects  that  are  far  too  distant  to  be 
seen  by  the  eyes  of  inexperienced  persons, 

476.  Background. — The  distance  at  which  the  outline  of  any  object 
can  be  distinguished,  depends  very  much  upon  the  color  of  adjacent 
objects,  or  of  the  background  on  which  the  object  appears  projected. 
Objects  are  most  distinctly  seen  when  the  color  of  adjacent  objects,  or 
the  background,  presents  a  strong  contrast  to  the  colors  of  the  object 
we  wish  to  see. 


OPTICS.  343 

Colored  signals. —-I? or  signal  flags  used  at  sea,  the  colors  red,  yellow,  blue,  and 
white  are  employed,  because  they  are  readily  distinguished,  and  are  easily  seen, 
with  the  water  or  the  sky  for  a  background.  For  railroad  signals,  the  colors 
red,  white,  and  Hack  are  mostly  used. 

477.  Sufficiency  of  illumination. — It  is  not  enough  for  distinct 
vision,  that  a  well-defined  image  of  the  object  shall  be  formed  on  the 
retina.    This  image  must  be  sufficiently  illuminated  to  affect  the  senses, 
and  at  the  same  time  not  so  intensely  illuminated  as  to  overpower  the 
organ.    An  image  may  be  so  faint  as  to  produce  no  sensation,  or  it  may 
be  so  intensely  brilliant  as  to  dazzle  the  eye,  destroy  the  distinctness 
of  vision,  and  produce  absolute  pain. 

When  we  look  at  the  meridian  sun,  its  light  is  so  brilliant  as  to  overpower 
the  eye  and  render  it  impossible  even  to  see  distinctly  the  solar  disc,  but  if  a 
sufficient  stratum  of  vapor  or  a  colored  or  smoked  glass  is  interposed,  we  see  a 
well-defined  image  of  the  sun. 

Many  stars  are  so  distant  that  the  rays  which  enter  the  pupil,  when  converged 
to  a  point  on  the  retina,  produce  no  appreciable  sensation,  but  when  th*e  amount 
of  light  from  the  same  stars  falling  upon  a  large  lens  is  concentrated  upon  the 
retina,  it  produces  sensation,  and  the  stars  become  visible. 

On  passing  from  a  dark  room  to  one  brilliantly  illuminated,  or  on  going 
out  into  the  open  air  at  night  from  a  well-illuminated  room,  the  sensations 
experienced  are  owing  partly  to  the  contraction  and  expansion  of  the  iris,  as 
explained  in  $  468,  and  also  to  the  fact  that  the  sensibility  of  the  retina  is 
diminished  by  long  exposure  to  intense  light,  and  increased  by  remaining  a  long 
time  in  feeble  light. 

478.  Distance  of  distinct  vision. — Although  the  human  eye  is 
capable  of  seeing  objects  at  both  great  and  small  distances,  most  per- 
sons, when  they  wish  to  see  the  minute  structure  of  an  object  clearly, 
instinctively  place  it  at  a  distance  of  from  six  to  ten  inches  from  the 
eye.     This  point,  called  the  limit  of  distinct  vision,  sometimes  varies  for 
the  two  eyes  of  the  same  person.     Persons  who  see  objects  at  very 
short  distances  are  called  near-sighted,  while  those  who  see  objects  dis- 
tinctly only  at  greater  distances,  are  said  to  be  long-sighted. 

479.  Visual  rays  nearly  parallel. — When  we  consider   that  the 
'diameter  of  the  pupil,  when  the  eye  is  adjusted  for  viewing  near  objects, 
is  only  about  one-tenth  of  an  inch,  if  we  take  the  limit  of  distinct  vision 
at  six  inches,  it  will  be  found  that  the  cone  of  rays  entering  the  eye, 
from  any  single  point,  is  included  within  an  angle  of  one  degree.     If 
we  *ake  the  limit  of  distinct  vision  at  ten  inches,  the  angular  divergence 
of  the  cone  of  rays  entering  the  eye  from  a  single  point  will  be  little 
more  than  half  a  degree.     In  either  case,  therefore,  the  rays  differ  but 
slightly  from  parallel  rays.     For  all  objects  more  remote,  the  rays  may 
properly  be  considered  as  parallel.   Distinct  vision  is  therefore  obtained 
only  by  rays  that  are  sensibly  parallel  or  very  slightly  divergent. 


344          PHYSICS  OF  IMPONDERABLE  AGENTS 

480.  Adaptation  of  the  eye  to  different  distances. — Although 
there  is  a  definite  distance  at  which  minute  objects  are  most  distinctly 
seen,  the  eye  has  a  wonderful  facility  of  adapting  itself  to  viewing 
objects  at  different  distances. 

Let  two  similar  objects  be  placed,  one  three  feet  from  the  eye  and  the  other  at 
a  distance  of  six  feet :  If  the  eye  is  fixed  steadily  upon  the  nearer  object  for  a 
few  moments,  it  will  be  distinctly  seen,  while  the  more  remote  object  will  appear 
indistinct,  but  if  the  eye  is  steadily  fixed  upon  the  remote  object,  that  object 
will  soon  be  clearly  seen,  and  the  nearer  object  will  appear  indistinct.  We  thus 
see  that  either  the  converging  power  of  the  eye  is  subject  to  rapid  variation,  or 
that  the  distance  of  the  crystalline  lens  from  the  retina  is  changeable.  The 
means  by  which  the  eye  thus  rapidly  adapts  itself  to  viewing  objects  at  different 
distances,  have  not  been  satisfactorily  determined. 

481.  Appreciation  of  distance  and  magnitude : — Aerial  per- 
spective.— The  appreciation  of  the  distance  and  magnitude  of  objects 
is  entirely  a  matter  of  unconscious  training,  or  education,  and  depends 
upon  a  variety  of  circumstances,  as  the  visual  angle,  optic  angle,  com- 
parison with  familiar  objects,  distinctness,  or  dimness  of  the  image 
caused  by  intervening  air  or  vapor. 

When  the  magnitude  of  an  object  is  known,  as  the  height  of  a  man,  a  house, 
era  tree,  the  visual  angle  under  which  it  is  seen  enables  us  to  appreciate  its  dis- 
tance. If  its  magnitude  is  unknown,  we  judge  of  its  size  by  comparing  it  with 
other  familiar  objects  situated  at  the  same  distance. 

In  viewing  a  range  of  buildings,  or  a  row  of  trees,  the  visual  angle  decreases 
as  the  distance  increases,  and  the  objects  decrease  in  apparent  size  in  the  same 
proportion,  but  the  habit  of  viewing  the  houses  or  trees,  and  their  known  altitude, 
causes  us  to  correct  the  impression  produced  by  the  visual  angle,  so  that  they  do 
not  appear  to  decrease  in  size  as  fast  as  their  distance  increases. 

Thus,  when  distant  mountains  are  seen  under  a  very  small  visual  angle, 
occupying  but  a  small  space  in  the  field  of  view,  being  accustomed  to  aerial  per- 
spective, we  unconsciously  restore  to  some  extent  their  real  magnitude. 

The  optic  angle,  or  binocular  parallax,  is  an  essential  element  in  appreciating 
distances.  This  angle  increases  or  diminishes  inversely  as  the  distance;  the 
movement  of  the  eyes  required,  to  cause  the  optic  axes  of  the  two  eyes  to  con- 
verge upon  any  object  which  we  are  viewing,  gives  us  an  idea  of  its  distance. 
It  is  only  by  habit  that  we  appreciate  the  relation  between  the  distance  of  an 
object  and  the  corresponding  movement,  required  to  direct  both  eyes  upon  it. 

Perfect  vision  cannot  then  be  obtained  without  two  eyes,  as  it  is  by  the  com- 
bined effect  of  the  images  produced  on  the  retinae  of  both  eyes,  and  the  different 
angles  under  which  objects  are  observed,  that  a  judgment  is  formed  respecting 
their  solidity  and  distances. 

A  man  restored  to  sight  by  couching  cannot  tell  the  form  of  a  body  without 
touching  it,  until  his  judgment  has  been  matured  by  experience,  although  a  per- 
fect image  may  be  formed  on  the  retina  of  each  eye.  A  man  with  only  one  eye 
cannot  readily  distinguish  the  form  of  a  body  which  he  had  never  previously 
seen,  but  quickly  and  unwittingly  moves  his  head  from  side  to  side,  so  that  his 
one  eye  may  alternately  occupy  the  different  positions  of  a  right  and  a  left  eye ; 
and,  if  we  approach  a  candle  with  one  eye  shut,  and  then  attempt  to  snuff  it,  we 


OPTICS.  345 

shall  experience  more  difficulty  than  we  might  have  expected,  because  the  usual 
mode  of  determining  the  correct  distance  is  wanting. 

Infants  plainly  have  no  notions  of  distances  and  magnitudes  till  taught  oy 
experience  and  comparison  of  optical  appearances  with  the  sense  of  touch. 

482.  Single  vision  with  two  eyes. — When  both  eyes  are  directed 
to  the  same  object,  images  are  produced  in  both  eyes,  and  the  inquiry 
is  most  natural  why  all  objects  thus  seen  do  not  appear  double  ?  Pass- 
ing by  much  learning  bestowed  on  this  subject,  the  simplest  and  most 
satisfactory  explanation  of  the  phenomenon  is  deduced  from  the  ana- 
tomical structure  of  the  optic  nerves,  and  their  relations  to  each  other, 
and  to  the  brain. 

The  eyes  may  be  compared  to  two  branches  issuing  from  a  single 
root,  of  which  every  minute  portion  bifurcates,  so  as  to  send  a  twig  to 
each  eye.  (Miiller.)  The  optic  nerve  from  the  right  lobe  of  the  brain 
sends  a  portion  of  its  fibres  to  each  eye,  and  also  sends  some  branches 
across  and  backward  to  the  left  lobe  of  the  brain.  A  portion  of  the 
optic  nerve  from  the  right  eye,  instead  of  proceeding  to  the  brain,  curves 
around  and  enters  the  optic  nerve  and  the  retina  of  the  left  eye.  In 
the  same  manner  the  optic  nerve  arising  from  the  left  lobe  of  the  brain 
is  connected  with  the  right  eye,  and  sends  branches  also  to  the  left  eye. 

Branches  of  the  same  nerve  fibres  which  go  to  the  external  side  of 
the  retina  of  one  eye,  go  to  the  internal  side  of  the  other  eye. 

It  is  thus  that  a  perfect  sympathy  and  correspondence  is  established  between 
similar  parts  of  both  eyes.  Hence  whatever  object  is  observed,  if  the  optic  axes 
of  both  eyes  are  directed  towards  it,  the  image  is  formed  on  corresponding  por- 
tions of  the  retina  in  both  eyes,  and  the  mind  receives  the  impression  of  a  single 
object }  but  the  impression  is  more  vivid  than  if  the  same  object  were  seen  with 
only  one  eye.  So  perfect  is  this  sympathy  between  the  two  eyes,  that  if  one  eye 
only  is  exposed  to  a  strong  light  the  pupils  of  both  eyes  contract.  If  one  eye  is 
diseased  and  protected  from  the  light,  it  suffers  pain  from  light  entering  only 
the  sound  eye. 

483.  Double  vision. — If  both  eyes   are  fixed  steadily  upon   one 
object,  any  other  object  seen  at  the  same  time  will  appear  double. 

Fix  both  eyes  steadily  upon  the  flame  of  a  lamp  or  candle,  and  a  finger  held 
between  the  eyes  and  the  light  will  appear  double. 

Drunken  persons,  or  persons  about  falling  asleep,  often  see  objects  double, 
owing  to  the  inability  to  direct  both  eyes  steadily  upon  the  same  object.  The 
same  phenomena  may  occur  when,  from  any  cause,  the  nerves  which  control  the 
eye  become  diseased. 

484.  Binocular  vision. — A  picture  of  an  object  is. formed  on  the 
retina  of  each  eye  ;  but  although  there  may  be  but  one  object  presented 
to  the  two  eyes,  the  picture  formed  on  the  two  retinas  are  not  precisely 
alike,  because  the  object  is  not  observed  from  the  same  point  of  view. 

If  the  right  hand  be  held  at  right  angles  to,  and  at  a  few  inches  from  the  faced 
32 


346  PHYSICS   OP   IMPONDERABLE    AGENTS. 

the  back  of  the  hand  will  be  seen  when  viewed  by  the  right  eye  only,  and  the 
palm  of  the  hand  when  viewed  by  the  left  eye  only ;  hence  the  images  formed 
on  the  retinae  of  the  two  eyes  must  differ,  the  one  including  more  of  the  right 
side,  and  the  other  more  of  the  left  side  of  the  same  solid  or  projecting  object. 
Again ;  if  we  bend  a  card  so  as  to  represent  a  triangular  roof,  place  it  on  the 
table  with  the  gable  end  towards  the  eyes,  and  look  at  it,  first  with  one  eye  then 
with  the  other,  quickly  and  alternately  opening  and  closing  one  of  the  eyes,  the 
card  will  appear  to  move  from  side  to  side,  because  it  is  seen  by  each  eye  under 
a  different  angle  of  vision.  If  we  look  at  the  card  with  the  left  eye  only,  the 
whole  of  the  left  side  of  the  card  will  be  plainly  seen,  while  the  right  side  will 
be  thrown  into  shadow.  If  we  next  look  at  the  same  card  with  the  right  eye 
only,  the  whole  of  the  right  side  of  the  card  will  be  distinctly  visible,  while  the 
left  side  will  be  thrown  into  shadow ;  and  thus  two  images  of  the  same  object, 
with  differences  of  outline,  light  and  shade,  will  be  formed,  the  one  on  the  retina 
of  the  right  eye  and  the  other  on  the  retina  of  the  left.  These  images  falling  on 
corresponding  parts  of  the  retinas  convey  to  the  mind  the  impression  of  a  single 
object,  while  experience  having  taught  us,  however  unconscious  the  mind  may 
be  of  the  existence  of  two  different  images,  that  the  effect  observed  is  always 
produced  by  a  body  which  really  stands  out  or  projects,  the  judgment  naturally 
determines  the  object  to  be  a  projecting  body.* 

485.  Near-sightedness. — Many  persons  are  unable  to  see  minute 
objects  distinctly  unless  they  are  placed  within  three  or  four  inches  of 
the  eye.     Such  persons  are  often  unable  to  see  ordinary  objects  dis- 
tinctly in  a  large  room  or  across  the  street ;  they  are  therefore  said  to 
be  near-sighted  (478).     This  defect  is  owing  to  a  too  great  convergent 
power,  the  eye  bringing  parallel  or  slightly  divergent  rays  to  a  focus 
before  they  reach  the  retina. 

To  secure  distinct  vision  in  such  cases,  it  is  necessary  to  bring  the  object  so 
near  the  eye  as  to  render  the  rays  entering  the  eye  considerably  divergent,  when 
the  image  will  be  formed  on  the  retina.  The  same  object  may  be  accomplished 
by  placing  a  concave  lens  before  the  eye,  when  the  rays  from  distant  objects  will 
be  rendered  divergent,  and  the  strong  convergent  power  of  the  eye  will  form  the 
image  on  the  retina.  Concave  lenses  for  near-sighted  persons  should  be  such 
as  have  a  focus  a  little  longer  than  the  distance  at  which  they  see  objects  most 
distinctly. 

486.  Long-sightedness  commonly  occurs  in  old  people,  when  the 
eye  becomes  flattened  by  diminution  of  its  fluids,  or  some  structural 
change  in  the  crystalline  lens  occurs,  by  which  its  convergent  power  is 
diminished.     In  such  cases  the  rays  of  light  tend  to  form  an  image 
behind  the  retina,  and  vision  is  most  distinct  when  the  object,  as  a 
book  when  reading,  is  held  at  a  considerable  distance  from  the  eyes,  so 
as  to  allow  the  image  to  be  formed  on  the  retina. 

This  defect  of  the  eyes,  when  not  accompanied  by  disease,  may  be  entirely 

*  For  a  discussion  of  this  subject,  see  Prof.  W.  B.  Rogers  on  Binocular  vision, 
Am.  Jour.  Sci.  [2]  vol.  XX. 


OPTICS.  347 

remedied  by  using  convex  glasses,  which  make  up  for  the  diminished  converg- 
ing power  of  the  eyes,  and  bring  the  rays  to  such  a  condition  that  the  eye  is 
enabled  to  bring  the  light  from  near  objects  to  a  distinct  focus  upon  the  retina. 
In  such  cases,  however,  the  power  of  accommodating  the  eye  to  different  dis- 
tances is  often  not  as  great  as  in  younger  persons ;  hence  many  people  in 
advanced  life  find  it  necessary  to  use  one  set  of  glasses  for  near,  and  another  for 
distant  objects. 

487.  Duration  of  the  impression  upon  the  retina. — Every  one 
knows  that  a  lighted  stick  whirled  rapidly  around  a  circle  appears  like 
a  ring  of  fire.     The  rapidity  of  revolution  required  to  produce  this 
impression  is  one-third  of  a  second  in  a  dark  room,  and  one-sixth  of  a 
second  by  daylight. 

When  a  meteor  darts  across  the  heavens,  it  appears  to  leave  a  luminous  track 
behind  it,  because  the  impression  produced  upon  the  retina  remains  after  the 
meteor  has  passed  a  considerable  distance  on  its  way.  The  zigzag  course  of  the 
lightning  appears,  for  the  same  reason,  as  a  continuous  track. 

Winking  does  not  interfere  with  distinct  vision,  because  the  continu- 
ance of  the  impression  of  external  objects  on  the  retina  preserves  the 
sense  of  continuous  vision. 

488.  Optical  toys. — Thaumatrope. — A  great  number  of  optical 
toys  and  pyrotechnic  exhibitions  owe  their  effect  to  the  continuance  of 
the  impression  upon  the  retina,  when  the  object  has  changed  its  place. 

If  a  horse  is  painted  on  one  side  of  a  card  and  a  rider  on  the  other  side,  the 
rapid  revolution  of  the  card  causes  the  rider  to  appear  seated  on  the  horse.  In 
the  same  manner,  if  any  object  which  takes  a  variety  of  positions  in  moving  is 
painted  in  successive  positions,  at  equal  distances  on  a  revolving  wheel,  so 
arranged  that  one  only  of  the  figures,  shall  be  seen  at  a  time,  the  object  is  seen 
performing  all  the  motions  of  real  life.  In  this  manner  a  horse  may  be  made  to 
appear  leaping  a  gate,  or  boys  playing  at  leap-frog.  These  toys  are  called 
thaumatropes  and  anorthoacopes.  Other  toys,  called phenakistoscopes  and phantas- 
copes,  are  variations  of  the  same  thing,  combined  with  mirrors  and  other  ingenious 
arrangements  on  the  same  principle. 

489.  Time  required  to  produce  visual  impressions. — If  an  object 
moves  with  sufficient  velocity,  it  is  entirely  invisible,  its  image  upon  the 
retina  not  remaining  long  enough  to  produce  any  impression.     This  is 
the  case  with  a  cannon-ball  or  rifle-ball,  viewed  at  right  angles  to  the 
direction  of  its  flight.     But  if  the  projectile  is  going  from  us,  or  coming 
towards  us,  it  preserves  the  same  direction  long  enough  to  produce  an 
impression.     Motions  describing  less  than  one  minute  of  arc  in  a  second 
of  time  are  not  appreciable  to  us.     Hence  we  do  not  see  the  movements 
of  the  hour  hand  of  a  clock,  or  of  the  heavenly  bodies. 

490.  Appreciation  of  colors. — Color  blindness. — The  power  of 
the  eye  to  distinguish  colors,  varies  greatly  in  different  persons.    Some 
eyes  fail  entirely  in  this  particular,  while  in  every  other  respect  they 


348 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


are  perfect.  Such  eyes  are  said  to  be  color-blind.  Some  confound 
certain  colors,  as  red  and  green,  while  they  distinguish  others,  or  while 
they  recognise  all  the  colors  of  the  spectrum,  they  cannot  appreciate 
delicate  shades  of  the  same  color. 

Colors  are  greatly  modified  by  proper  contrast  with  other  colors. 
Thus  the  complementary  colors  mutually  enhance,  while  those  not  com- 
plementary diminish  each  other's  beauty  when  contrasted.  The  sensi- 
bility of  the  eye  is  much  diminished  by  long  inspection  of  any  color, 
and  its  power  of  perceiving  the  complementary  color  is  proportionally 
increased.  This  principle  is  the  key  to  harmony  of  colors  in  nature 
and  art,  and  serves  to  explain  the  modification  of  color  by  contrast,  and 
proximity  of  two  or  more  colors. 

491.  Chevreul's  classification  of  colors,  and  chromatic  dia- 
gram.— The  chromatic  diagram  of  Chevreul,  fig.  375,  greatly  facilitates 

375 


REDDISH  OKANG 


ORAN&E 


YELLOWISH 


ENISH  BLUE 


the  study  of  complementary  colors,  and  the  modifications  produced  by 
their  mutual  proximity. 

Three  radii  of  a  circle  represent  Brewster's  three  cardinal  colors,  red,  yellow, 
and  blue  ,•  between  these  are  placed  orange,  green,  and  violet.  Between  these 
six  colors  are  placed  reddish  orange,  orange  yellow,  yellowish  green,  greenish  blue, 
violet  blue,  and  violet  red.  We  thus  obtain  twelve  principal  colors,  each  of 
which  may  be  again  divided  into  five  scales  or  hues,  which  gradually  approach 
the  succeeding  color. 

We  thus  have  the  circumference  of  the  circle,  which  represents  the  prismatic 


OPTICS.  349 

spectrum,  divided  into  sixty  scales  of  pure  colors.  Each  radius  representing  a 
scale  of  colors  is  divided  into  twenty  tones,  to  represent  the  intensity  of  each 
color  in  its  own  scale.  The  tone  of  any  color  may  be  lowered  by  the  addition 
of  white,  when  it  will  remain  in  the  same  radius  or  scale,  but  take  a  position  at 
a  lower  tone,  or  nearer  the  centre  of  the  circle.  A  color  modified  by  black,  is 
called  a  broken  color,  but  as  the  color  is  deeper,  the  tone  is  carried  towards  the 
circumference  of  the  circle.  To  represent  the  modifications  produced  by  black, 
Chevreul  employs  a  movable  quadrant,  not  easily  introduced  in  our  illustration. 

When  two  complementary  colors  are  mixed,  their  combination  produces  white, 
if  the  colors  are  pure.  The  combination  of  two  colors  not  complementary  pro- 
duces a  certain  quantity  of  white,  but  principally  a  color  which  will  be  found 
in  the  diagram  intermediate  between  the  two  colors,  if  they  are  of  the  same 
tone,  or  nearer  to  the.  color  of  deeper  tone,  when  their  tones  or  intensities  are 
different.  The  complementary  color  in  the  diagram  is  found  at  the  opposite 
extremity  of  the  diameter  of  the  circle. 

This  diagram  thus  explains  the  effect  which  two  colors  produce  upon  each 
other  by  their  mutual  proximity. 

When  two  colors  are  placed  near  each  other,  each  color  appears  modified  as 
though  mixed  with  a  small  portion  of  tlie  complement  to  fJte  color  which  is  near  it. 

Examples. — (a)  Suppose  blue,  and  yellow  to  be  placed  side  by  side;  at  one 
extremity  of  a  diameter  we  read  yellow,  and  at  the  opposite  violet,  hence  the 
proximity  of  yellow  gives  to  the  blue  a  shade  of  violet,  or  makes  it  approach 
violet  blue.  In  the  same  manner  we  find  orange  complementary  to  blue  ;  hence 
the  blue  gives  a  shade  of  .orange  to  the  yellow,  or  makes  it  approach  orange 
yellow. 

(b)  Let  green  and  yellow  be  contiguous,  the  yellow  will  receive  red,  the  com- 
plement of  green,  and  will  become  orange  yellow,  while  the  green  will  receive 
from  the  yellow  its  complementary  violet.  A  part  of  the  yellow  in  the  green 
will  thus  be  neutralized,  and  the  green  will  appear  bluer  or  less  yellow,  in  fact, 
greenish  blue. 

492.  The  study  of  colors  upon  the  principles  here  laid  down  is 
of  great  importance  to  the  artist  and  manufacturer,  whether  in  repro- 
ducing the  beauties  of  nature,  or  in  architectural  decoration ;  also  in 
weaving,  embroidery,  and  costume. 

The  skillful  salesman  knows  how  to  enhance  the  brilliancy  or  beauty  of  his 
goods  by  artfully  contrasting  the  pieces  which  he  hopes  to  sell  by  others  having 
complementary  colors.  Good  taste  in  dress  never  violates  these  principles, 
regarding  with  care  the  complexion  of  the  wearer  in  contrast  to  the  colors 
selected.  Florid  skins  can  bear  dark  hues  in  dress,  while  delicate  complexions 
arc  made  pallid  by  heavy  colors.  A  green  dress  or  wreath  increases  the  freshness 
of  a  rosy  complexion.  A  crimson  dress  and  scarlet  shawl  worn  together  appear 
mutually  dull  and  heavy,  while  either,  with  the  contrast  of  an  appropriate  shade 
of  green,  would  be  attractive  and  tasteful.  These  topics  will  be  found  fully  con- 
sidered in  "  Chevreul  on  Colors." 

•§  6.  Optical  Instruments. 

493.  Magnifying    glasses. — Single   lenses,    used   for   magnifying 
small  objects,  occupy  an  important  place  in  the  arts.     They  are  used 
by  watch-makers,  jewelers,  engravers,  and  other  artisans,  whose  labors 

32* 


350  PHYSICS    OF    IMPONDERABLE    AGENTS 

ar&  performed  upon  minute  structures.  These  instruments  occupy  a 
middle  place  between  spectacles  and  the  regular  microscope  composed 
of  a  variety  of  parts. 

'A  thorough  knowledge  of  the  uses  and  powers  of  simple  lenses  forms  the  basis 
of  all  calculations  of  the  powers  and  uses  of  more  complex  instruments,  like 
the  compound  microscope  and  the  telescope. 

The  eye  takes  no  cognisance  of  real  magnitude,  which  it  can  only  estimate  by 
inference,  but  notices  directly  apparent  magnitude,  which  is  determined  in  all 
cases  by  the  visual  angle  under  which  objects  are  seen  (472). 

We  have  seen  (479)  that  it  is  essential  to  distinct  vision  that  the  rays  entering 
the  pupil  from  any  one  point  of  an  object  should  be  parallel,  or  slightly  diver- 
gent, the  distance  of  most  distinct  vision  being  generally  from  five  to  ten  inches. 
For  near-sighted  persons,  this  distance  is  as  small,  sometimes,  as  two  or  three 
inches,  and  for  eyes  enfeebled  by  age,  it  extends  from  fifteen  even  to  thirty 
inches. 

494.  The  magnifying  power  of  a  lens  is  found  with  sufficient 
accuracy  for  ordinary  purposes  by  dividing  the  limit  of  distinct  vision 
(ten  inches)  by  the  distance  of  the  principal 
focus  of  the  lens. 

Let  A  B,  fig.  376,  be  an  object  placed 
before  a  convex  lens,  so  much  nearer  to  the 
lens  than  the  focus,  F,  that  the  rays,  after 
refraction  by  the  lens,  shall  be  in  that  state 
of  slight  divergence  best  adapted  to  produce  distinct  vision,  that  is, 
diverging  as  though  emanating  from  a  point  at  a  distance  of  ten 
inches  or  the  limit  of  distinct  vision.  Let  a  6  represent  the  virtual 
image,  formed  where  the  refracted  rays  would  meet  if  extended  back- 
ward, then  a  b  will  be  as  much  greater  than  A  B,  as  its  distance  from 
the  lens  is  greater  than  the  distance  of  the  object,  AB,  from  the  lens. 
The  divergence  of  rays  of  light  entering  the  small  opening  of  the 
pupil,  from  a  point  ten  inches  distant,  is  so  small  that  we  may  consider 
them  parallel,  and  then  the  object,  AB,  will  be  nearly  at  F,  the  prin- 
cipal focus  of  the  lens. 

To  estimate  the  magnifying  power  of  a  lens  more  accurately,*  let  the  distance 
of  most  distinct  vision  be  represented  by  e;  with  a  lens  interposed,  the  eye 
sees  a  virtual  image  of  the  object,  therefore,  in  the  formula  for  a  convex  lens,  let 

v  =  —  e,  and  then = .-.  u  = ,  which  is  the  distance  of  the 

e        f         u  .+/ 

object  from  the  lens.     If  the  eye  is  placed  close  to  the  lens,  the  magnifying 

power  represented  by  M  will  be,  M  =  -  =  L-ZLl  -.=  1  -j-  1. 

«  /  / 

If  the  eye  is  placed  at  a  distance  from  the  lens  represented  by  d,  we  shall  have 
the  distance  of  the  virtual  image  a  6  from  the  lens  represented  by  e'  =  e  —  d, 

and  the  magnifying  power  will  become,  M  =  1  -j 


OPTICS. 


351 


If  the  eye  is  placed  at  a  distance  from  the  lens  equal  to  its  principal  focus, 
or,  d  =  /,  then  M  =  -,  and  in  that  case  the  magnifying  power  for  different 

eyes  varies  as  the  limit  of  most  distinct  vision. 

If  the  eye  is  placed  at  a  distance  from  the  lens  equal  to  the  distance  at  which 

it  sees  objects  most  distinctly,  then  —  —  0,  and  M  =.  1,  or  the  object  is  not 

magnified  by  the  action  of  the  lens. 

The  superficial  magnifying  power  is  equal  to  the  square  of  the  linear 
magnifying  power  given  by  the  rule  stated  above  ;  but  the  linear  mag- 
nifying power  is  alone  commonly  used  in  scientific  treatises. 

495.  The  simple   microscope   acts  in  the  same  manner  as  the 
single  lens  or  magnifying  glass.    Instead  of  a  single  lens,  a  doublet  or 
triplet,  acting  as  a  single  lens,  is  often  used. 

Raspail's  dissecting  microscope,  -shown  in 
fig.  377,  is  the  most  complete  simple  microscope.  The 
magnifying  lens,  o,  mounted  in  a  dark  cup,  A,  to 
protect  the  eye  from  extraneous  light,  is  fixed  in  the 
end  of  a  movable  arm  which  can  be  rotated  on  its 
support,  elevated  and  depressed  by  the  milled  head 
E,  or  lengthened  by  turning  the  milled  head  C. 
Below  the  lens  is  the  stage  B,  which  supports  the 
object  to  be  examined.  The  concave  mirror,  M,  can 
be  so  adjusted  as  to  illuminate  the  object  by  a  con- 
centrated pencil  of  transmitted  light. 

In  using  this  microscope,  the  eye  is  placed  over 
the  lens  o,  which  may  be  elevated  or  depressed  till 
the  focus  is  adjusted  to  give  the  most  distinct  view  of  the  object  on  the  stage. 
Opaque  objects  are  illuminated  by  a  bull's  eye  lens. 

By  using  lenses  of  different  foci,  magnifying  powers  may  be  obtained  with  this 
instrument,  varying  from  two  to  one  hundred  and  twenty  diameters. 

496.  The    compound   microscope    consists,    essentially,    of  two 
lenses,  so  arranged  that  when  an  object  is  placed  37S 

a  little  beyond  the  principal  focus  of  the  first 
lens,  its  image  may  be  formed  in  the  principal 
focus  of  the  second  lens,  by  which  it  is  viewed 
as  an  object  is  viewed  by  a  common  magnifier. 

The  arrangement  of  the  lenses  in  the  compound 
microscope  is  shown  in  fig.  378,  and  also  the  position 
of  the  object,  and  the  images  both  real  and  virtual. 

The  object,  s  r,  being  placed  near  the  first  lens,  a  b, 
called  the  object-glass,  an  image,  inverted  and  much 
enlarged,  is  formed  at  R  S,  in  the  focus  of  the  second 
lens,  d  c,  called  the  eye-glass.  By  this  lens,  the  rays 
are  transmitted  slightly  divergent,  and  in  the  exact 
condition  to  produce  distinct  vision  when  viewed  by 
the  eye.  The  rays  transmitted  through  the  eye-glass,  if  traced  backward  to  the 


352  PHYSICS    OF    IMPONDERABLE    AGENTS. 

distance  of  distinct  vision,  form  a  virtual  image  at  R'  S',  much  larger  tLan  the 
real  image  R  S,  formed  by  the  action  of  the  first  lens. 

Such  a  compound  microscope  as  the  one  shown  in  this  figure,  is  subject  to 
chromatic  and  spherical  aberration,  and  the  image  viewed  by  the  eye  is  not 
straight  as  shown  in  the  figure,  but  curved  so  as  to  appear  convex  towards  the 
eye.  These  imperfections  are  almost  entirely  corrected  in  the  achromatic  com- 
pound microscope  described  in  $  511. 

497.  The  telescope  is  an  instrument  constructed  for  viewing  dis- 
tant objects. 

Telescopes  are  of  two  kinds.  Refracting  telescopes  are  constructed 
of  lenses.  Reflecting  telescopes  contain  one  or  more  metallic  reflectors. 

498.  The  telescope  used  by  G-alileo  in  1609,  is  the  oldest  form 
of  which  we  have  any  definite  description.     The  Galilean  telescope 
consists  of  a  convex  lens,  of  long  focus,  and  a  concave  lens  of  short 
focus  placed  at  a  distance  apart,  equal  to  the  difference  of  their  princi- 
pal foci.     The  light  from  distant  objects  collected  by  the  large  surface 
of  the  convex  field-lens,  is  brought  to  such  a  state  of  divergence  by  the 
concave  eye-lens  as  to  produce  distinct  vision  in  the  eye. 

The  magnifying  power  of  the  Galilean  telescope  is  found  by  dividing 
the  principal  focus  of  the  convex  lens  by  the  principal  focus  of  the  con- 
cave lens. 

The  convex  lens>  M  N,  fig.  379,  tends  to  form  an  image  of  a  distant  object, 
A  B,  very  near  its  principal  focus,  as  at  a  b.  The  concave  lens,  E  F,  being 

379 


Z>' 

placed  between  the  convex  lens  and  the  image,  a  b,  renders  the  rays  which  were 
converging  to  a,  slightly  divergent,  as  though  emanating  from  a  point,  a',  at 
the  distance  of  distinct  vision,  about  ten  inches.  The  same  effect  is  produced 
on  the  rays  converging  to  b.  The  direction  of  the  obliqne  pencils  is  changed, 
and  the  extremities  of  the  image  appear  in  the  secondary  axis  a  0'  a',  and  b  0'  b', 
drawn  from  a  and  b  through  0',  the  optical  centre  of  the  lens  B  F.  It  is  espe- 
cially to  be  noticed,  that  while  the  rays  from  any  one  point  in  the  object  are 
rendered  parallel,  or  slightly  divergent,  by  the  concave  lens,  the  pencils  from  the 
extreme  points  converge  at  0'  much  more  than  at  0,  making  the  visual  angle 
a'  0'  b' ,  under  which  the  object  is  seen  by  the  telescope,  much  greater  than  the 
visual  angle  a  0  6,  under  which  the  object  would  appear  without  the  telescope. 

Since  the  angle  A  0  B  is  equal  to  a  0  b,  and  a'  0'  b'  is  equal  to  a  0'  b,  the 
visual  angle  «'  0'  b'  is  to  the  angle  A  0  B  as  0  F  is  to  0'  F,  and  the  image  a'  b1 
appears  as  much  greater  than  the  object  as  the  focal  length  0  F  of  the  convex 
lens  exceeds  the  focal  length  0'  F,  of  the  concave  lens. 


OPTICS. 


353 


The  opera-glass  consists  generally  of  two  Galilean  telescopes,  placed 
near  together,  to  allow  Of  distinct  vision  by  both  eyes. 

Night-glasses,  used  by  seamen,  are  constructed  like  large  opera- 
glasses.  They  serve  to  concentrate  a  large  amount  of  light  in  such  a 
condition  as  to  allow  of  distinct  vision,  and  thus  enable  the  eye  to  see 
objects  distinctly  in  the  night.  They  have  a  low  magnifying  power. 

With  the  Galilean  telescope  in  all  its  forms  the  object  appears  erect. 

499.  The   astronomical   telescope   may  be   constructed   with   a 
convex  lens  placed  beyond  the  image  formed  by  the  field-lens.     The 
second  lens  then  magnifies  the  image  formed  by  the  first  lens.     The 
object  appears  inverted,  but  this  occasions  very  little  inconvenience  in 
astronomical  observations. 

500.  Eye-pieces  are  certain  combinations  of  lenses  used  in  both 
telescopes  and  microscopes  to  magnify  the  image  formed  by  the  lens 
nearest  to  the  object.   They  have  less  spherical  and  chromatic  aberration 
than  a  single  lens,  and  also  enable  the  eye  to  take  in  a  larger  extent 
of  the  object  to  be  examined  than  could  otherwise  be  seen. 

The  positive  eye-piece,  invented  by  Ramsden,  consists  of  two 
plano-convex  lenses,  with  their  convex  surfaces  turned  towards  each 
other,  and  placed  at  such  a  distance  that  the  object  or  image  to  be 
viewed  by  it  is  seen  distinctly  when  brought  very  nearly  in  contact 
with  the  first  lens.  To  secure  this  result,  the  distance  between  the 
lenses  must  be  a  very  little  less  than  one-half  the  sum  of  their  focal 
lengths  for  parallel  rays.  The  spherical  aberration  produced  by  this 
eye-piece  is  only  about  one-fourth  as  much  as  if  a  single  lens  were  used. 
The  chromatic  aberration  also  is  less  than  with  a  single  lens. 

Let  F  F,  fig.  380,  be  the  field-lens,  and  E  E  the  eye-lens  of  the  positive  eye- 
piece. Let  m  n  be  an  image  formed  by  the 
object-glass  either  of  a  telescope  or  a  micro- 
scope, then  each  ray  from  the  image  on 
passing  the  lens  F  F  becomes  colored,  c  v,  bv, 
representing  the  violet  rays,  and  c  r,  b  r, 
representing  the  red  rays.  The  red  rays, 
which  are  least  refracted  by  the  first  lens, 
fall  near  the  borders  of  the  second  lens,  where  the  refractive  power  is  greater 
than  where  the  more  refrangible  violet  rays  fall ;  hence  the  second  lens  tends  to 
correct  the  chromatic  dispersion  of  the  first,  and  the  violet  and  red  rays  enter 
the  eye  very  nearly  as  though  emanating  from  a  common  point.  This  is  an 
important  excellence  of  the  positive  eye-piece ;  but  a  yet  more  important  advan- 
tage of  this  eye-piece  is,  that  the  image  is  less  distorted  than  when  only  a  single 
lens  is  used. 

The  negative  eye-piece,  which  was  invented  by  Huyghens,  con- 
sists generally  of  two  plano-convex  lenses,  having  the  convex  surfaces 


380 


354          PHYSICS  OF  IMPONDERABLE  AGENTS. 

of  both  turned  towards  the  object-glass.  The  two  lenses  are  placed  at 
a  distance  from  each  other  equal  to  one-half  the  sum  of  their  focal 
lengths.  The  image  is  formed  between  the  lenses.  This  arrangement 
considerably  enlarges  the  field  of  view,  and  diminishes  the  spherical 
aberration ;  the  chromatic  aberration  is  also  less,  and  it  is  more 
equalized  in  all  parts  of  the  field  than  in  other  eye-pieces. 

In  the  most  perfect  form  of  the  negative  eye-piece,  according  to  Prof.  Airy, 
the  first,  or  field  lens,  is  a  meniscus  whose  radii  are  as  four  to  eleven,  with  the 
convex  side  toward  the  object,  and  an  eye-lens  having  the  form  of  least  spherical 
aberration  (454),  with  the  more  convex  side  towards  the  object. 

The  focal  lengths  of  the  field  and  eye  lenses  should  be  to  each  other  as  3  to  1, 
and  their  distance  apart  equal  to  one-half  the  sum  of  their  focal  lengths. 

In  eye-pieces  designed  for  the  microscope,  instead  of  estimating  the  principal 
focal  length  of  the  field-lens,  we  must  take  its  conjugate  focus  when  the  object 
is  placed  in  the  position  of  the  object-glass  of  the  microscope. 

The  action  of  the  negative  eye-piece  will  be  more  fully  explained  in  connection 
with  the  compound  achromatic  microscope  (511). 

The  terrestrial  eye-piece  consists  of  four  lenses,  two  of  them  being 
added  solely  to  produce  an  erect  image. 

Fig.  381  shows  a  section  of  the  common  spy-glass  or  terrestrial  telescope,  with 

381 


the  erecting  eye-piece.     The  several  tubes  which  shut  one  within  another,  allow 
the  instrument  to  be  reduced  to  a  convenient  length  when  not  in  use. 

501.  Reflecting  telescopes  are  extensively  used  for  astronomical 
observations.     A  variety  of  forms  have   been   invented   by  different 
observers,  but  in  all  a  metallic  speculum  is  employed  to  form  an  image 
of  distant  objects,  and  an  eye-piece  is  used  to  magnify  the  image. 

502.  Sir  William  Herschel's  telescope,  shown  in  fig.  382,  con- 

382 


eists  of  a  speculum,  S  S,  set  in  a  tube  somewhat  larger  than  the  diameter 
of  the  speculum,  and  an  eye-piece,  ef,  placed  at  one  side  of  the  open 


OPTICS.  355 

end  of  the  tube.  The  axis  of  the  speculum,  represented  by  the  dotted 
line  a  N,  is  so  inclined  that  parallel  rays,  falling  on  every  part  of  the 
speculum,  will  be  reflected,  converging  to  the  side  of  the  tube  where 
the  eye-piece  is  placed  to  receive  them.  The  size  of  the  tube,  and  the 
inclination  of  the  axis  of  the  speculum,  is  so  adjusted  that  the  eve  of 
the  observer  may  be  placed  at  E  without  intercepting  any  part  of  the 
light  which  can  fall  upon  the  speculum  in  such  a  direction  as  to  be 
reflected  to  the  eye-piece. 

Sir  William  Herschel's  great  telescope  had  a  speculum  four  feet  in  diameter, 
three  and  a  half  inches  thick,  weighing  two  thousand  one  hundred  and  eighteen 
pounds.  Its  focal  length  was  forty  feet,  and  it  was  set  in  a  sheet-iron  tube 
thirty-nine  and  a  half  feet  long,  and  four  feet  ten  inches  in  diameter.  When 
directed  to  the  fixed  stars  it  would  bear  a  magnifying  power  of  six  thousand 
four  hundred  and  fifty  diameters. 

.  This  is  called  the  front  view  telescope,  because  the  observer  sits  with  his  back 
to  the  object  and  looks  into  the  front  end  of  the  telescope. 

503.  Lord  Rosse's  telescope. — By  far  the  largest  reflecting  tele- 
scope ever  constructed  was  made  by  the  Earl  of  Rosse.     It  was  com- 
menced in  1842,  and  was  so  far  completed  as  to  be  used  for  the  first 
time  in  February,  1845. 

The  great  speculum  is  six  feet  in  diameter,  has  a  focal  length  of 
fifty-four  feet,  and  weighs  four  tons.  An  additional  speculum  to  be 
used  in  the  same  instrument  weighs  three  and  a  half  tons.  The  tube 
is  of  wood,  hooped  with  iron,  seven  feet  in  diameter,  and  fifty-two  feet 
in  length. 

This  telescope  has  fittings  to  mount  the  eye-pieces  either  for  front  view,  as  in 
Herschel's  telescope,  or  at  the  side,  as  in  the  Newtonian  form  :  for  this  purpose  a 
small  speculum  is  placed  at  an  angle  of  45°,  reflecting  the  rays  at  a  right  angle 
through  an  orifice  in  the  side  of  the  tube,  where  the  eye-piece  is  placed. 

The  base  of  the  instrument  is  supported  upon  a  universal  joint ;  and  by  chains 
and  windlasses  this  mammoth  telescope  is  moved  with  ease,  between  two  lofty 
walls  supporting  movable  galleries,  which  enable  the  observer  to  follow  the 
instrument  in  any  required  position. 

The  amount  of  light  on  any  surface  being  as  the  square  of  the  diameter,  if  we 
reckon  the  pupil  of  the  human  eye  at  one-tenth  of  an  inch  in  diameter,  this 
telescope  will  be  seven  hundred  and  twenty  times  as  broad  as  the  pupil,  or  have 
an  area  five  hundred  and  eighteen  thousand  and  four  hundred  times  as  great  as 
the  unaided  eye.  If  one-half  the  light  is  lost  by  reflection  from  the  mirror,  we 
shall  still  have  two  hundred  and  fifty  thousand  times  as  much  light  as  commonly 
enters  the  eye.  We  need  not  wonder  therefore  at  the  marvellous  power  with 
which  this  instrument  penetrates  the  remoter  regions  of  celestial  space. 

504.  Achromatic  telescopes. — The  principle  of  achromatism  has 
been  briefly  explained  in  §  466,  where  it  has  been  shown  that  a  convex 
lens  of  crown  glass  may  be  combined  with  a  concave  lens  of  longer 
focus,  made  of  flint  glass,  which  has  a  higher  refractive  and  dispersive 


356  X.    PHYSICS    OF    IMPONDERABLE    AGENTS. 

power,  the  combination  producing  refraction  without  dispersion,  and 
consequently  forming  an  image  free  from  the  primary  prismatic  colors. 

The  common  form  of  achromatic  compound  lens  is  a  plano-concave  lens  of 
flint  glass,  united  with  a  double  convex  lens  of  crown  glass.  Such  lenses  are 
found  in  opera-glasses  and  spy-glasses,  called  achromatic,  used  both  on  land  and 
at  sea.  This  form  of  lens  is  also  often  employed  in  the  smaller  astronomical 
telescopes.  But  in  such  glasses  a  certain  amount  of  spherical  aberration  remains 
uncorrected. 

To  secure  perfect  correction  of  spherical  and  chromatic  aberration  at  the  same 
time,  a  double  concave  lens  of  flint  glass  has  been  placed  between  two  double 
convex  lenses  of  crown  glass,  the  curved  surfaces  of  the  several  lenses  being 
carefully  estimated  in  view  of  the  refractive  and  dispersive  powers  of  the  two 
kinds  of  glass  employed. 

The  refractive  and  dispersive  powers  of  glass  are  so  variable,  that  the  optician 
is  obliged  to  determine  them  anew  for  every  new  specimen  of  glass,  and  estimate 
again,  by  the  formulae  already  given,  the  proportional  curvatures  of  the  lenses 
to  be  constructed  from  it. 

Sir  John  Herschel  found  that  an  achromatic  object-glass  of  the  form 
shown  in  fig.  383,  will  be  nearly  free  from  spherical  aberration,  if  the 
exterior  surface  of  the  crown  lens  is  6'72,  and  the  exterior  sur-     333 
face  of  the  flint  lens  14'20,  the  focal  length  of  the  combination 
being  lO'OO  ;  and  the  interior  surfaces  of  the  two  lenses  being 
computed  from  these  data  to  destroy  the  chromatic  aberration 
by  making  the  focal  lengths  of  the  two  glasses  in  the  direct 
ratio  of  their  dispersive  powers  (467).    The  two  interior  surfaces 
that  come  in  contact  may  be  cemented  together  if  the  lenses  are 
small. 

Until  quite  recently,  almost  insuperable  obstacles  interfered  with  the  manu- 
facture of  flint  glass  in  large  pieces  of  uniform  density,  free  from  veins  and 
imperfections. 

In  1828,  an  achromatic  lens  fourteen  inches  in  diameter  was  considered  a  true 
marvel  of  optical  art.  The  object-glass  in  the  great  achromatic  refracting  tele- 
scope at  Cambridge,  Mass,  (one  of  the  largest  in  use),  is  about  sixteen  inches  in 
diameter,  with  a  clear  aperture  of  fifteen  inches,  and  it  cost,  unmounted,  about 
$15,000.  Mr.  Bontemps,  a  French  artist,  employed  in  the  glass  works  of  Messrs. 
Chance,  Brothers  &  Co.,  Birmingham,  Eng.,  has  succeeded  in  producing  a  disk 
of  flint  glass  twenty-nine  inches  in  diameter,  two  and  a  half  inches  thick,  weigh- 
ing two  hundred  pounds,  and  pronounced  by  the  most  skillful  opticians  very 
nearly  faultless. 

505.  Equatorial  mountings  for  telescopes. — With  telescopes  of 
great  power,  the  diurnal  motion  of  the  earth  causes  a  celestial  object  to 
pass  out  of  the  field  of  view  too  rapidly  to  allow  of  satisfactory  observa- 
tion. To  obviate  this  difficulty,  a  system  of  machinery  called  au 
equatorial  mounting,  has  been  devised,  to  give  to  the  telescope  such  a 
uniform  motion  as  to  keep  any  celestial  object  constantly  in  the  field 
of  view. 


OPTICS. 


357 


An  axis  firmly  supported  is  placed  parallel  to  the  axis  of  the  earth,  and  is 
Mused  to  revolve  by  clock-work  with  a  motion  exactly  equal  to  the  sidereal 
(notion  of  the  heavens.  A  second  axis,  across  which  the  telescope  is  mounted, 
is  fixed  upon  the  first  axis,  and  at  right  angles  with  it.  The  telescope  can 
be  elevated  or  depressed  in  declination  by  motion  of  the  second  axis,  and  it  can 
be  moved  in  right  ascension  by  motion  on  the  first  axis.  When  the  telescope 
has  been  thus  directed  to  any  celestial  object,  it  may  be  clamped  on  both  axes, 
and  the  movement  of  the  clock-work  will  cause  it  to  follow  the  motion  of  the 
object  in  the  heavens. 

506.  The  Cambridge  telescope  with  equatorial  mountings  is 

shown  in  tig.  384. 

It  stands  on  a  granite  pier  surmounted  by  a  single  block  of  granite  ten  feet 
»n  height,  to  which  the  metallic  bed-plate  of  the  telescope  is  secured  by  bolts 

384 


and  screws.  It  is  covered  by  a  dome  moving  on  a  circular  railway,  which  is 
easily  rotated  so  as  to  allow  the  great  telescope,  twenty-three  feet  in  length,  tr 
be  directed  to  any  part  of  the  heavens'.  A  narrow  window,  closed  by  shutters 

33 


358  PHYSICS  OF  IMPONDERABLE  AGENTS. 

moved  by  chains,  is  opened  when  the  telescope  is  in  use.  The  hour  circle 
attached  to  the  equatorial  axis  is  eighteen  inches  in  diameter,  divided  on  silver, 
and  reads  by  two  verniers  to  one  second  of  time.  The  declination  circle  is 
twenty-six  inches  in  diameter,  divided  on  silver,  and  reads  by  four  verniers  to 
four  seconds  of  arc. 

The  movable  portion  of  the  telescope  and  machinery  is  estimated  to  weigh 
about  three  tons,  but  it  is  so  perfectly  counterpoised  and  adjusted  that  the 
observer  can  direct  the  instrument  to  any  part  of  the  heavens  by  a  very  slight 
pressure  of  the  hand  upon  the  balance  rods.  This  great  achromatic  telescope 
has  eighteen  different  eye-pieces,  giving  to  the  instrument  magnifying  powers 
varying  from  103  to  2000  diameters. 

507.  The  visua"  power  of  telescopes,  or  the  aid  which  they  afford 
in  viewing  distant  objects,  depends  upon  the  combined  effects  of 
increased  light  and  magnifying  power. 

Sir  William  Herschel  relates  that,  on  a  certain  occasion,  when  on 
account  of  the  darkness  a  distant  steeple  was  invisible,  a  telescope 
showed  very  distinctly  the  time  by  the  clock  on  the  tower.  Here  but 
little  magnifying  power  was  required,  and  there  was  a  deficiency  of 
illumination,  yet  the  telescope  supplied  both. 

To  understand  the  principles  upon  which  this  power  of  telescopes 
dopends,  it  is  necessary  to  attend  to  the  following  particulars : — 

1.  Magnifying  power  is  measured  by  the  enlargement  of  the  image 
seen  in  the  telescope,  as  compared  with  the  apparent  dimensions  of  the 
object  as  seen  by  the  naked  eye. 

2.  The  illuminating  power  of  the  telescope  is  the  amount  of  light 
which  it  collects  from  any  object,  and  transmits  to  the  eye  for  the  pur- 
poses of  vision,  as  compared  with  the  amount  of  light  from  the  same 
object  received  by  the  unassisted  eye. 

The  illuminating  power  of  the  telescope  should  be  carefully  distinguished  from 
illumination  of  the  object. 

3.  Penetrating  power  is  the  ratio  of  the  distances  at  which  the  eye  and 
telescope  would  collect,  for  the  purposes  of  vision,  an  equal  amount  of 
light.     Hence  the  penetrating  power  of  a  telescope  is  equal  to  the 
square  root  of  the  illuminating  power. 

4.  The  visual  power  of  a  telescope  is  found  by  extracting  the  square 
root  of  the  product  obtained  by  multiplying  the  penetrating  power  by 
the  magnifying  power. 

Putting  P  for  the  penetrating  power  of  a  refracting  telescope,  x  for  the  pro- 
portion of  light  transmitted  by  a  single  lens,  »  for  the  number  of  lenses  in  the 
instrument,  A  the  available  diameter  of  the  field-lens,  and  a  for  the  diameter  of 

A2xn 
the  pupil  of  the  eye,  we  shall  have  the  illuminating  power  =  — — . 


\A?xn       A.       • 

The  penetrating  power,       P  =  */  — —  =  —  |/a:n. 


OPTICS.  359 

The  value  of  x  in  this  equation  will  vary  with  the  thickness  of  the  lenses,  the 
degree  of  polish,  and  the  amount  of  curvature ;  but  for  ordinary  purposes  of 
calculation  we  may  consider  its  value  as  varying  from  y8^  to  y9^. 

Let  M  represent  the  magnifying  power  and  F  the  visual  power  of  a  telescope, 

(       A    £  )   i 

and  we  shall  have  generally,       V=i/MP  =  j  M.-.xZ   [•  *. 

It  will  be  evident  that  the  best  effect  with  the  telescope  will  be  obtained  when 
the  penetrating  and.  magnifying  powers  are  nearly  equal.  If  the  magnifying 
power  is  in  excess,  though  the  image  may  be  enlarged,  it  will  be  too  faint  to 
produce  a  clear  impression.  If  the  magnifying  power  is  too  small  in  proportion 
to  the  penetrating  power,  the  eyes  will  be  dazzled  by  the  excess  of  light,  while 
the  several  parts  of  the  image  will  not  be  clearly  separated  upon  the  retina. 

The  magnifying  power  of  the  telescope  is  therefore  varied  by  the  use  of  dif- 
ferent eye-pieces  (506)  to  suit  the  state  of  the  atmosphere  and  the  degree  of 
illumination  of  the  object  viewed. 

508.  Achromatic  object  glasses  for  microscopes,  if  constructed 
of  the  forms  used  in  telescopes,  are  very  unsatisfactory.     In  the  first 
place,  it  is  found  exceedingly  difficult  to  construct  such  lenses  sufficiently 
small  for  the  high  magnifying   powers   required  in   the  microscope. 
Secondly,  the  largest  achromatic  lenses  for  telescopes  have  but  a  small 
diameter  in  proportion  to  the  length  of  their  foci,  and  if  lenses  for  the 
microscope  have  a  diameter  equally  small  in  proportion  to  their  foci, 
they  admit  too  little  light  to  be  of  much  practical  utility.     But  if  their 
diameter  is  increased,  the  light  admitted  through  the  borders  of  the 
lenses  produces  fringes,  with  colors  in  the  inverse  order  of  the  solar  spec- 
trum, showing  that  while  the  color  is  perfectly  corrected  in  the  centre, 
the  correction  effected  by  the  concave  lens  is  too  great  at  the  margin. 

509.  Lister's  aplanatic  foci,  and  compound  objectives. — The 
discoveries  of  Joseph  Jackson  Lister,  Esq.,  communicated  to  the  Royal 
Society  in  1830,  have  proved  of  the  utmost  value  in  perfecting  the  com- 
pound achromatic  microscope.    His  preliminary  principles  are,  1st,  that 
plano-convex  achromatic  lenses,  shown  in  fig.  371,  are  most  easily  con- 
structed.    2d,  that  if  the  convex  and  concave  lenses  have  their  inner 
surfaces  of  the  same  curvature,  and  are  cemented  together,  much  less 
light  is  lost  by  reflection  than  if  the  lenses  are  not  cemented.     Mr. 
Lister  discovered  that  every  such  piano-  335 

convex  achromatic  combination  as  A  A,  /*- 

fig.  385,  has  some  point,  as  f,  not  far    , £. 

from  its  principal  focus,  from  which  F 
radiant  light  falling  upon  the  lens  will 
be  transmitted  free  also  from  spherical 
aberration.  This  point  is  therefore  called  an  aplanatic  focus.  The 
incident  ray,  f  d,  makes  with  the  perpendicular,  id,  an  angle  con- 
siderably less  than  the  emergent  ray,  eg,  makes  with  eh  the  perpen- 
dicular at  the  point  of  emergence.  The  angle  of  emergence  is  nearly 


360  PHYSICS    OF    IMPONDERABLE    AGENTS. 

three  times  as  great  as  the  angle  of  incidence,  and  the  rays  emerge  from 
the  lens  nearly  parallel,  or  converging  towards  a  focus  at  a  moderate 
distance  from  the  lens. 

If  the  radiant  point  is  now  made  to  approach  the  lens,  so  that  the  ray  fdeg 
becomes  more  divergent  from  the  axis,  as  the  angles  of  incidence  and  emergence 
become  more  nearly  equal  to  each  other,  the  spherical  aberration  becomes  nega- 
tive or  over-corrected.  But  if  the  radiant  point,  /,  continues  to  approach  the 
glass,  the  angle  of  incidence  increases,  and  the  angle  of  emergence  diminishes 
and  becomes  less  than  the  angle  of  incidence,  and  the  negative  spherical  aberra- 
tion produced  by  the  outer  curves  of  the  compound  lens  becomes  again  equal  to 
the  opposing  positive  aberrations  produced  by  the  inner  curves  which  are 
cemented  together.  When  the  radiant  has  reached  this  point  /'  (at  which  the 
angle  of  incidence  does  not  exceed  that  of  emergence  so  much  as  it  had  at  first 
come  short  of  it),  the  rays  again  pass  the  glass,  free  from  spherical  aberration. 
The  point/'  is  called  the  shorter  aplanatic  focus. 

For  all  points  between  the  two  aplanatif.  foci/ and/  the  spherical  aberration 
is  over-corrected,  or  negative;  and  for  all  radiant  points  more  distant  than  the 
longer  aplanatic  focus/,  or  less  distant  than  the  shorter  aplanatic  focus  f,  the 
spherical  aberration  is  under-corrected,  or  positive.  These  aplanatic  foci  have 
another  singular  property.  If  a  radiant  point  in  an  oblique  or  secondary  axis 
is  situated  at  the  distance  of  the  longer  aplanatic  focus,  the  image  situated  in 
the  corresponding  conjugate  focus  will  not  be  sharply  defined,  but  will  have  a 
coma  extending  outwards,  distorting  the  image.  If  the  shorter  aplanatic  focus 
is  used,  the  image  of  a  point  in  the  secondary  axis  will  have  a  coma  extending 
towards  the  centre  of  the  field.  These  peculiarities  of  the  coma  produced  by 
oblique  pencils  are  found  to  be  inseparable  attendants  on  the  two  aplanatic  foci. 

These  principles  furnish  the  means  of  entirely  correcting  both  chro- 
matic and  spherical  aberration,  and  of  destroying  the  coma  of  oblique 
pencils,  and  also  of  transmitting  a  large  angular  pencil  of  light  free 
from  every  species  of  error. 

Two  plano-convex  achromatic  lenses,  A  M,  fig.  386,  are  so  arranged 
that  the  light  radiating   from 
the  shorter  aplanatic  focus  of 

the  anterior  combination  is  re-   „       — .^ 

ceived  by  the  second  lens  in  the    " 
direction  off",  its  longer  apla- 
natic focus. 

If  the  two  compound  lenses  are  fixed  in  this  position,  the  radiant 
point  may  be  moved  backwards  or  forwards  within  moderate  limits,  and 
the  opposite  errors  of  the  two  compound  lenses  will  ba-  357 

lance  each  other.  ~~~   ~  - 

Achromatic  lenses  of  other  forms  have  similar  pro-  >^il 
perties.     It  is  found  in  practice  that  larger  pencils  free     \  ~^^iijM 
from  errors  can  be  transmitted  by  employing  three  com-        xs^flit^ 
pound   lenses,  the    middle   and  posterior  combinations       w^iiMa 
being  so  united  as  to  act  as  a  single  lens,  together  balancing  the  aber- 
rations of  the  more  powerful  anterior  combinations.     Fig.  387  shows 


OPTICS. 


361 


a  common  form  of  the  triple  aplanatic  and  achromatic  objective,  used 
for  the  compound  microscope. 

510.  Aberration  of  glass  cover  corrected. — If  an  object  viewed 
with  an  achromatic  microscope,  which  has  all  its  aberrations  corrected 
for  an  uncovered  object,  is  covered  with  even  a  thin  film  of  glass  or 
mica,  spherical  aberration  is  again  produced,  thus  sensibly  impairing 
the  distinctness  of  vision  when  a  high  power  is  used. 

Let  abed,  fig.  388,  be  a  film  of  glass  or  mica  bounded  by  parallel  surfaces. 
If  rays  of  light,  diverging  from  0,  pass  through  this  film,  the  ray  0  T'  R'  E' 
will  suffer  greater  displacement  than  the  ray  0  T  R  E, 
which  makes  a  smaller  angle  with  the  perpendicular 
OP.  If  R  E  and  R'  E'  are  extended  backward,  ^hey 
will  cross  the  axis  or  perpendicular  at  the  points  X  and 
Y.  This  separation  of  the  points  X  and  Y  is  exactly 
similar  to  the  spherical  aberration  of  ^concave  lens,  and 
is  therefore  called  negt^ive  spherical  aberration.  Chro- 
matic aberration  is  aiso  produced  by  .the  same  means. 
The  effect  observed  by  the  eye  in  such  cases  is,  that  lines  are  not  so  sharply 
defined,  and  the  outline  of  an  object  appears  bordered  with  broader  fringes,  with 
colors  of  the  secondary  spectrum  upon  the  borders  of  the  object.  These  errors 
are  easily  corrected  by  diminishing  the  distance  between  the  anterior  and 
posterior  combinations  of  the  compound  objective,  which  is  furnished  with  an 
adjusting  screw  for  this  purpose. 

511.  The  compound  achromatic  microscope  is  composed  of  the 

389 


rfk* 


triple  achromatic  objective,  AMP,  fig.  389,  and  the  negative  eye-piece, 
formed  of  the  field-lens  F  F,  and  the  eye-lens  E  E. 

The  section  drawn  in  the  figure,  shows  how  the  light  is  acted  upon  in  passing 
through  the  different  parts  of  the  instrument.  Pencils  of  rays  from  all  parts  of 
the  object,  « t,  pass  through  the  compound  objective  AMP,  and  tend  to  form  a 
red  image  at  R  R,  and  a  violet  image  at  V  V,  the  object-glass  being  slightly 
over-corrected,  so  as  to  project  the  violet  rays  as  far  beyond  the  red  as  may  be 
necessary  to  make  up  for  the  want  of  absolute  achromatism  in  the  eye-piece. 
The  converging  pencils  S,  C,  T,  being  intercepted  by  the  field-lens  F,  are  fore- 
shortened, and  at  the  same  time  the  lateral  pencils  are  bent  inward,  so  that  the 
images  v  v,  r  r,  are  smaller,  nearer  together  than  V  V,  R  R,  and  curved  in  an 
opposite  direction.  The  reversion  of  the  curvature  of  the  images  is  produced  by 
the  form  of  the  field-lens,  which  meets  the  central  pencil,  C,  much  farther  from 
33* 


362          PHYSICS  OF  IMPONDERABLE  AGENTS. 

the  images  V  V,  R  R,  than  where  it  meets  the  lateral  pencils  S  T ;  thus  the  focu» 
of  the  central  pencil  is  more  shortened  than  the  others.  The  field-lens  of  the 
negative  eye-piece  does  not  reverse  the  curvature  in*every  variety  of  instrument, 
but  it  always  changes  the  form  of  the  images  so  as  to  improve  the  definition. 
The  violet  rays  S  n,  T  n,  fall  upon  the  eye-lens  nearer  its  axis,  than  the  red  rays 
S  m,  T  in,  which  are  less  refrangible,  and  hence  the  eye-lens  counteracts  the 
divergence  of  the  colored  rays  which  were  separated  by  the  field-lens,  and  causes 
them  to  pass  to  the  eye  so  nearly  parallel  that  they  appear  to  diverge  from  the 
same  point  of  the  virtual  image  S  T,  formed  at  the  distance  of  distinct  vision. 
The  distance  between  the  red  and  violet  images  r  r,  v  v,  is  just  equal  to  the  dif- 
ference between  the  red  and  violet  foci  of  the  lens,  and  these  images  being  curved 
just  enough  to  bring  every  part  into  exact  focus  for  the  eye-lens,  the  eye  sees 
the  image  at  S'  T'  spread  out  in  its  true  form  on  a  flat  field. 

By  means  of  this  beautiful- system  of  compensations,  for  the  various  errors  of 
chromatic  and  spherical  aberration  and  curvature  of  the  image,  which  interfere 
with  the  performance  of  a  single  lens,  the  compound  achromatic  microscope  has 
been  brought  to  a  degree  of  perfection  unsurpassed  by  any  instrument  employed 
in  practical  physics.  % 

512.  Solid   eye-piece. — A   negative   eye-piece,  constructed   of  a 
single  piece  of  glass,  has  been  patented  by  Mr.  R.  B.  Tolles,  of  Canas- 
tota,  N.  Y.      In  the  solid  eye-piece  there  is  much  less  loss  of  light 
by  reflection,  as  there  are  only  one-half  as  many  refracting  surfaces 
as  in  the  ordinary  eye- piece.     The  image  is  of  course  formed  in  the 
substance  of  the  glass.      This  eye-piece   allows  the  use  of  a  higher 
magnifying  power  than  the  eye-piece  formed  of  two  lenses,  and  it  is 
thought  also  to  give  more  perfect  definition. 

513.  Visual  power  of  the  achromatic  microscope. — The  great 
distinction  between  the  telescope  and  the  microscope  consists  in  the 
fact  that  while  the  former,  practically  speaking,  is  suited  to  receive 
parallel  rays  from  a  distant  object,  the  latter  has  to  deal  with  rays 
which  diverge  from  a  closely  approximate  point.     On  this  account  the 
formula  for  visual  power  will  require  some  modification. 

Angular  aperture. — The  angular  breadth  of  the  cone  of  light  which 
a  microscope  receives  from  an  object,  and  transmits  to  the  eye,  is  called 
its  angular  aperture. 

Illuminating  power  in  the  microscope  depends  upon  the  square  of  the 
angular  aperture,  due  allowance  being  made  for  the  light  lost  in  its 
passage  through  the  instrument. 

When  the  formula  for  visual  power  is  applied  to  the  microscope,  A  must  repre- 
sent the  angular  aperture  of  the  instrument  measured  in  degrees ;  and  o  will 
represent  the  angular  breadth  of  a  cone  of  light  which  can  enter  the  pupil  of 
the  eye  from  an  object  at  the  distance  of  distinct  vision  =  1°  very  nearly.  We 
shall  then  have: — 

The  penetrating  power  of  the  microscope,  P  =  A  \/xn ;  or  the  penetrating 
power  varies  directly  as  the  angular  aperture.  This  is  not  absolutely  correcti 
for  the  loss  of  light  by  reflection  causes  a-  to  diminish  as  A  increases. 


OPTICS 


303 


Let  C  =  \/'xn,  and  we  shall  hats  . —  The  visual  power  of  the  microscope, 


F=  \MP  =  iJfAO  =  | A  X  lMC: 

Or  (since  the  magnifying  power,  or   the  eye-piece,  which  may  be  employed, 
varies  with  the  angular  aperture),  generally  : — 

The  visual  power  of  the  microscope  is  proportional  to  the  square  root  of  the 
angular  aperture  of  the  object- glaax. 

Defining  power,  or  sharpness  of  minute  details  in  an  object  seen  by  the  micro- 
scope, requires  perfect  correction  of  chromatic  and  spherical  aberration. 

In  fig.  390,  A,  B,  C,  D,  show  the  successive  appearances  of  a  scale  of  Mor~ 
pho  Menelaus,  by  regular  enlargements  of  the  angular  aperture  of  the  miero- 

390 
A  BOD 


scope  with  which  it  was  viewed.     The  available  angular  aperture  of  a  single 
lens  seldom  exceeds  fifteen  or  twenty  degrees.     In  the  triple  achromatic  objec- 
tive,   the   aperture   for   ordinary  391 
observations    has  been  extended 
to  100°.    With  the  highest  powers 
used  for  viewing  infusoria,  both 
English  and  American  opticians 
Tiave  advanced  the  angular  aper- 
ture to  150°,  and  in  some  glasses 
\o  175°. 

514.  The  mechanical  ar- 
rangement of  the  micro- 
scope is  well  exhibited  in 
fig.  3\^1,  which  has  been  en- 
graved from  a  very  excellent 
instrument,  manufactured  by 
J.  &  W.  Grunow,  NGW  Haven, 
Conn. 

The  instrument  is  mounted  on 
trunnions,  which  allow  it  to  be 
inclined  at  any  angle.  The  body 
of  the  microscope  is  moved  in  a 
grooved  support,  by  a  rack  and 
pinion  motion  for  adjusting  the 
focus.  The  stage  has  a  fine,  deli- 
cate movement,  by  a  screw  and 
milled  head,  acting  upon  a  lever 
at  the  back  of  the  instrument,  \>y 
which  movement  the  focus  can  be 
adjusted  with  the  utmost  delicacy. 

The  stiige  itself  can  be  moved  freely  in  any  direction  by  a  lever  at  the  right. 


304 


PHYSICS  OF  IMPONDERABLE  AGENTS. 


A  mirror,  coj  cave  on  one  side,  and  plane  on  the  other,  is  so  mounted  below  tha 
Btage  as  to  illuminate  the  object  with  either  parallel  or  converging  rays. 

Polarizing  apparatus,  and  other  accessories,  are  fitted  to  the  stage,  and  to  tha 
body  of  the  microscope. 

515.  The  magic  lantern  is  an  instrument  for  projecting  upon  a 
screen,  images  of  transparent  pictures  painted  on  glass. 

A  lamp  is  placed  in  a  dark  box,  before  a  parabolic  reflector,  M  N,  fig.  392, 
which  throws  the  light  upon  a  convex  lens,  A,  by  which  it  is  strongly  condensed 

392 


upon  the  object  painted  on  the  glass  slide,  inserted  at  C  D.  The  magnifying 
lens,  B,  forms  an  image  of  the  illuminated  picture  upon  a  screen  E  F,  placed  at 
its  conjugate  focus.  The  picture  is  placed  in  an  inverted  position,  to  produce 
an  erect  image  upon  the  screen. 

A  great  variety  of  objects  painted  on  glass  can  thus  be  exhibited  either  fop 
amusement  or  instruction.  The  magnifying  power  of  the  magic  lantern  is 
equal  to  the  distance  of  the  screen  from  the  lens,  B,  divided  by  the  distance  of 
the  lens  from  the  object. 

516.  The  solar  microscope  is  a  species  of  magic  lantern  illumi- 
nated by  the  sun.  It  is,  however,  much  more  perfect  in  its  structure, 
and  it  is  commonly  employed  for  viewing  on  a  screen  images  of  natural 
objects,  very  highly  magnified. 

The  structure  and  arrangement  of  the  solar  microscope  are  shown  in  fig.  393. 


It  is  mounted  over  an  opening  in  the  shutter  of  a  dark  room,  on  the  side  towards 
the  sun.     A  plane  mirror,  M,  is  so  arranged  outside  the  shutter  as  to  reflect  the 


OPTICS.  365 

rays  of  sunlight,  S,  through  the  condensing  lens,  A,  into  the  microscope.  By  turn- 
ing the  screw,  B,  the  mirror  may  be  elevated  or  depressed,  and  by  means  of  another 
screw,  T,  it  can  be  rotated  on  the  axis  of  the  microscope,  so  as  to  follow  the  motions 
of  the  sun.  A  small  lens,  B,  moved  by  the  rack  and  pinion  with  the  milled  head 
C,  serves  to  condense  the  light  upon  the  object  slide,  0.  The  slide  0,  which  carries 
the  object,  is  secured  between  the  brass  plates  K  K,  by  the  screws,  H  H. 

The  object,  strongly  illuminated,  is  adjusted  to  the  focus  of  the  small  lens,  L 
(which  may  be  either  a  small  globule  of  glass,  or  a  compound  achromatic  objec- 
tive, of  short  focus),  and  an  image,  a  b,  greatly  enlarged,  formed  in  the  conjugate 
focus  of  the  lens,  is  received  upon  a  white  screen  placed  in  a  convenient  position. 
By  diminishing  the  distance  between  the  object  and  the  lens,  L,  the  conjugate 
focus  will  be  more  distant,  the  screen  may  be  placed  farther  from  the  lens,  and 
the  magnifying  power  will  be  proportionally  enlarged. 

Instead  of  employing  the  light  of  the  sun,  the  solar  microscope  may  be  illu- 
minated by  the  electric,  or  by  the  oxyhydrogen  light. 

517.  The  camera  obscura  consists  of  a  dark  chamber  in  which 
images  of  external  objects  are  formed  by  the  aid  of  a  mirror,  and  a 
concave  lens.     This  instrument  affords  a  con-  394 

nient  method  of  sketching  natural  scenery. 

A  plane  mirror,  m,  fig.  394,  placed  at  an  angle  of 
45°  with  the  horizon,  reflects  the  light  downward, 
through  a  converging  lens,  placed  in  the  top  of  the 
dark  chamber.  A  sheet  of  paper  placed  on  the  table 
in  the  focus  of  the  lens,  receives  the  image  of  a  land- 
scape or  other  object,  which  can  be  traced  with  a 
pencil  by  the  artist,  sitting,  as  shown  in  the  figure, 
with  his  head  and  shoulders  protected  from  extra- 
neous light  by  a  dark  curtain. 

The  student  can  easily  prepare  an  instrument  of 
this  kind,  by  inserting  a  spectacle  glass  in  an  ori- 
fice in  the  top  of  a  box  about  two  feet  high,  and 
placing  a  common  mirror  at  the  required  angle 
above  it.  The  paper  on  the  table  can  be  placed  on  j 
a  drawing-board^  and  fixed  at  such  a  distance  from1 
the  lens  as  .gives  the  most  distinct  image.  A  cloak  thrown  over  the  side  of  the 
box  where  the  observer  sits,  will  darken  the  chamber  so  as  to  permit  sketches  to 
be  made  with  great  facility.  395 

Instead  of  the  mirror  and  lens  shown  in  fig.  394,  a  rectangu- 
lar prism  is  often  used  as  a  reflector,  and  if  one  side  of  the  prism 
is  ground  in  the  form  of  a  lens,  the  two  parts  of  the  instrument 
are  combined  in  one. 

518.  Wollaston's  camera  lucida  is  another  instru- 
ment used  for  sketching  from  nature.     It  consists  of  a 
prism,  abed,  fig.  395,  of  which  the  angle,  6,  is  a  right 
angle,  the  angle,  d,  is  135°,  and  the  angles  at  a  and  c 
are  each  67  £°.      „ 

It  is  mounted  on  a  suitable  stand,  and  the  eye,  P  P',  placed  < 
as  shown  in  the  figure,  sees  the  image  of  a  distant  object  as  though  projected 


366          PHYSICS  OF  IMPONDERABLE  AGENTS. 

upon  the  paper  M  N,  where  the  outline  may  be  traced  by  the  pencil  S,  the  eye 
seeing  the  image  and  the  pencil  at  the  same  time.  The  light  from  a  distant 
object  entering  the  prism  nearly  at  right  angles  with  the  face,  b  c,  twice  suffers 
total  reflection,  and  emerges  perpendicular  to  the  face  a  b,  when  it  enters  the 
eye,  and  appears  as  if  coming  from  the  paper,  MN.  The  image  projected  upon 
the  paper  is  as  much  smaller  than  the  object  as  its  distance  from  the  prism  is 
less  than  the  distance  of  the  object.  The  image  can  be  made  to  assume  any 
required  dimensions  by  varying  the  relative  distances  of  the  paper  and  the 
object.  This  instrument  is  principally  employed  by  artists  for  sketching  land- 
scapes. 

A  number  of  other  forms  of  camera  lucida  are  employed  to  suit  different  pur- 
poses, but  in  all  of  them,  either  the  object,  or  the  pencil  and  paper,  are  viewed 
by  reflected  light,  made  to  coincide  in  direction  with  the  direct  light. 

519.  Photography  is  the  art  of  producing  pictures  by  the  chemical 
action  of  light.     The   daguerreotype,    ambrotype,    crystallotype,  and 
photo-lithograph,   are   all   produced   by  modified   applications  of  the 
camera  obscura.     Instead  of  the  plain  paper  and  pencil  used  by  the 
artist  for  sketching  with  the  camera,  a  surface  of  silver  or  collodion, 
made  sensitive  by  iodine,  bromine,  or  some  other  chemical  preparation, 
is  placed  in  the  camera  and  subjected  to  the  action  of  the  light  of  the 
image  projected  there  by  the  leus.  396 

A  camera  employed  for  photography  in  any 
of  its  forms,  requires  to  be  achromatic,  and 
also  that  the  chemical  rays  shall  be  brought  to 
a  focus  at  the  same  point  as  the  visual  rays,  or 
at  a  well-defined  distance  from  them.  As  objects 
copied  by  photography  are  seldom  flat,  tbe  objec- 
tive of  the  camera  requires  to  be  so  constructed 
as  not  only  to  give  perfect  definition  of  all  objects 
situated  in  the  focal  plane,  but  also  it  should  be  adapted  to  give  toleraWy  good 
definition  of  parts  of  an  object  that  are  situated  a  little  anterior  or  posterior  to 
the  focal  plane. 

The  usual  form  of  the  camera  employed  in  photography,  is  shown  in  fig.  396. 
The  achromatic  compound  lens,  A,  is  attached  to  the  box,  C,  and  can  be  moved 
backwards  or  forwards  by  turning  the  milled  head,  D.  The  second  box,  B, 
slides  within  the  first.  A  plate  of  ground  glass  set  in  the  frame,  E,  is  inserted 
in  B,  and  when  the  focus  is  so  adjusted  as  to  give  a  perfect  image  on  the  ground 
glass,  this  is  removed,  and  the  sensitive  plate  covered  by  a  dark  screen  is  inserted 
in  its  place.  The  dark  screen  is  then  removed,  and  the  light  produces  a  chemi- 
cal change  where  the  image  is  projected.  This  image  is  then  made  permanent 
by  vapor  of  mercury  or  other  chemical  applications. 

520.  Railway    illumination. — For    illuminating    railroads,    it   is 
important  to  throw  upon  the  track  a  powerful  beam  of  light,  consisting 
of  rays  nearly  parallel.     When  the  track  is  thus  illuminated,  objects 
upon  it  are  more  readily  distinguished  by  contrast  with  surrounding 
darkness;  it  is  therefore  desirable  to  limit  the  lightfto  the  immediate 
vicinity  of  the  track. 

The  common  method  of"  effecting  this  object  is  to  place  an  Argand  lamp  iu 


OPTICS. 


367 


the  focus  of  a  large  parabolic  reflector  (325),  situated  in  front  of  the  locomotive. 
The  light  is  thus  thrown  forward  in  parallel  lines,  and  the  lateral  illumination 
produced  by  light  radiated  directly  from  the  lamp  is  comparatively  small. 

521.  The  Presnel  lens,  a  section  of  which  is  shown  at  o Kg,  fig. 
397,  is  also  employed  for  projecting  a  powerful  beam  of  parallel  light 
upon  objects  to  be  illuminated  at  a  dis-  397 

tance.     This  form  of  lens,  invented  and 

0 —• — — 

first    applied    to    practical    purposes   by 

Fresnel,  consists  of  a  central  plano-convex 

lens,    surrounded    by    segmentary    rings, 

with  curvatures  successively  diminishing 

as   much    as    is    necessary   to  avoid   the 

spherical  aberration  of  a  single  lens,  the 

central  lens,  and  all   the   angular  segments  having  their  curves   .so 

adjusted  as  to  have  a  common  focus. 

The  segmentary  rings  are  sometimes  made  entire,  but  generally,  when  the 
size  is  considerable,  each  ring  is  composed  of  several  parts.  The  central  lens 
and  lateral  segments  are  all  cemented  to  a  plate  of  glass,  as  shown  in  the  figure. 

For  most  purposes,  where  the  Fresnel  lens  is  employed,  it  is  necessary  to  give 
the  illuminating  beam  of  light  a  slight  degree  of  divergence.  It  will  be  easily 
seen  from  the  figure,  that  if  the  centre  of  the  lamp  is  placed  at  the  principal 
focus  of  the  lens,  F,  the  divergence  of  the  beam,  after  passing  the  lens,  will  be 
equal  to  the  angle  b  A  b,  which  the  flame  of  the  lamp  subtends  at  the  surface  of 
the  lens.  A  concave  mirror  is  also  placed  behind  the  lamp,  to  throw  forward 
the  light  in  a  condidon  to  be  refracted  nearly  parallel  by  the  lens  in  front  of  the 
lamp.  A  much  more  brilliant  beam  of  light  is  obtained  in  this  manner  than  by 
the  parabolic  reflectors  alone.  This  lens  is  also  used  in  France  for  railway 
illumination. 

522.  Sea-lights,  designed  as  beacons  to  the  mariner  upon  danger- 
ous coasts,  or  for  lighting  harbors,  are  usually  placed  in  towers,  called 
light-houses.     The  great  elevation  of  the  light 

permits  it  to  be  seen  far  out  at  sea.  It  is  evident 
that  all  light  thrown  out  above  or  below  the 
plane  of  the  horizon,  is  of  no  avail  to  the 
mariner. 

By  an  ingenious  application  of  the  principles  of  the 
Fresnel  lens,  a  sheet  of  light  is  thrown  out  in  every 
direction  in  the  plane  of  the  horizon.  If  fig.  398  is 
revolved  about  the  central  perpendicular  line,  as  an 
axis,  it  will  generate  the  apparatus  known  as  the 
Fresnel  fixed  lir/ht.  The  central  zone  will  consist  of  a 
series  of  hoops  whose  perpendicular  section  is  everywhere  the  same  as  a  section 
of  the  Fresnel  lens.  This  zone  will  therefore  so  act  upon  the  light  of  a  lamp 
placed  at  the  centre,  as  to  project  a  sheet  of  light  in  every  direction  in  the  plane 
of  the  horizon.  Above  and  below  the  central  zone,  are  series  of  triangular 


368 


PHYSIOS    OF   IMPONDERABLE    AGENTS. 


400 


hoops.     A  section  of  one  of  these  hoops,  and  its  action  upon  light  radiating 

from  the  central  lamp,  is  shown  in  fig.  399 ;  A  C  and  B  C  are  plane  faces,  while 

A  B  is  a  convex  surface.     Light  from  the  focus,  F,  399 

is  refracted  on  entering  the  face  B  C,  it  undergoes  -Aw 

total  reflection  at  the  surface  A  B,  and   a  second  ~  \|; ';|?->r. 

refraction  at  AC,  from  which  it  emerges  in  lines   

parallel  to  the  horizon. 

The  focus  of  each  prismatic  hoop  is  carefully 
calculated  for  the  place  it  is  to  occupy,  so  that 
every  part  of  the  apparatus  throws  out  the  light 
that  falls  upon  it  in  a  horizontal  direction. 

523.  Revolving  lights. — To  distinguish 
one  lighthouse  on  the  coast  from  another,  the 
Fresnel  light  is  so  modified  as  to  give  a 
steady  light,  and  also  revolving  flashes  of  light  of  very  great  intensity. 

In  the  revolving  Fresnel  light,  the  triangular 
prismatic  hoops  ahove  and  below  the  central  zone 
are  the  same  as  for  the  fixed  light,  but  the  central 
zone  is  made  of  eight  Fresnel  lenses,  fig  400,  set 
as  shown  in  the  lower  part  of  figure.  The  upper 
part  of  the  same  figure  shows  a  front  view  of  the 
central  zone.  While  the  entire  apparatus  revolves 
as  shown  by  the  direction  of  the  arrows,  each  of 
the  eight  lenses  gives  a  very  intense  light  in 
certain  directions,  and  between  any  two  there  is 
no  light  from  the  central  zone  of  lenses.  The 
light  seen  from  any  position  appears  gradually 
to  increase  to  very  great  brilliancy,  and  then  to 
fade  away  to  much  less  than  half  its  maximum 
intensity,  after  which  it  again  increases  to  its 
former  brilliancy.  These  changes  are  repeated  at 
regular  intervals. 

Fig.  401  shows  a  plan  of  a  revolving  Fresnel  light  fixed  in  the  tower  of  a 
lighthouse.  At  A  B  are  the  parts  shown  in  fig.  400  which  produce  the  flashes 
of  light.  The  whole  apparatus  is  made  to  revolve  by  means  of  the  clock-work 
shown  at  M,  which  is  moved  by  the  weight  P.  The  balcony  surmounting  the 
tower  is  seen  in  the  lower  part  of  the  figure,  also  the  stairs  leading  to  the  light. 
A  dome,  supported  on  iron  frame-work,  protects  the  illuminating  apparatus. 
The  distance  at  which  the  light  can  be  seen  will  depend  upon  the  height  of  the 
tower  in  which  it  is  placed. 

The  lamp  used  for  the  Fresnel  light  is  an  Argand  burner,  with  four 
concentric  wicks,  with  currents  of  air  passing  up  between  them. 

The  wicks  are  defended  from  the  excessive  heat  of  their  united  flames  by  a 
superabundant  supply  of  oil,  which  is  thrown  up  from  below  by  a  clock-work 
movement,  and  constantly  overflows  the  wicks.  A  very  tall  chimney  is  required 
to  supply  a  sufficiently  strong  current  of  air  to  support  the  combustion.  The 
dimensions  of  the  Fresnel  light,  and  the  number  of  lenses  and  hoops  of  which 
M  consists,  are  varied  to  suit  the  purposes  for  which  it  is  used ;  the  light  pro- 


OPTICS. 


369 


duced  varying  in  intensity  from  twenty-five  to  three  thousand  Argand  lamps  of 
common  size. 

401 


i1  if'1 


524.  The  telestereoscope. — The  image  upon  the  retina  of  every 
human  eye  represents  a  perspective  projection  of  the  objects  situated 
in  the  field  of  view.  As  the  positions  from  which  these  projections  are 
taken  are  somewhat  different  for  the  two  eyes  of  the  same  individual, 
the  perspective  images  themselves  are  not  identical,  and  we  make  use 
of  their  difference  to  obtain  an  idea  of  the  distances  from  the  eye  of  the 
different  objects  in  the  field  of  view. 

The  images  of  the  same  object  on  the  two  retinae  are  more  different 
from  each  other  as  the  object  is  brought  nearer  to  the  eyes.  In  the 
case  of  very  distant  objects,  the  difference  between  the  pictures  on  the 
34 


370  PHYSICS    OF    IMPONDERABLE    AGENTS 

retinae  of  the  two  eyes  becomes  imperceptible,  and  we  kse  the  aid  just 
spoken  of  in  estimating  their  distance  and  bodily  figure. 

The  telestereoscope  is  an  instrument  which  causes  distant  objects  to 
appear  in  relief.  It  increases  the  binocular  parallax  of  distant  objects, 
and  by  presenting  to  each  eye  such  a  view  as  would  be  obtained  if  the 
distance  between,  the  two  eyes  were  greatly  increased,  it  gives  the  same 
appearance  of  relief,  as  if  the  402 

objects  were  brought  near  to 
the  observer. 

Let  6  and  b',  fig.  402,  be  two 
plane  mirrors  placed  at  angles  of 
45°  with  the  line  of  vision;  let 
t-  and  c'  be  two  smaller  mirrors 
placed  parallel  to  b  and  b',  and 
let  d  and  d'  represent  the  position  of  the  two  eyes  of  the  observer.  It  is  evident 
that  the  light  from  distant  objects  falling  upon  the  mirrors  in  the  direction  a  b 
and  a'  b1,  will  be  reflected  to  the  small  mirrors  c  and  c',  where  it  will  be  again 
reflected  to  the  eyes  at  d  and  d'.  The  two  views  seen  by  the  eyes  will  evidently 
be  the  same  as  if  the  eyes  were  separated  to  the  positions  m  and  m'.  The  relief 
with  which  objects  will  be  seen  by  this  instrument,  will  obviously  be  increased 
as  much  as  the  distance  b  b'  exceeds  the  distance  between  the  eyes  d  and  d'. 

But  while  this  instrument  increases  the  perspective  difference  of  the  images  seen 
by  the  two  eyes,  the  visual  angle  under  which  each  object  is  seen  remains  un- 
changed, and  hence,  as  the  apparent  distance  of  the  objects  is  diminished,  their 
dimensions  appear  diminished  in  the  same  proportion.  If  the  small  mirrors  are 
made  to  rotate  on  perpendicular  axes,  while  the  large  mirrors  are  fixed,  the 
distortion  of  figure  may  be  easily  corrected  by  turning  the  small  mirrors  until 
objects  appear  in  their  true  proportions. 

If  the  lenses  of  an  opera  glass  are  inserted  in  the  instrument,  the  convex  field- 
glasses  being  inserted  at /and/',  between  the  large  and  small  mirrors,  and  the 
concave  eye-glasses  between  the  eyes  and  small  mirrors,  the  effect  will  be  to 
increase  the  visual  angle  of  every  object  in  the  field  of  view.  If  the  glasses 
magnify  as  many  diameters  as  the  distance  between  the  large  mirrors  exceeds 
the  distance  between  the  eyes,  every  object  will  appear  in  its  due  propor- 
tions, and  the  effect  will  be  surprising.  The  appearance  will  be  as  though 
the  observer  had  been  actually  transported  to  the  immediate  vicinity  of  the 
objects  themselves.  The  distance  between  the  large  mirrors  of  the  telestereo- 
scope should  not  exceed  the  breadth  of  an  ordinary  window,  unless  it  is  to  be 
used  in  the  open  air,  when  it  may  be  made  of  any  dimensions  that  are  desired, 
and  the  effect  produced  will  be  in  proportion  to  its  magnitude. 

525.  The  stereoscope  (from  ffrepsos,  solid,  and  azoxia),  to  see)  is 
an  instrument  so  constructed  that  two  flat  pictures,  taken  under  certain 
conditions,  shall  appear  to  form  a  single  solid  or  projecting  body. 

In  order  to  produce  this  illusion,  different  images  as  observed  by  the 
two  eyes  (484)  must  be  depicted  on  the  respective  retinas,  and  yet 
appear  to  have  emanated  from  one  and  the  same  object.  Two  pictures 
are  therefore  taken  from  the  really  projecting  or  solid  body,  the  one  aa 


OPTICS. 


371 


observed  by  the  right  eye  only,  and  the  other  as  seen  by  the  left. 
These  pictures  are  then  placed  in  the  box  of  the  stereoscope,  which  is 
furnished  with  two  eye-pieces,  containing  lenses  so  constructed  that  the 
rays  proceeding  from  the  respective  pictures,  to  the  corresponding  eye- 
pieces, shall  be  refracted  or  bent  outward,  at  such  an  angle  as  each  set 
of  rays  would  have  formed  had  they  proceeded  from  a  single  picture  in 
the  centre  of  the  box  to  the  respective  eyes  without  the  intervention 
of  the  lenses. 

It  is  an  axiom  in  optics  that  the  mind  always  refers  the  situation  of 
an  object  to  the  direction  from  which  the  rays  appear  to  proceed  when 
they  enter  the  eyes ;  both  pictures  will  therefore  appear  to  have 
emanated  from  one  central  object.  As  one  picture  represents  the  real 
or  projecting  object  as  seen  by  the  right  eye,  and  the  other  as  observed 
by  the  left,  though  appearing  by  refraction  to  have  both  proceeded  from 
the  same  object,  the  sensation  conveyed  to  the  mind,  and  the  judgment 
formed  thereon,  will  be  precisely  the  same  as  if  both  images  were 
derived  from  one  solid  or  projecting  body,  instead  of  from  two  pictures. 
Consequently  the  two  pictures  will  appear  to  be  converted  into  one 
solid  body. 

If  two  pictures  of  an  octahedron,  as  A 
and  B,  fig.  403,  such  as  would  be  formed 
on  ,he  retinae  of  two  eyes,  are  placed  in 
the  stereoscope,  fig.  404,  they  give  to 
the  observer  the  idea  of  a  real  solid  octa- 
hedron, instead  of  the  ordinary  picture,  C.  Photographs  of  natural  scenery, 
taken  from  two  positions,  when  viewed  in  this  instrument,  appear  in  relief  like 
real  objects. 

The  construction  and  action  of  the  stereoscope  will  be  readily  understood  by 
reference  to  figs.  405  and  406.  From  a  double  concave  lens,  A  B  A'  D,  two 
eccentric  lenses,  represented  by  the  smaller  406 

circles,  are   formed.     E  A  e,  in   the  lower  0* 

part  of  the  figure,  represents   a  transverse 
section  of  one  of  these  eccentric  lenses,  and  /.-/    ,..-. 

E  A'  e  the   other.     Each  lens  is  equivalent 
to  a  triangular  prism  E  A  e,  with  a  plano- 
404  405 


403 


eonvex.  lens  cemented  to  each  refracting  face  of  the  imsin      Fig.  406  shows  a 


372 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


section  of  the  stereoscope,  the  eccentric  eye-lenses  A  E,  A' E',  being  ph.  red  at 
the  ordinary  distance  of  the  eyes,  with  their  thin  edges  towards  each  other  Let 
P  and  P'  represent  two  corresponding  points  in  the  stereoscopic  photographs 
which  are  to  be  examined.  The  rays  of  light,  diverging  from  the  point  P,  fall- 
ing upon  the  eye-lens,  are  refracted  nearly  parallel,  and  by  the  prismatic  form 
of  the  lens  are  deflected  from  their  course,  and  emerge  from  the  lens  in  the 
same  direction  as  if  emanating  from  the  point  0.  In  the  same  manner  the  rays 
from  the  point  P  also  appear  to  diverge  from  the  point  0.  The  same  is  true  of 
all  similar  parts  of  the  two  pictures;  thus  the  pictures  appear  superimposed 
upon  each  other,  and  together  produce  the  appearance  of  relief,  for  which  the 
stereoscope  is  so  much  admired. 

The  eccentric  lenses  of  the  stereoscope  are  sometimes  fixed  in  position,  but 
they  are  often  inserted  in  tubes,  as  in  fig.  404,  which  can  be  extended  to  adapt 
the  focus  to  different  eyes,  or  separated  to  a  greater  or  less  distance,  to  suit  the 
distance  between  the  eyes  of  different  persons. 

If  stereoscopic  photographs  are  taken  from  positions  too  widely  separated 
from  each  other,  objects  stand  out  with  a  boldness  of  relief  that  is  quite  un- 
natural, and  the  objects  appear  like  very  reduced  models.  In  taking  stereoscopic 
miniatures  especially,  great  care  is  required  to  preserve  a  natural  appearance. 
In  general,  a  difference  of  a  few  inches  in  the  two  positions  of  the  cameras,  gives 
sufficient  relief  to  the  pictures  when  seen  in  the  stereoscope. 

For  public  buildings  and  landscapes,  two  cameras  are  usually  employed, 
placed  on  a  stand  three  or  four  feet  from  each  other.  If  it  is  desired  to  show  a 
great  extent  of  a  distant  landscape,  or  to  exhibit  in  miniature  the  grouping  and 
form  of  distant  mountains,  two  stations  should  be  selected  that  are  widely  sepa- 
rated ;  but  in  such  cases,  care  should  be  taken  that  no  near  objects  are  admitted 
into  the  picture. 

526.  The  stereomonoscope  (described  by  Mr.  Claudet,  of  London) 
is  an  instrument  by  which  a  single  image  is  made  to  present  the 
appearance  of  relief  commonly  seen  in  the  stereoscope,  and  by  means 
of  which  several  individuals  can  observe  these  effects  at  the  same 
time. 

Let  A,  fig.  407,  be  an  object  placed  before  a  large  convex  lens,  L,  an  image 
of  the  object  will  be  formed  at  a,  in  the  conjugate  focus  of  the  lens,  and  from 
the  image  a  the  rays  of  407 

light  will  diverge  as  from 
a  real  object,  which  will 
be  seen  by  the  eyes  placed 
at  e  e,  e'  e',  or  any  other 
position,  in  the  cone  of 
rays  b  a  c.  Thus  several 
persons  may  at  the  same 
time  see  the  image  sus- 
pended in  the  air.  If  a  screen  of  ground  glass  is  placed  at  S  S,  the  image  will 
appear  spread  out  upon  the  glass,  but  it  will  appear  with  all  the  perspective 
relief  of  a  real  object.  An  image  thus  formed  on  ground  glass  can  be  seen  only 
in  the  direction  of  the  incident  rays.  This  is  not  the  case  with  an  image  formed 
on  paper,  which  radiates  the  light  in  all  directions,,  and  is  hence  incapable  of 
giving  a  stereoscopic  effect  in  such  circumstances. 


OPTICS. 


378 


M 


The  stereomonoscope  consists  c  f  a  screen  of  ground  glass,  S  S,  fig.  408,  and 
two  convex  lenses,  A  L,  B  L,  so  placed  as  to  form  images  of  two  stereoscopic 
pictures,  M  and  N,  at  the  408 

point  a  on  the  screen 
S  S.  Though  the  two 
pictures  have  their  images 
superimposed  on  the  same 
part  of  the  screen  S  S, 
each  picture  can  be  seen 
only  by  the  rays  proceed- 
ing from  the  photograph 
by  which  it  was  formed.  If  the  eyes  are  so  placed  that  the  right  eye  is  in  the 
direction  of  the  rays  coming  from  one  lens,  and  the  left  eye  in  the  direction  of 
rays  coming  from  the  other  lens,  the  object  will  appear  in  relief  as  in  the  stereo- 
scope, and  several  persons  can  witness  the  effect  at  the  same  time. 

\  7.  Physical  Optics. 

I.     INTERFERENCE,  DIFFRACTION,  FLUORESCENCE,  &C. 

527.  Interference  of  light. — The  interference  of  vibrations  and 
waves,  has  been  already  alluded  to  in  the  theory  of  undulations  (328, 
333),  but  the  phenomena  of  luminous  interference  require  some  further 
special  consideration. 

Let  A  B,  B  C,  fig.  409,  be  two  plane  mirrors,  making  with  each  other  a  very 
obtuse  angle  (very  near  180°)  ;  let  a  beam  of  sunlight,  entering  a  dark  room  by 
a  small  opening,  be  brought  to  a  focus  by  a  lens,  L  j  409 

if  this  light,  diverging  from  a  focus,  F,  is  allowed 
to  fall  very  obliquely  upon  the  two  mirrors,  as 
shown  in  the  figure,  it  will  be  reflected  as  if  diverg- 
ing from  two  luminous  points,  M  and  N,  and  the 
light  thus  reflected  will  be  in  a  condition  to  inter- 
fere. Draw  0  P  perpendicular  to  M  N,  from  a 
point  0,  midway  between  them.  It  is  evident  that 
every  point  in  the  line  B  P,  will  be  equally  distant 
from  the  luminous  points  M  and  N ;  the  waves  of 
light  which  cross  each  other  in  the  line  B  P,  will 
therefore  be  in  the  same  phase  of  vibration,  and 
consequently  produce  a  line  of  light  of  double 
intensity.  Let  the  smooth  circular  arcs  represent 
the  phases  of  elevation,  and  the  dotted  arcs  phases 
of  depression ;  then  where  a  dotted  arc  crosses  a 
smooth  arc,  the  two  waves  should  counteract  each  other  and  produce  darkness. 
The  open  dots  represent  vibrations  meeting  in  the  same  phase,  and  the  black 
dots  represent  vibrations  meeting  in  opposite  phases,  which  produce  darkness. 
The  symmetrical  curves  formed  by  the  intersection  of  light  from  the  two  points 
M  and  N,  on  both  sides  of  the  central  line,  are  of  the  form  known  in  geometry 
as  hyperbolas. 

The  distance  on  each  side  of  the  line  B  P,  where  the  luminous  waves  will  be 
again  in  a  like  state  of  accordance  represented  by  the  crossing  of  the  smooth 
arcs  in  the  figure,  will  depend  on  the  interval  between  them,  which  is  different 
for  different  colors;  for  red,  it  is  half  as  much  again  as  for  violet  light j  hence 


374  PHYSICS    OF    IMPONDERABLE    AGENTS. 

the  distance  between  the  curves  of  double  intensity  will  be  least  for  violet  light, 
greatest  for  red,  and  intermediate  for  the  other  colors  of  the  spectrum,  so  that 
while  all  the  colors  are  united  in  the  central  line  B  P,  they  will  be  separated  in 
the  other  bars,  and  form  a  series  of  colored  fringes.  In  experiments,  this  serves 
to  distinguish  the  central  bar,  namely,  that  the  other  bars  are  colored  sym- 
metrically on  each  side  of  it. 

Half  way  between  two  places  of  complete  accordance  there  must  occur  a 
place  of  complete  discordance,  where  the  difference  of  distances  from  M  and  N 
is  £  an  interval,  or  f ,  f ,  or  |,  <fcc. ;  and  according  to  the  undulatory  theory, 
there  would  be  complete  darkness.  Between  these  and  the  places  of  complete 
accordance,  there  would  be  intermediate  stages  of  accordance  and  discordance; 
hence  there  would  be  bright  bars  shading  into  dark  ones,  all  more  or  less  colored 
except  the  central  bars,  where  all  the  colors  are  in  a  state  of  complete  accordance. 

By  careful  measurement  of  distances  between  the  luminous  and  dark  bars, 
the  lengths  of  luminous  waves  of  different  colors  have  been  very  accurately 
ascertained. 

528.  Facts  at  variance  with  theory. — When  the  atmosphere  is 
free  from  clouds,  and  the  sunlight  is  brightest,  the  central  bar  (which, 
according  to  theory,  should  be  bright]  is  found  to  be  a  black  one,  what- 
ever be  the  material  of  which  the  mirrors  are  composed.     But  when 
the  sun  is  near  setting,  the  central  bar  has  been  seen  undoubtedly  a 
bright  one.     It  has  also  been  seen  as  a  bright  bar  when  the  luminous 
point  was  formed  at  a  hole  in  a  thin  plate  of  metal,  and  the  light  which 
had  grazed  the  edge  of  the  hole  was  used. 

The  existence  of  a  central  Hack  bar,  in  normal  circumstances,  where  the 
vibrations  must  meet  in  the  same  phase,  is  thought  to  be  inconsistent  with 
the  undulatory  theory  of  light. 

It  appears  that  light  is  so  modified  in  passing  through  haze,  or  at  an  opaque 
edge  of  a  small  hole,  as  to  acquire  an  anatropy  or  inversion  of  properties.*" 

529.  Interference  colors  of  thin  plates  are  seen  in  thin- films  of 
varnish,  cracks  in  glass,  films  of  mica,  various  crystals,  and  in  other 
transparent  substances,  as  in  soap  bubbles.     The  colors  of  such  thin 
films  are  due  to  the  interference  of  light  twice  reflected  by  the  surfaces 
of  the  film. 

Two  surfaces  of  glass,  pressed  together,  furnish  a  thin  plate  of  air  between 
two  reflecting  surfaces.  Let  CAD  B,  fig.  410,  be 
a  transparent  film,  such  as  a  thin  blown  bulb  of 
glass,  or  a  soap  bubble ;  let  S  A  B  T  be  the  trans- 
mitted ray,  S  A  R  the  ray  reflected  at  the  first  sur- 
face, S  A  B  A'  R'  the  portion  reflected  from  the 
second  surface,  and  emergent  at  the  first  surface, 
S  A  B  A'  B'  T'  the  portion  emerging  from  the  second 
surface,  after  the  two  internal  reflections,  then  the 
ray  A'  R'  will  be  retarded  behind  the  ray  A  R,  by  the  interval  n  m,  owing  to  the 

*  Potter's  Physical  Optics. 


OPTICS.  375 

increased  length  of  path  it  has  to  travel  in  twice  traversing  the  film,  and  B'  T' 
will,  in  a  similar  manner,  fall  behind  the  ray  B  T,  by  the  interval  p  q.  If  these 
retardations  equal  the  interval  of  an  odd  number  of  half  vibrations,  they  will 
interfere,  as  they  originated  from  a  common  wave,  in  the  ray  S  A.  The  reflected 
rays  do  not  differ  greatly  in  intensity,  which  is  for  each  about  one-thirtieth  that 
of  the  incident  light  for  glass,  and  therefore  their  interference  produces  black- 
ness where  they  destroy  each  other.  The  transmitted  light  has  the  principal 
beam  of  little  less  intensity  than  the  incident  beam,  having  lost  only  about  one- 
thirtieth  part  by  reflection  at  each  of  the  points  A  and  B ;  but  the  intensity  of 
the  twice  reflected  beam  which  interferes  with  it  is  about  one-thirtieth  of  one- 
thirtieth,  or  one  nine-hundredth  of  that  of  the  incident  beam ;  hence  the  differ- 
ence of  the  intensities  of  the  bright  and  dark  bands  formed  by  transmitted  light 
is  never  as  great  as  in  the  reflected  beams.  But  the  difference  between  the 
bright  and  dark  bands  is  different  for  different  colors  of  the  spectrum,  being 
least  for  violet  light,  and  greatest  for  red.  This  fact  is  thought  to  be  contrary 
to  what  should  have  been  expected,  according  to  the  undulatory  theory. 

530.  Newton's  rings. — If  a  plane  plate  of  polished  glass  is  pressed 
against  a  plano-convex  lens  whose  radius  of  curvature  is  known,  the 
interference  bands  become  colored  rings,  and  the  exact  thickness  of  the 
film  of  air  by  which  each  color  is  produced  is  easily  estimated. 

The  form  of  this  apparatus  is  shown  in  fig.  411.  The  letters  and  explanation 
of  the  figure  are  similar  to  the  preceding.  When  the  two  glasses  are  pressed 
sufficiently  near  together,  the  centres  appear  black  ^-Q 

by  reflected  light,  and  bright  by  transmitted  light. 
The  thickness  of  the  film  of  air  where  the  first    V    ll 
color  appears,  is  equal  to  one-half  the  retardation 
producing  that  color ;  hence  the  length  of  the  wave, 
or  vibration,  for  any  color,  is  estimated  as  equal  LJy 


color  appears.  The  colors  succeed  each  other  in 
the  order  of  the  length  of  the  vibrations  required 
to  produce  them.  A  second,  third,  and  fourth  series  of  colored  rings  will  be 
found,  where  the  thickness  of  the  film  is  an  exact  multiple  of  the  thickness 
required  to  produce  the  first  series  of  colors.  The  distance  between  the  first  and 
second  series  depends  on  the  rapidity  with  which  the  thickness  of  the  film 
increases.  In  the  case  of  a  lens  pressed  against  a  plate  of  glass,  the  distance 
between  the  glasses,  or  the  thickness  of  the  film,  increases  as  the  square  of  the 
distance  from  the  centre.  The  diameters  of  the  bright  rings  will  therefore  be  as 
the  square  roots  of  the  numbers  1,  2,  3,  &c.,  and  the  diameters  of  the  dark  rings 
will  be  as  the  square  roots  of  the  numbers  1J,  2i,  3J,  <fcc.  The  distance  between 
successive  rings  of  violet  will  be  much  less  than  the  distance  between  successive 
rings  of  red  j  one  series  of  colors  will  therefore  overlap  some  of  the  colors  in 
the  succeeding  series  of  colored  images,  and  by  their  admixture  produce  colors, 
the  successive  groups  of  which  are  designated  as  Newton's  first,  second,  third, 
&c.,  orders  of  colors. 

531.  Length  of  luminous  waves  or  vibrations. — By  such  means 
as  we  have  described,  the  lengths  of  the  vibrations  required  to  produce 
different  colors  have  been  estimated. 


376 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


The  following  table  exhibits  the  numerical  results  which  have  been  deduced 
for  the  length  and  velocity  of  luminous  vibrations  of  different  colors. 


Length  of  undulations 
Colors.             |    in  parts  Of  an  inch. 

Number  of  undula- 
tions in  an  inch. 

Number  of  undulations 
per  second. 

Extreme  red,  .     |          0-0000266 

37640 

458,000000,000000 

Red,  .... 

0-0000256 

39180 

477,000000,000000 

Orange,       .     . 

0-0000240 

41610 

506,000000,000000 

Yellow,        .     . 

0-0000227 

44000 

535,000000,000000 

Green,    .     .     . 

0-0000211 

47460 

577,000000,000000 

Blue,       .     .     . 

0-0000196 

51110 

622,000000,000000 

Indigo,  .     .     . 

0-0000185 

54070 

658,000000,000000 

Violet,    .     .     . 

0-0000174 

57490 

699,000000,000000 

Extreme  violet, 

0-0000167 

59750 

727,000000,000000 

412 


According  to  Eisenlohr  (Am.  Jour.  Sci.  [2]  XXIL),  the  length  of  the  vibra- 
tions in  the  extreme  red  ray  is  just  double  the  length  of  the  vibrations  of  the 
invisible  rays  beyond  the  violet,  which,  by  concentration,  produce  the  lavender 
light  of  Herschel.  The  entire  range  of  visible  rays  differs  in  the  length  of 
vibrations  only  by  the  amount  of  one  octave  in  music. 

When  we  consider  the  almost  inconceivable  velocity  with  which  these  wonder- 
fully minute  vibrations  are  propagated,  it  is  evident  that  absolute  demonstration 
of  the  real  nature  of  light  must  be  among  the  profoundest  researches  of  physical 
science. 

532.  Diffraction. — If  a  razor  is  held  with  its  flat  surface  towards 
the  rays  of  the  sun,  the  rays  that  pass  in  close  proximity,  both  to  the 
edge  and  to  the  back,  will  be  deflected  as  shown  in  fig.  412.  A  portion 
of  the  rays  are  deflected  outwards,  appearing  to  suffer  reflection ;  the 
back  of  the  razor  deflecting  the  rays  outward,  more  than  the  sharp 
edge ;  but  the  edge  of  the  razor  deflects 
more  light  into  the  place  of  the  geometri- 
cal shadow,  than  is  deflected  inwards  by 
the  back  of  the  instrument.  These  differ- 
ences are  represented  by  the  closeness 
of  the  lines  drawn  to  represent  the  rays 
where  the  greatest  amount  of  light  is  de- 
flected. If  the  body  interposed  is  narrow, 
like  a  fine  needle  or  a  hair,  the  rays  de- 
flected inwards  cross  each  other,  and  pro- 
duce the  phenomena  of  interference  in 
accordance  with  the  undulatory  theory.  The  rays  deflected  outward 
produce  interference  with  the  rays  not  deflected,  but  bright  lines  appear 
where  the  undulatory  theory  would  give  dark  lines.  All  the  bright 
and  dark  lines  are  bordered  with  colored  fringes,  as  in  ordinary  cases 
•f  interference.  These  phenomena  are  best  seen  in  a  dark  room  by 


OPTICS.  377 

looking  through  an  eye-lens  at  a  hair  or  needle,  at  a  considerable  dis- 
tance from  a  lamp,  or  by  looking  at  a  beam  of  sunlight  admitted  to  a 
dark  room  between  two  sharp  parallel  edges.  The  rays  that  have  been 
diffracted  or  bent  into  the  geometrical  shadow,  are  not  as  readily 
deflected  again  in  the  same  direction,  but  are  more  easily  deflected  in 
the  opposite  direction  than  rays  which  have  undergone  no  such  pre- 
vious change. 

533.  Fluorescence. — Epipolic    dispersion. — Certain   bodies,    as 
fluor-spar,  glass  colored  yellow  by  oxide  of  uranium,  called  canary 
glass,  solution  of  sulphate  of  quinine,  infusion  of  the  bark  of  the  horse- 
chestnut,  and  many  other  vegetable  infusions,  possess  the  remarkable 
property  of  so  dispersing  some  part  of  the  light  passing  through  them, 
that  the  course  of  the  luminous  rays  becomes  visible. 

These  phenomena  are  best  exhibited  by  bringing  a  pencil  of  light  to  a  focus 
in  the  interior  of  any  of  these  substances,  by  means  of  a  convex  lens,  when  the 
course  of  the  rays  will  become  visible,  as  though  the  portion  through  which  the 
light  passed  had  become  self-luminous.  The  rays  of  light  of  high  refrangibility, 
especially  the  violet  and  the  invisible  chemical  rays,  are  subject  to  this  kind  of 
dispersion,  their  refrangibility  is  at  the  same  time  changed,  and  probably  the 
length  of  their  luminous  waves  is  increased,  so  that  rays  previously  invisible 
may  be  seen  by  the  eye.  These  phenomena  have  been  called  by  various  names, 
as  internal  dispersion,  epipolic  dispersion,  and  fluorescence.  The  latter  term, 
derived  from  fluor-spar,  and  adopted  by  Mr.  Stokes,  is  considered  the  more 
appropriate  term,  as  it  involves  no  theory. 

This  change  of  the  refrangibility  and  length  of  luminous  waves  is  anala- 
gous  to  the  change  of  pitch  in  reflected  sounds  heard  in  certain  remarkable 
echoes  (§  355). 

534.  Phosphorescence. — Certain  bodies  after  being  exposed  to  the 
action  of  light,  acquire  the  property  of  shining  in  the  dark  (399).     The 
most  remarkable  phosphorescent  bodies  are  the  sulphurets  of  barium, 
strontium    and  calcium,  some   kinds  of  diamonds,  most  varieties   of 
fluoride  of  calcium,  particularly  the  variety  known  as  chlorophane, 
compounds  of  lime,  magnesia,  soda  and  potash,  salammoniac,  succinic 
and  oxalic  acids,  borax,  dried  paper,  silk,  sugar,  sugar  of  milk,  teeth,  &c. 

The  time  during  which  these  bodies  emit  light  varies  from  a  fraction 
of  a  second  to  several  hours,  and  the  intensity  of  the  emitted  light 
varies  in  a  similar  manner. 

The  study  of  these  phenomena  requires  the  use  of  delicate  apparatus  adapted 
to  the  purpose. 

1.  The  more  refrangible  rays  of  the  spectrum  in  general  .act  more  powerfully 
to  produce  phosphorescence  in  bodies  exposed  to  their  influence  than  the  less 
refrangible  rays.     In  some  cases  the  invisible  rays  of  the  spectrum,  i.  e.,  the 
rays  beyond  the  violet,  produce  a  brilliant  phosphorescence. 

2.  The  least  refrangible   rays,  as    the  red,  not   only  generally  produce    no 
phosphorescence,  but  even  counteract  the  influence  of  the  more  refrangible  rays 
when  mixed  with  them. 


378 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


3.  The  wave  lengths  of  light  emitted  in  the  dark  by  phosphorescent  bodies 
are  in  general  greater  than  those  of  the  exciting  rays;  i.  e.}  the  phosphorescent 
light  shows  a  color  belonging  to  a  part  of  the  spectrum  nearer  to  the  red  than 
the  light  which  produced  it,  though  in  a  few  cases  the  color  is  unaltered. 

4.  The  refrangibility  of  the  light  emitted  by  phosphorescent  bodies  depends 
upon  their  molecular  condition,  and  not  merely  upon  their  chemical  constitution. 
Each  phosphorescent  body  appears  to  be  adapted  to  vibrate  in  harmony  with  the 
wave  lengths  of  some  colors  more  readily  than  with  others. 

5.  One  and  the  same  body  may  emit  rays  of  very  different  colors,  according  to 
the  time  which  intervenes  between  the  action  of  light  and  the  moment  of  observa- 
tion.    This  last  result  shows  that  vibrations  of  different  velocities  are  preserved 
for  unequal  times  in  different  bodies ;  sometimes  it  is  the  vibrations  correspond- 
ing to  the  less  refrangible  rays  which  continue   longest,  as  in  bisulphate  of 
quinine,  double  cyanide  of  potassium  and  platinum,  diamond,  Ac.     Sometimes 
the  most  refrangible  rays  are  most  durable,  as  in  Iceland  spar. 

6.  Many  bodies,  such  as  glasses  and  certain  compounds  of  uranium,  owe  their 
fluorescence  entirely  to  the  persistence  of  the  luminous  impressions  for  a  very 
short  time,  not  exceeding  a  few  hundredths  of  a  second ;  the  intensity  of  the 
emitted  light  is  then  very  brilliant. 

It  is  probable  that  phosphorescence  and  fluorescence  differ  from  one  another 
only  in  the  time  during  which  a  luminous  impression  is  preserved  in  bodies. 

These  conclusions,  which  support  the  theory  of  undulation  as  at  present 
admitted,  prove  that  luminous  vibrations,  when  transmitted  to  any  body,  or  at 
least  to  a  great  many  bodies,  compel  its  molecules  to  vibrate  for  a  time,  and 
with  an  amplitude  and  wave  length  which  depend  not  only  on  the  chemical  con- 
stitution of  the  body  but  also  on  its  physical  condition.* 

535.  Colors  of  grooved  plates. — Fine  lines  engraved  upon  polished 
steel,  and  lines  drawn  upon  glass  with  a  diamond  point,  if  sufficiently  near 
together,  cause  a  beautiful  iridescence  by  the  interference  of  light  re- 
flected from  such  surfaces.  The  beautiful  play  of  colors  seen  upon  mother 
of  pearl  is  caused  by  the  delicate  veins  with  which  the  surface  is  covered. 

II.     OPTICAL  PHENOMENA  OF  THE  ATMOSPHERE. 

536.  The  rainbow  is  one  of  the  most  wonderful  and  beautiful  pheno 
mena  in  nature.     In  it  reflec- 
tion, refraction,  dispersion,  and 

interference  of  light,  are  all 
combined.  It  is  seen  in  that 
part  of  the  heavens  opposite  to 
the  sun,  when  the  sun  is  less 
than  forty- two  degrees  above 
the  horizon.  The  shadow  of 
the  eye  of  the  observer  will 
always  point  to  the  centre  of 
the  circle  of  which  the  rainbow 
forms  a  part:  hence,  as  the  sun  descends  near  the  horizon,  the  rainbow 


Edmond  Becquerel,  BiVintheqnc  Universelle,  vol.  XVI.  p.  21. 


OPTICS.  379 

rises  higher,  and  as  the  sun  ascends  the  morning  sky,  the  height  of  the 
rainbow  diminishes. 

To  understand  the  formation  of  the  rainbow,  we  must  first  examine  the  action 
of  a  single  drop  of  water  upon  parallel  rays  of  light.  Let  the  circle,  fig.  413, 
represent  a  drop  of  water,  and  S  A,  SB,  &c.,  parallel  rays  of  light  falling  upon 
it.  The  ray  S  A,  which  falls  perpendicularly  upon  the  drop,  will  suffer  no  devia- 
tion in  its  direction,  but  will  be  partially  reflected  backward  in  the  line  of  inci- 
dence, though  it  will  principally  pass  through  the  drop.  The  ray  S  a,  will  be 
refracted  to  b,  where  it  will  be  reflected  to  c,  and  will  emerge  in  the  direction  c  d, 
making  a  certain  angle  with  the  direction  of  the  original  ray  S  a.  As  the  distance 
of  the  incident  ray  from  A  increases,  the  emergent  ray  will  make  a  greater  angle 
with  the  incident  ray,  till  we  arrive  at  B,  where  two  successive  rays  will  emerge 
parallel,  as  shown  by  the  heavy  line,  S  B  #  e  p,  which  deviates  more  from  the 
direction  A  S,  than  any  ray  incident  at  a  greater  or  less  distance  from  A.  As 
we  proceed  from  A,  towards  C,  the  deviation  of  the  emergent  ray  will  diminish, 
and  every  ray  between  B  and  C  will  emerge  parallel  to  some  other  ray,  which 
entered  the  drop  between  A  and  B  ;  S  y  will  emerge  in  r.1 '  m,  parallel  to  e"  n,  which 
entered  the  drop  at  the  ray  S  x.  The  ray  S  C,  which  is  tangent  to  the  drop,  will 
be  refracted  to  i,  and  emerge  in  the  direction  Ic  o,  making  an  angle  of  about 
twenty-five  degrees  with  e  p,  the  line  of  greatest  deviation. 

The  light  which  enters  the  drop  in  parallel  rays  will  therefore  emerge,  spread 
over  the  entire  space  between  ep  and  c  d;  but  having  its  greatest  intensity  near 
the  direction  e  p,  and  rapidly  diminishing  towards  c  d. 

If  A  Y,  fig.  414,  represent  the  position  of  the  line  e  p  of  fig.  413,  the  dotted 
curve,  by  its  height  above  A  X,  will  show  how  rapidly  the  intensity  of  the 
light  fades  away,  as  the  distance  from  ep  increases  414 

toward  c  rf,  where  the  intensity  is  zero. 

Since  we  have  at  every  angle  between  ep  and  c  d , 
parallel  rays  which  have  traversed  different  paths 
through  the  drop,  we  shall  have  all  the  phenomena  of 
bright  and  dark  bands,  produced  by  interference. 

The  intersection  of  the  emergent  rays  will  form  a 
caustic  curve  k  q,  tangent  to  the  circle  at  k,  and  ap- . 
proaching  constantly  to  parallelism  with  the  asymptote  ep,  which  it  will  never 
meet.  If  the  emergent  rays  between  c  and  e  were  extended  backwards,  they 
would  form  another  caustic  h  I,  having  e  p  produced  backward  for  its  asymptote. 
The  caustic  curve  h  I,  commences  in  a  direction  perpendicular  to  the  surface  of 
the  drop,  and  approaches  the  asymptote  without  ever  touching  it.  The  curves 
q  r,  formed  by  unwrapping  a  thread  from  the  caustic  k  q,  and  q  r',  formed  by  a 
thread  from  the  caustic  I  h,  show,  by  their  gradual  separation,  the  amount  of 
retardation  of  the  wave  surface  of  the  two  sets  of  parallel  rays  which  interfere 
between  e  p  and  c  d. 

According  to  the  undulatory  theory,  we  shall  have  bright  bands  where  the 
rays  have  traversed  equal  distances,  or  distances  differing  by  any  number  of 
entire  vibrations,  and  dark  bands  where  the  rays  differ  by  an  odd  number  of  half 
vibrations. 

These  bright  and  dark  bands  are  readily  seen,  with  proper  precautions,  with 
light  reflected  from  a  drop  of  water  suspended  at  the  point  of  a  fine  glass  tube. 
When  monochromatic  light  is  used,  thirty  or  forty  of  these  bright  and  dark  bands 
may  be  counted. 

The  breadth  of  the  bright  and  dark  bands  varies  with  the  size  of  the  drop 


380  PHYSICS    OF    IMPONDERABLE    AGENTS. 

from  which  the  light  is  reflected.  The  interference  bands  vary  also  for  the  dif- 
ferent colors,  being  nearly  twice  as  broad  for  red  as  for  violet  light.  When 
white  light  is  employed,  the  first  red  band  only  is  pure,  the  other  bands  being 
more  or  less  confused  by  the  unequal  super-position  of  different  colors. 

If  we  consider  only  the  first  two  bright  bands  of  each  color,  we  can 
easily  explain  the  common  phenomena  of  the  rainbow.  A  little  within 
the  caustic  curve,  k  q,  fig.  413,  on  its  convex  side,  we  shall  have  a 
bright  light,  represented  in  intensity  by  the  curve  a,  fig.  414,  and  a 
second  band  of  the  same  color  at  6,  of  feebler  intensity.  As  the  refrac- 
tive index  for  red  rays  is  less  than  for  the  other  colors,  the  red  will 
diverge  more  from  the  incident  ray,  after  refraction,  than  the  violet, 
and  other  colors  will  appear  intermediate. 

Suppose  now  that  in  a  shower  of  rain  a  ray  of  light  from  the  sun 
falls  upon  a  drop  of  water  at  r,  fig.  415,  and  is  reflected  from  its  posterior 
surface,  so  as  to  give  to  the  eye  the  415 

red  ray  of  maximum  intensity,  r  E,  a 
drop  below  it  will  give  a  violet  ray  of 
maximum  intensity,  v  E,  and  interme- 
diate colors  will  be  formed  in  the  same 
manner  by  intermediate  drops.  Let 
the  planes  of  incidence  and  reflection 
revolve  about  a  line  S  E  S,  drawn  from 
the  sun  through  the  eye  of  the  ob- 
server ;  the  position  of  the  drop 
from  which  light  can  reach  the  eye 
will  describe  the  arch  of  the  rainbow. 

The  radius  of  the  primary  rainbow  measured  from  the  extreme  red 
n-as  found,  by  Sir  Isaac  Newton,  to  be  42°  4X. 

The  purity  of  the  several  colors  in  the  rainbow  is  the  result  of  inter- 
ierence,  which  produces  dark  bands  for  each  particular  color,  giving  a 
clear  space  for  the  delineation  of  the  other  colors  of  the  rainbow  before  the 
first  color  is  repeated.  When  the  rain-drops  differ  greatly  in  size,  as  is 
often  the  case,  the  different  colors  of  the  first  and  second  interference 
bands  overlap  and  mingle  together,  and  the  bow  is  but  imperfectly 
developed. 

A  secondary  rainbow,  with  violet  above  and  red  below,  is  formed  by  light 
which  has  been  twice  reflected  within  the  drops,  as  shown  in  fig.  415,  the  rays 
entering  the  lower  border  of  the  drop,  and  emerging  near  the  upper  border.  The 
same  principles  of  interference  determine  the  purity  of  colors,  and  angle  of 
maximum  intensity,  as  in  the  primary  bow.  The  loss  of  light  occasioned  by 
two  reflections  accounts  for  the  feebler  intensity  of  the  secondary  bow.  In 
the  secondary  bow,  the  order  of  colors  is  the  reverse  of  the  primary,  violet 
being  outermost. 


OPTICS.  381 

Newton  found  the  distance  between  the  primary  and  secondary  rainbows  to 
be  8°  30'. 

A  spurious  rainbow  is  often  seen  within  the  primary  bow,  as  shown  at 
p  q,  fig.  415.  This  is  formed  by  the  second  bright  band  of  each  color,  tLo 
position  and  intensity  of  which  is  represented  at  b,  fig.  414.  A  third  and  four!  ii 
bow  is  also  sometimes  seen,  still  interior  to  the  second,  but  the  colors  of  tl.u 
third  and  fourth  orders  are  so  much  mingled  that  only  two  or  three  appear  in  ai;y 
bow  interior  to  the  first  spurious  bow. 

537.  Fog-bows. — Halos. — Coronas. — Parhelia. — Fog-bows,  which 
are  sometimes  seen,  differ  from  the  rainbow  by  the  extreme  minuteness 
of  the  spherules  of  water  from  which  the  reflection  takes  place. 

Halos  are  prismatic  rings  seen  around  the  sun  or  moon,  varying 
from  2°  to  46°  in  diameter:  these  are  explained  by  reflection  from 
minute  crystals  of  ice  floating  in  the  atmosphere. 

Coronas,  encircling  the  moon,  are  formed  by  reflection  from  the 
external  surface  of  watery  vapor,  the  light  thus  reflected  interfering 
with  direct  light  from  the  same  source.  They  generally  indicate  change 
of  weather. 

Parhelia,  and  bands  of  light  passing  through  the  sun,  are  also  attri- 
buted to  reflection  from  prisms  of  ice. 

Many  of  these  phenomena  require  for  their  explanation  a  refinement  of  inves- 
tigation not  proper  to  be  introduced  in  an  elementary  work. 

538.  Atmospheric   refraction  causes   all  bodies  not  directly  in 
the   zenith  to  appear  more  elevated  than  they  416 

really  are. 

Let  A  B  C  D,  fig.  416,  represent  the  external  surface 
of  the  atmosphere,  and  the  inner  circles  strata  of  in- 
creasing  density  around  the  earth,  E.  Light  from  any 
of  the  heavenly  bodies  situated  at  a  or  c  will  suffer 
refraction  by  every  stratum  of  air  more  dense  than  the 
preceding ;  and  by  a  gradually  increasing  density,  it 
will  be  made  to  travel  in  curved  lines,  until  entering  the  eye  of  the  observer,  the 
bodies  at  a  and  c  will  appear  situated  at  b  and  d.  417 

539.  Looming    is   a   term   applied  to  the   elevation 
of  objects  at  sea  which  appear  raised  above  their  real 
position  by  atmospheric  refraction. 

Islands  often  appear  thus  raised  above  the  water,  «nd  an 
inverted  image  is  seen  below  them.  Distant  vessels  sometimes 
appear  above  the  horizon,  when  their  distance  is  so  great  that 
they  would  be  far  below  the  horizon  if  they  were  not  elevated  in 
appearance  by  extraordinary  refraction. 

In  peculiar  states  of  the  atmosphere,  ships  have  appeared 
suspended  in  the  clouds,  and  occasionally  an  inverted  image 
has  appeared  below,  when  the  real  ship  was  mostly  below  the 
horizon,  as  shown  in  fig.  417. 

540.  The    mirage,    often   seen    in    Egypt,    and    sandy   deserts,    ie 

35 


382 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


caused  by  rays   reflected  from   strata  of.  air   heated  by  the  burning 
sands.     Distant   objects  are   seen  reflected  by  the  heated   air   as   in 

418 


the  waters  of  a  beautiful  lake,  which  disappears  as  the  thirsty 
traveler  approaches.  The  phenomena  of  the  mirage  are  shown  in 
fig.  418. 

III.     POLARIZATION  OF  LIGHT. 

541.  Direction   of  luminous    vibrations. — The   phenomena  of 
polarized  light  are  justly  regarded  as  the  most  wonderful  in  the  whole 
science  of  optic's.     These  phenomena  are  most  readily  explained  and 
understood  by  reference  to  the  undulatory  theory.     It  has  been  stated 
(398)  that  the  vibrations  of  light  move  at  right  angles  with  the  direc- 
tion of  the  rays. 

This  species  of  vibration  may  be  illustrated  by  those  of  a  cord,  made  fast  at 
one  end,  and  moved  rapidly  upward  and  downward  by  the  hand  shaking  the 
other  extremity,  as  shown  in  fig.  419.  If  419 

we  suppose  another  cord  vibrating  from  B 
right  to  left,  and  others  in  every  inter-  i  ____„£__/,. 
mediate  direction,  we  may  form  a  tolerably 
clear  idea  of  the  vibrations  of  a  collection 
of  rays  in  a  beam  of  ordinary  light.  A 
single  lufhinous  atom  may  be  supposed  to  originate  vibrations  moving  in  only 
a  single  plane,  but  an  infinite  number  of  independent  luminous  atoms,  consti- 
tuting a  luminous  body,  will  produce  vibrations  moving  in  every  possible  plane, 
which  may  be  illustrated  by  revolving  that  plane  around'the  line  representing 
the  direction  of  a  ray  of  common  light. 

542.  Transmission  of  luminous  vibrations. — Opaque  substances 
allow  no  luminous  vibrations  to   pass   through   them.     Some  bodies 


OPTICS. 


383 


420 


transmit  nearly  all  the  luminous  vibrations  which  fall  upon  them ; 
other  bodies  are  capable  of  transmitting  only  those  vibrations  of  light 
contained  in  a  single  plane,  or  that  portion  of  the  vibrating  force  which 
can  be  resolved  into  vibrations  in  that  plane.  Other  bodies,  capable 
of  vibrating  in  two  directions,  reduce  all  the  vibrations  which  they 
transmit  to  vibrations  in  the  two  planes  in  which  these  bodies  them- 
selves are  capable  of  vibrating.  Some  bodies,  by  reason  of  the  position 
in  which  an  incident  beam  of  light  falls  upon  them,  alter  the  direction 
of  the  vibrations  which  they  transmit,  and  thus  produce  a  beam  of 
light,  whose  vibrations  are  all  limited  to  a  single  plane. 

543.  Change  produced  by  polarization  of  light. — A  beam  of 
light  is  said  to  be  plane  polarized  when  all  its  vibrations  move  in  a  single 
plane,  or  in  planes  parallel  to  each  other.     This  may  be  illustrated  by 
a  bundle  of  stretched  cords,  all  vibrating  in  one  direction.     If. the  cords 
differ  in  size  or  tension,  the  lengths  of  their  vibrations  will  differ.    This 
may  illustrate  the  vibrations  of  different 

colors,  which  vary  in  the  lengths  of  their 
vibrations  (531).  A  round  rod  may  be 
taken  to  represent  a  small  beam  of  com- 
mon light,  and  the  radii  shown  in  fig. 
420  may  represent  the  transverse  vibra- 
tions by  which  light  is  propagated  in 
ordinary  media.  Fig.  421  will  then  represent  a  transverse  section  of  a 
polarized  beam,  with  vibrations  in  planes  parallel  to  each  other. 

544.  Resolution  of  vibrations. — The  principle  of  resolution  of 
forces  (50)  will  enable  us  to  understand  how  vibrations,  in  an  infinite 
number  of  planes  passing  through  the  general  direction  of  a  beam  of 
light,  may  be  resolved  into  vibrations  in  two  planes,  making  with  each 
other  any  required  angle.    If  0  E,  fig.  422,  represents  the  direction  and 
intensity  of  a  vibration,  it  will  be  equivalent 

to  0  a  and  0  c,  in  axes,  at  right  angles  to 
each  other.  Vibrations  represented  by  O  F, 
0  G,  and  0  H,  may,  in  the  same  manner,  be 
resolved  into  vibrations  in  the  axes  A  B  and 
0  D.  Then  Oa  +  Oa'  +  0&  +  O6'  will 
represent  the  intensity  of  the  resulting  vibra- 
tions in  the  axis  A  B,  and  0  c  -f-  0  c'  -f  0  d 
+  0  d'  will  represent  the  intensity  of  the 
resulting  vibrations  in  the  axis  C  D.  If  we 
thus  resolve  vibrations  in  an  infinite  number 
of  planes  into  vibrations  in  the  axes  A  B  and  C  D,  the  sum  of  the 
resulting  intensities  in  the  axis  A  B  will  be  exactly  equal  to  the  sum 


422 


384  PHYSICS    OF    IMPONDERABLE    AGENTS. 

of  the  intensities  in  the  axis  CD.  A  ray  of  common  light  may  there- 
fore be  considered  as  consisting  of  vibrations  moving  in  two  planes  at 
right  angles  to  each  other.  Any  medium  that  will,  either  by  its  posi- 
tion or  internal  constitution,  separate  light  into  two  parts,  vibrating  in 
planes  at  right  angles  to  each  other,  will  produce  that  change  denomi- 
nated polarization  of  light. 

545.  Light  polarized  by  absorption. — Certain  crystals  have  the 
remarkable  property  of  polarizing  all  the  light  which  passes  through 
them  in  particular  directions.     They  appear  to  absorb  part  of  the  light, 
and  cause  the  remainder  to  vibrate  in  a  single  direction  only. 

If  a  transparent  tourmaline  is  cut  into  plates  one-thirtieth  of  an  inch  thick 
and  polished,  the  plane  of  section  being  parallel  to  the  vertical  axis  of  the 
hexagonal  prism  in  which  this  mineral  crystallizes,  the  light  transmitted  through 
such  a  plate  will  be  polarized.  If  a  second  plate  is  placed  parallel  to  the  first, 
as  shown  in  fig.  423,  the  light  transmitted  423  424 

through  the  first  plate  will  also  be  trans- 
mitted through  the  second  plate;  but  the 
light  will  be  entirely  obstructed  if  the  axis 
of  the  second  plate  is  placed  at  right  angles 
with  that  of  the  first,  as  shown  in  fig.  424. 
A  plate  of  tourmaline  becomes,  therefore,  a 
convenient  means  of  polarizing  light,  and 
also  an  instrument  for  determining  whether 
a  ray  of  light  has  been  polarized  by  other  means.  A  tourmaline  plate  so  used  is 
called  an  analyzer.  Crystalline  plates  of  sulphate  of  iodo-quinine  (called  Hera- 
pathite,  from  the  name  of  their  discoverer,  Mr.  Herapath),  act  in  all  respects 
like  plates  of  tourmaline. 

546.  Polarization  by  reflection. — When  light  falls  upon  a  trans- 
parent medium,  at  any  angle  of  incidence  whatever,  some  portion  of 
the  light  is  reflected.     When  the  incident  light  falls  upon*  the  medium 
at  a  particular  angle,  which  varies  with  the  nature  of  the  substance,  all 
the  reflected  light  is  polarized. 

Let  Or,  G,  fig.  425,  be  a  plate  of  glass  or  any  other  transparent  medium,  and 
let  a  ray  of  light,  a  b,  fall  upon  it  at  such  an  angle  that  the  reflected  ray,  b  c, 
shall  make  an  angle  of  90°  with  the  refracted  ray,  425 

b  d,  then  the  reflected  ray  b  c,  which  represents  but 
a  small  portion  of  the  incident  light,  will  be  polarized. 
If  the  medium  is  bounded  by  parallel  surfaces,  the 
portion  of  the  light  reflected  from  the  second  surface 
will  also  be  polarized. 

The  angle  of  polarization  by  reflection  may  be  de- 
termined by  the  following  law.  The  tangent  of  the 
angle  of  incidence  for  which  the  reflected  ray  is  polarized,  is  equal  to  the  index 
of  refraction  for  the  reflecting  medium.  This  law  supposes  the  reflecting  sub- 
stance more  dense  than  the  surrounding  medium.  If  the  light  is  reflected  from 
the  second  surface,  as  when  passing  from  glass  or  water  into  air ;  the  index  of 
refraction  equals  the  cotangent  of  the  angle  of  polarization.  The  polarizing 
angle  for  reflection  from  glass,  is  56°  25',  reckoned  from  the  perpendicular. 


OPTICS. 


385 


The  polarizing  angle  for  water  is  53°  11'.     As  the  index  of  refraction  varies  for 
different  colors,  the  polarizing  angle  varies  in  the  same  manner. 

If  a  polarized  ray  falls  upon  a  reflecting  surface  at  the  angle  of  polarization, 
and  the  reflecting  surface  is  rotated  around  the 
polarized  ray  as  an  axis,  when  it  is  so  placed  that 
the  plane  of  incidence  corresponds  with  the  plane 
in  which  the  ray  was  polarized,  the  polarized  light 
will  be  reflected  just  as  if  it  were  not  polarized  ; 
but  when  the  plane  of  incidence  makes  an  angle 
of  90°  with  the  plane  of  polarization,  the  light  is 
entirely  intercepted,  as  shown  in  fig.  426.  In  this 
respect  a  reflecting  surface,  at  the  proper  angle  of 
incidence,  serves  the  purpose  of  an  analyzer,  just 
like  a  plate  of  tourmaline. 

Polarization  by  metallic  reflection. — To  obtain  a  beam  of  plane 
polarized  light  by  reflection  from  metallic  plates,  the  light  must  be 
reflected  many  times  at  the  angle  most  favorable  to  polarization.  A  ray 
of  light  once  reflected  from  a  metallic  plate  at  the  most  favorable  angle 
appears  to  consist  of  light  vibrating  in  two  planes,  in  one  of  which  the 
phase  of  vibration  is  retarded  from  0  to  £  of  a  vibration  behind  the  light 
vibrating  in  the  other  plane.  This  is  called  elliptical  polarization. 

When  the  two  planes  of  vibration  are  at  right  angles  to  each  other, 
and  the  phases  of  vibration  differ  by  £  of  a  vibration,  the  light  is  said 
to  be  circularly  polarized. 

The  diamond,  sulphur,  and  all  bodies  possessing  an  adamantine 
lustre,  produce  elliptical  polarization,  and  if  employed  as  analyzing 
reflectors,  they  change  plane  polarized  to  elliptieally  polarized  light. 
The  investigation  of  these  varieties  of  polarized  light  would  exceed  the 
limits  of  an  elementary  work. 

547.  Polarization    by  refraction. — When   light  is   polarized   by 
reflection  from  either  the  first  or  the  second  surface  of  a  transparent 
medium,  a  portion  of  the  transmitted  light  is  polarized  by  refraction. 
The  amount  of  light  polarized  by  refraction  is  just  equal  427 

to  the  amount  polarized  by  reflection,  but  as  the  amount 
of  light  transmitted  by  transparent  substances  very 
much  exceeds  the  amount  reflected  from  their  surfaces, 
only  a  small  portion  of  the  transmitted  rays  are  polar- 
ized, or,  more  properly,  the  light  transmitted  through  a 
single  plate  is  but  partially  polarized. 

548.  Polarization  by  successive  refractions. — 
If  a  ray  of  light,  R  Rx,  is  transmitted  obliquely  through 
a  number  of  parallel  transparent  plates,  as  shown  in  fig. 
427,  a  portion  of  the  light  is  polarized  at  every  refrac- 
tion, and  after  a  sufficient  number  of  refractions  the  whole  of  the  trans- 
mitted light  is  polarized. 

85* 


386 


PHYSICS   OF   IMPONDERABLE    AGENTS. 


Light  polarized  by  refraction,  is  polarized  in  a  plane  at  right  angles  with  the 


Light  polarized  by  reflection  vibrates  at 
428 


plane  of  polarization  by  reflection 
right    angles    with    its   plane   of 
polarization,  or  its  plane  of  reflec- 
tion, as  shown  at  B,  fig.  428. 

Light  polarized  by  refraction, 
vibrates  also  at  right  angles  with 
its  plane  of  polarization,  but  pa- 
rallel to  its  plane  of  refraction,  as 
shown  at  C,  fig.  428.  Light  not 
polarized,  though  vibrating  in  an 
infinite  number  of  planes,  is  equiva- 
lent to  a  system  of  vibrations  in 
two  planes  at  right  angles  to  each, 
as  shown  at  A,  fig.  428. 

549.  Partial  polarization. — Light  reflected   or   refracted   at   any 
oblique  angle  is,  in  general,  partially  polarized,  and  by  repeated  reflec- 
tions or  refractions  the  degree  of  polarization  is  increased,  until,  after 
a  sufficient  number  of  reflections  or  refractions,  it  is  apparently  com- 
pletely polarized. 

Let  M  N,  fig.  429,  represent  the  plane  of  refraction,  and  A  B,  CD,  the  axes  of 
vibration  for  common  light,  then  by  repeated  re-  429 

fractions  these  axes  will  be  gradually  made  to 
approach  each  other,  until  they  sensibly  coincide, 
as  shown  in  the  figure,  when  the  light  is  said  to 
be  completely  polarized.  The  portion  of  light  _v 
reflected,  undergoes  a  similar  series  of  changes,  until  the  axes  of  vibration 
sensibly  coincide,  in  a  plane  at  right  angles  to  their  position  in  light  polarized 
by  refraction. 

550.  Double  refraction  is  a  property  in  certain  crystals  that  causes 
the  light  passing  through  them  in  particular  directions  to  be  separated 
into  two  portions,  which   pursue   different  paths,  and  which  causes 
objects  seen  through  the  crystals  to  appear  double. 

The  most  remarkable  substance  of  this  kind  with  which  we  are  familiar,  is 
Iceland  spar,  or  carbonate  of  lime,  which  crystallizes 
in  the  rhombic  system,  as  shown  in  fig.  430.  The 
line  a  b,  about  which  all  its  faces  are  symmetrically 
arranged,  is  called  the  major  axis  of  the  crystal,  and 
the  plane  a  c  b  d,  passing  through  the  axis,  and 
through  the  obtuse  lateral  edges,  is  called  the  plane 
of  principal  section. 

If  a  crystal  of  Iceland  spar,  from 
half  an  inch,  upwards,  in  thickness,  is 
laid  upon  a  sheet  of  paper,  on  which 
are  drawn  various  lines,  they  will 
appear  double,  as  shown  in  fig.  431. 

A  B,  C  D,  E  F,  G  H,  are  the  real  lines,  seen  in  their  true  positions.     The  dotted 
lines  show  the  position  of  the  additional  lines,  caused  by  extraordinary  refrac- 


OPTICS.  387 

lion.     The  line  A  B,  in  the  plane  of  principal  section,  is  not  doubled.     Any  line 
parallel  to  A  B,  will  also  appear  single. 

The  index  of  refraction  for  the  ordinary  ray  remains  constant,  in  whatever 
direction  light  passes  through  the  crystal.  The  index  of  refraction  for  the 
extraordinary  ray,  when  parallel  to  the  axis,  is  the  same  as  that  of  the  ordinary 
ray,  and  differs  most  from  the  ordinary  ray  when  it  passes  through  the  crystal 
at  right  angles  with  the  axis. 

The  index  of  refraction  for  the  ordinary  ray  in  Iceland  spar  is  con- 
stantly 1.6543  =  m.  The  index  of  refraction  for  the  extraordinary  ray, 
when  it  makes  an  angle  of  90°  with  the  major  axis,  is  1.4833  =  n.  Let 
x  =  the  angle  which  the  extraordinary  ray  makes  with  the  major  axis 
in  any  other  position,  and  let  N=  the  corresponding  index  of  refraction 
for  the  extraordinary  ray,  its  value  may  be  determined  by  the  following 
formula : — 

N  =  -]/m^+W—m2)  »in2*  =  1/2.7367—0.5365  sin2 a. 

551.  Positive  and  negative  crystals. — Positive  crystals  are  those 
in  which  the  index  of  refraction  for  the  extraordinary  ray  is  greater 
than  for  the  ordinary  ray,  and  the  extraordinary  ray  is  refracted  nearer 
to  the  axis  than  the  ordinary  ray.     Quartz  and  ice  are  examples  of  this 
class. 

Negative  crystals  are  such  as  have  the  index  of  refraction  for  the 
extraordinary  ray  less  than  for  the  ordinary  ray,  the  extraordinary  ray 
being  refracted  farther  from  the  axis  than  the  ordinary  ray.  Iceland 
spar,  tourmaline,  corundum,  sapphire,  and  mica,  are  examples  of  nega- 
tive crystals. 

Some  crystals  have  two  axes  of  double  refraction,  as  nitrate  of  potash, 
sulphate  of  barytes,  and  some  varieties  of  mica. 

552.  Polarization  by  double  refraction. — When  the  light  trans- 
mitted through  a  doubly  refracting  substance  is  examined  with  an 
analyzer,  it  is  found  that  both  the  ordinary  and  extraordinary  rays  are 
completely  polarized,  whatever  be  the  color  of  the  light  employed.    The 
tourmaline  plate,  or  other  analyzer,  will,  in  one  position,  transmit  the 
ordinary  image  and  wholly  intercept  the  other,  but  when          432 

the  tourmaline  has  been  rotated  90°,  the  ordinary  ray  is 
intercepted,  and  the  extraordinary  ray  is  transmitted. 

553.  Nicol's  single  image  prism  is   an   instrument 
formed  of  Iceland  spar,  by  which  the  ordinary  image,  pro- 
iuced  by  double  refraction,  is  thrown  out  of  the  field,  and 
only  a  single  image  (the  extraordinary)  is  transmitted. 

An  elongated  prism  of  Iceland  spar  is  cut  through  by  a  plane, 
E  F,  at  right  angles  with  the  principal  section,  from  the  obtuse 
solid  angle  E,  fig.  432,  making  an  angle  of  22°  with  the  obtuse 
lateral  edge  K.  The  terminal  face,  P,  is  ground  away,  so  as  to  make  an  angle 


388 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


of  68°  with  the  obtuse  lateral  edge.  K,  and  the  )pposite  face,  P',  is  ground  in 
the  same  manner.  All  the  new  faces  are  carefulJy  polished,  and  the  two  parts 
are  cemented  together  again  with  Canada  balsam,  in  the  same  position  they 
previously  occupied.  The  lateral  faces  of  this  compound  prism  are  all  painted 


433 


black,  leaving  only  the  terminal  faces  for  the  transmission  of 
light. 

When  a  ray  of  light,  a  b,  fig.  433,  falls  upon  this  prism,  it  is  re- 
fracted into  the  ordinary  ray  b  c,  and  the  extraordinary  ray  b  d.  The 
index  of  refraction  of  Iceland  spar,  for  the  ordinary  ray,  being  1.654, 
and  that  of  balsam  only  1.536,  the  ordinary  ray  cannot  pass  through 
the  balsam,  unless  the  incident  ray  diverges  widely  from  the  axis 
of  the  prism,  but  it  suffers  total  reflection,  and  is  absorbed  by  the 
blackened  side  of  the  prism.  The  extraordinary  ray  has  a  refrac- 
tive index  in  the  Iceland  spar  generally  less  than  in  the  balsam, 
varying,  for  Nicol's  prism,  between  1.5  and  1.56  ;  therefore  it  passes 
through  the  balsam  into  the  lower  part  of  the  prism,  and  emerges 
in  the  direction  g  h,  parallel  to  the  incident  ray. 

These  prisms  are  capable  of  transmitting  a  colorless  pencil  of 
light,  perfectly  polarized,  from  20°  to  27°  in  breadth. 

554.  Polarizing  instruments  are  made  in  a  variety  of  forms,  to 
suit  particular  purposes.     A  simple  instrument,  and  yet  one  of  the 
most  convenient  in  use  for  exhibiting  the  phenomena  of  polarized  light, 
is  shown  in  fig.  434.  434 

A  mirror,  M,  made  of  plate  glass, 
covered  with  black  varnish  or  cloth 
on  the  back,  or,  better,  a  bundle  of 
ten  to  twenty  thin  plates  of  polished 
glass,  is  mounted  on  a  mahogany 
support  at  the  polarizing  angle.  A 
Nicol's  prism,  or  a  tourmaline  plate, 
at  E,  serves  as  an  analyzer.  The 
objects  to  be  examined  are  mounted  in  discs  of  wood  or  cork,  and  supported  at 
A  or  B,  where  they  are  most  distinctly  seen  by  the  eye,  looking  through  the 
analyzer.  The  student  who  has  not  a  tourmaline,  or  a  Nicol's  prism,  can  use 
as  an  analyzer  a  small  piece  of  plate  glass,  mounted  so  as  to  rotate  on  an  axis 
parallel  to  the  base  of  the  instrument. 

Polarized  light  may  be  applied  to  the  microscope,  by  mounting  a 
Nicol's  prism  beneath  the  stage  as  a  polarizer,  and  another  for  an 
analyzer,  in  the  body  of  the  microscope,  above  the  object  glass. 

555.  Colored  polarization. — When  a  thin  plate  of  selenite,  mica, 
or  any  other  doubly  refracting  substance,  is  placed  between  the  polarizer 
and  the  analyzer  in  the  polariscope,  the  light  is  separated  into  two 
beams,  which  follow  different  paths,  and  as  the  vibrations  of  one  ray 
are  more  retarded  than  those  of  the   other,  when  they  are  reunited 
they  interfere,  and  produce  the  most  beautiful  colors,  varying  with  the 
thickness  of  the  plates,  and  the  position  of  thoir  axes  with  reference  to 
the  axes  of  the  polarizer  and  the  analyzer. 


OPTICS.  389 

If  the  film  is  rotated,  while  the  polarizer  and  analyzer  remain  fixed,  the  color 
will  appear  at  every  quadrant  of  revolution,  and  disappear  in  intermediate 
positions.  If  the  film  and  the  polarizer  remain  fixed,  and  the  analyzer  is  rotated, 
the  color  will  change  to  the  complementary  at  every  quadrant  of  revolution  ; 
that  is,  the  same  color  will  be  seen  in  positions  of  the  analyzer  differing  180°, 
and  the  complementary  color  will  be  seen  at  90°  and  270°,  from  the  first  position. 

Films  of  selenite,  varying  between  0-00124  and  0-01818  of  an  inch  in  thickness, 
will  give  all  the  colors  between  the  white  of  Newton's  first  order,  and  white 
resulting  from  the  mixture  of  all  the  colors.  If  two  films  of  selenite  are  placed 
over  each  other,  with  their  axes  parallel,  the  color  produced  will  be  that  which 
belongs  to  the  sum  of  their  thicknesses.  But  when  the  two  films  are  placed  with 
their  axes  at  right  angles,  the  resulting  tint  is  that  which  belongs  to  the  differ- 
ence of  their  thicknesses. 

556.  Rotary  polarization   is  a  property  which  some  substances 
possess  of  changing  the  plane  of  vibration  in  a  ray  of  polarized  light, 
even  when  it  falls  perpendicularly  upon  it.     The  entire  amount  of 
rotation   depends    upon   the   thickness  of  the  medium.     Quartz,  cut 
transversely  to  its  major  axis,  solution  of  sugar,  camphor  in  the  solid 
state,  and  most  of  the  essential  oils,  possess  the  power  of  rotating  the 
plane  of  polarization  of  a  ray  passing  through  them. 

Different  substances,  and  sometimes  different  specimens  of  the  same  substance, 
rotate  the  plane  of  polarization  in  contrary  directions.  When  the  rotation  takes 
place  in  the  direction  of  the  motion  of  the  hands  of  a  watch,  the  medium  is 
said  to  have  right-handed  polarization.  Thus  we  have  right-handed  quartz,  and 
left-handed  quartz. 

In  a  beam  of  white  light,  the  vibrations  which  produce  red  have  their  plane 
of  polarization  rotated  much  more  than  the  colors  of  greater  refrangibility. 
This  property  varies  inversely  as  the  squares  of  the  lengths  of  the  luminous 
waves  which  produce  the  several  colors.  The  power  of  rotating  the  plane  of 
polarization  becomes  a  valuable  test  for  speedily  determining  the  nature  of 
various  chemical  substances,  or  the  strength  of  a  solution  of  any  substance 
having  this  power.  Solid's  saccharimeter,  for  measuring  the  relative  amount 
of  cane  and  grape  sugar  in  solutions  or  syrups,  is  constructed  on  this  principle. 
Such  an  instrument  affords  also  a  ready  method  of  detecting  the  presence  of 
sugar  in  diabetic  urine. 

557.  Arago's  chromatic  polariscope  is  a  very  simple  instrument 
for  testing  polarized  light,  and  for  determining  its  plane  of  polarization. 
In  one  end  of  a  brass  tube  is  inserted  a  prism  of  Iceland  spar ;  in  the 
other  end  of  the  tube  a  circular  opening  is  covered  by  two  plates  of 
quartz  cut  parallel  to  the  axis  and  united  by  their  edges,  one  of  these 
plates  having  right-handed,  and  the  other  left-handed,  rotary  polari- 
zation. 

When  polarized  light  is  viewed  through  this  instrument  (the  Iceland 
spar  being  turned  towards  the  eye),  the  circular  opening  appears 
double,  and  in  each  image  is  seen  the  line  dividing  the  two  plates  of 
rotary  quartz,  with  complementary  colors  on  opposite  sides  of  the  line. 


390 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


If  the  instrument  is  now  rotated,  two  positions  will  be  found  at  right 
angles  to  each  other  where  both  parts  of  the  opening  in  the  same  image 
appear  of  a  uniform  tint,  though  the  two  images  still  have  comple- 
mentary colors. 

When  both  segments  of  the  extraordinary  image  have  a  uniform  red 
tint,  the  principal  section  of  the  prisrn  is  parallel  to  the  plane  in  which 
the  light  has  been  polarized,  and  when  both  segments  of  the  extra- 
ordinary image  are  uniformly  green,  the  plane  of  polarization  is 
perpendicular  to  the  principal  section  of  the  prism. 

A  plate  of  selenite  or  mica,  or  a  single  plate  of  quartz,  may  be  substituted  for 
the  two  segments  of  right  and  left-handed  quartz,  and  two  images  with  com- 
plementary colors  will  be  seen  as  before.  All  the  phenomena  of  atmospheric 
polarization  may  be  demonstrated  with  this  form  of  the  instrument,  and  the 
plane  of  polarization  may  be  determined,  but  with  less  accuracy  than  in  the 
first  form  of  the  instrument.  As  before,  when  the  extraordinary  image  is  red, 
the  plane  of  polarization  is  parallel  to  the  principal  section  of  the  prism.  When 
the  extraordinary  image  is  green,  the  plane  of  polarization  is  perpendicular  to 
the  principal  section  of  the  prism. 

558.  Colored  rings  in  crystals. — Colored  rings  of  great  beauty, 
with  a  black  cross,  are  seen  in  thin  plates  of  doubly  refracting  crystals, 
when  viewed  in  certain  directions,  with  polarized  light. 

Figs.  435  and  436,  show  the  appearance  of  the  rings  and  cross  in  thick  plates 
of  quartz,  in  positions  at  90°  from  each  other.     Other  uniaxial  crystals  show  a 
similar  system  of  rings  beautifully  colored.     Figs.  437  and  438  show  the  form 
435  436  437  438 


of  the  colored  rings  in  biaxial  crystals ;  e.  y,  some  micas.  Every  doubly 
refracting  crystal  presents  some  peculiarity  in  the  form  and  arrangement  of  the 
colored  rings  seen  in  its  thin  sections.  This  subject  is  of  great  interest  to  the 
mineralogist. 

559.  Polarization  by  heat,  and  by  compression. — Glass  irregu- 
larly heated,  or  heated  and  irregularly  cooled,  possesses  the  power  of 
double  refraction,  and  when  viewed  by  polarized  light,  it  exhibits  dark 
crosses,  bands,  or  rings,  varying  with  the  form  of  the  glass,  and  differ- 
ence of  density  in  different  parts.  Similar  phenomena  may  be  produced 
by  compression,  or  by  bending  rods  or  plates  of  glass. 


OPTICS.  391 

560.  Magnetic  rotary  polarization. — If  a  thick  plate  of  glass  is 
applied  to  the  poles  of  a  powerful  electro-magnet,  the  glass  is  neither 
attracted  nor  repelled ;  but  if  a  ray  of  polarized  light  is  transmitted 
through  the  plate  in  a  certain  direction,  the  plane  of  polarization  is 
rotated  as  by  a  plate  of  quartz,  or  other  rotary  polarizer,  showing 
that  light  and  magnetism  have  some  intimate  relation  to  each  other. 

This  rotary  effect  may  depend  upon  change  in  the  tension  of  the  molecules 
of  the  glass  by  the  magnetic  force,  and  not  upon  any  direct  relation  between 
light  and  magnetism. 

561.  Atmospheric  polarization  of  light. — The  light  of  the  sun 
reflected  by  the  atmosphere  is  more  or  less  polarized,  depending  upon 
the  angular  distance  from  the  sun. 

If  the  earth  had  no  atmosphere,  the  sky  would  everywhere  appear  perfectly 
black.  The  color  of  the  sky  is  produced  by  light  reflected  by  the  atmosphere. 
If  we  look  at  the  sky  through  a  Nicol's  prism,  we  shall  find,  on  rotating  the 
prism,  that  light  from  some  parts  of  the  sky  is  polarized  to  a  very  appreciable 
extent.  There  are  several  points  in  the  sky  where  no  polarization  is  perceptible. 
The  point  in  the  heavens  directly  opposite  to  the  sun  is  called  the  anti-solar 
point.  At  a  distance  above  the  anti-solar  point,  varying  from  11°  to  18°,  there 
is  a  point  of  no  polarization,  and  another  neutral  point  at  an  equal  distance  below 
the  anti-solar  point.  Another  neutral  poiat,  or  point  of  no  polarization,  is 
found  from  12°  to  18°  above  the  sun,  and  a  similar  one  below  it ;  but  the  latter 
is  observed  with  great  difficulty.  When  the  sun  is  in  the  zenith,  these  two  points 
coincide  in  the  sun.  At  all  other  points  in  the  sky,  the  light  is  more  or  less 
polarized,  the  degree  of  polarization  amounting  sometimes  to  more  than  one- 
half  as  much  as  by  reflection  from  glass  at  the  angle  of  complete  polarization. 

562.  The  eye  a  polariscope. — The  structure  of  the  crystalline  lens 
is  such,  that  the  unaided  eye  is  capable  of  analyzing  a  beam  of  light 
polarized  by  reflection  or  by  double  refraction.     A  person  accustomed 
to  use  his  eyes  in  viewing  the  phenomena  of  polarization,  can  thus 
detect  with  ease  facts  of  this  nature,  which  are  wholly  inscrutable  to 
one   not  familiar  with  such  observations;    another  of  the  numerous 
proofs  we  have  that  the  eye  is  capable  of  very  exact  training ;  but 
nevertheless  it  is  a  proof  also  of  an  imperfection  in  the  eye  itself. 

M.  Haidinger  has  observed  a  remarkable  phenomenon  of  polarized  light,  by 
which  it  may  be  recognised  by  the  naked  eye,  and  its  plane  of  polarization 
ascertained.  This  phenomenon  consists  in  the  appearance  of  two  brushes  of  a 
very  pale  yellow  color,  the  axis  of  which  coincides  always  with  the  trace  of 
the  plane  of  polarization ;  these  are  accompanied,  on  either  side,  by  two  patches 
of  light  of  a  complementary  or  violet  tint.  In  order  to  see  them,  the  plane  of 
the  polarization  of  the  light  must  be  turned  quickly  from  one  position  to  another ; 
this  may  be  done  by  revolving  before  the  eye  a  Nicol's  prism  directed  towards 
a  white  cloud. 

The  most  probable  explanation  is  that  given  by  M.  Jamin,  in  which  the  pro- 
duction of  the  phenomenon  is  ascribed  to  the  refracting  coats  of  the  eye,  they 
being  compared  to  a  pile  of  parallel  plates  of  glass. 


392  PHYSICS   OF   IMPONDERABLE    AGENTS. 

563.  The  practical  applications  of  polarized  light  are  nunie* 

rous.     The  water  telescope  consists  of  an  ordinary  marine  telescope, 
with  a  Nicol's  prism  inserted  in  the  eye-piece. 

The  light  reflected  from  the  surface  of  the  water  is  the  principal  obstruction 
to  viewing  objects  beneath  its  surface.  Nicol's  prism,  in  a  certain  position, 
entirely  cuts  off  the  polarized  portion  of  the  reflected  light,  and  allows  objects 
far  below  the  surface  to  be  seen  in  the  telescope.  A  Nicol's  prism,  in  the  same 
manner,  will  enable  the  fisherman  to  direct  his  spear  with  greater  certainty. 

Amateurs,  in  visiting  galleries  of  paintings,  find  Nicol's  prisms 
mounted  as  spectacles  of  great  service.  Let  the  observer  place  him- 
self in  an  oblique  position,  and  look  at  an  oil  painting ;  when  the  sheen 
of  reflected  light  renders  the  objects  in  the  painting  invisible,  he  has 
but  to  look  through  a  Nicol's  prism,  set  in  a  proper  position,  and  the 
entire  details  of  the  painting  at  once  become  visible  in  all  their  proper 
colors.  An  opera-glass,  provided  with  Nicol's  prisms,  would  be  a 
valuable  instrument  in  examining  a  picture  gallery.  Polarizedjight 
is  also  of  great  value  in  microscopic  investigations. 

Fig.  439  shows  the  appearance  of  a  grain  439  440 

of  starch,  brilliantly  illuminated  on  a  dark 
ground,  when  seen  in  the  microscope  with 
polarized  light.  By  rotating  the  analyzer, 
the  field  becomes  light,  and  the  dark  cross 
changes  its  position,  as  shown  in  fig.  440. 
The  appearance  of  the  starch  distinguishes 
it  from  every  other  substance.  Different 
kinds  of  starch  are  also  thus  readily  dis- 
tinguished from  each  other. 


By  means  of  polarized  light,  the  chemist  can  detect  one  thirteen- 
millionth  of  a  gramme  of  soda,  and  distinguish  it  from  potassa  or  any 
other  alkali.  In  physiological  chemistry,  especially  in  the  examination 
of  crystals  found  in  various  cavities  and  fluids  of  both  animals  and 
plants,  the  use  of  polarized  light  is  especially  important. 

Instead  of  a  few  isolated  facts,  of  interest  only  to  the  curious  inquirer, 
the  polarization  of  light  presents  itself  as  a  great  fact  in  nature,  meet- 
ing us  with  wonderful  revelations  in  almost  every  department  of  natural 
science.  By  this  marvelous  property  of  light,  the  astronomer  determines 
that  the  planets  shine  by  reflected  light,  and  that  the  stars  are  self- 
luminous  bodies. 


Problems  in  Optics. 
Velocity  and  Intensity  of  Light. 

177.  What  time  is  required  foi  light  to  come  to  the  earth  from  the  sun,  the 
distance  being  95,000,000  miles? 


OPTICS.  393 

178.  How  long  does  it  take  the  light  of  the  north  star  to  reach  the  earth,  the 
distance  being  estimated  2,961,000  times  greater  than  the  distance  of  the  earth 
from  the  sun  ? 

179.  Two  lights  give  equal  illumination  upon  Bunsen's  photometer,  when  it 
•-S  placed  between   them  at  a  distance  of  3  feet  from  one  light,  and  4  feet  7 
inches  from  the  other;  what  is  their  relative  illuminating  power? 

180.  A  screen  is  equally  illuminated  by  two  flames,  when  one  of  them  is  40  inches 
from  it,  but  when  a  plate  of  glass  is  interposed,  the  same  light  is  required  to  be 
brought  to  a  distance  of  38  inches  that  the  illumination  may  be  again  equal ; 
what  proportion  of  the  light  is  transmitted  by  the  glass  ? 

181.  At  one  extremity  of  a  bar,  100  inches  long,  is  placed  a  standard  candle 
turning  120  grains  per  hour  (the  usual  standard  in  photometric  measurements 
of  gas),  at  the  other  end  is  a  gas  burner  consuming  5  cubic  feet  per  hour.     A 
Bunsen's  screen,  moving  on  this  bar,  is  distant  17^  inches  from  the  candle, 
when  both  sides  are  equally  illuminated  j  what  is  the  illuminating  power  of  the 
gas  in  terms  of  the  candle  as  a  unit  ? 

182.  By  a  similar  trial,  the  photometer  is   19^   inches   distant  from   the 
standard  candle  when  the  disc  is  equally  illuminated,  but  it  is  found  that  the 
candle  is  burning  129  grains  per  hour,  while  the  gas  burner  consumes  only  4£ 
cubic  feet  of  gas  per  hour ;  what  is  the  illuminating  power  of  5  cubic  feet  of 
this  sample  of  gas  in  terms  of  the  standard  candle  at  120  grains  as  a  unit  ? 

Reflection  of  Light. 

183.  At  what  angle  must  two  mirrors  be  inclined,  so  that  a  ray  of  light  inci- 
dent parallel  to  one  mirror  may,  after  reflection  at  each  mirror,  be  parallel  to 
the  other  ? 

184.  How  many  images  will  be  seen  in  a  kaleidoscope  when  the  two  mirrors 
of  which  it  is  composed  are  placed  at  an  angle  of  20°  ? 

185.  A  concave  mirror  collects  solar  light  to  a  focus  6  inches  from  its  surface ; 
where  will  it  form  an  image  of  an  object  placed  12  feet  in  front  of  it? 

186.  A  luminous  point  is  placed  at  a  distance  of  3  feet  in  front  of  a  concave 
mirror  of  1  foot  radius  ;  find  the  distance  of  the  focus  of  reflected  rays. 

187.  What  must  be  the  position  of  a  luminous  point  before  a  concave  mirror, 
that  the  distance  between  the  foci  of  incident  and  reflected  rays  may  be  equal  to 
the  radius  of  the  mirror  ? 

Refraction  of  Light. 

188.  Find  the  thickness  of  a  plane  glass  mirror  silvered  at  the  back,  so  that 
an  object  one  foot  in  front  of  its  first  surface  may  have  the  image  formed  by 
reflection  at  the  second  surface  twice  as  distant  from  the  object  as  if  the  reflec- 
tion took  place  from  the  first  surface;  the  index  of  refraction  being  n  =  1£. 

189.  A  fish  is  seen  in  a  position  known  to  be  4  feet  below  the  surface  of  the 
water,  and  the  direction  in  which  it  is  seen  makes  an  angle  of  45°  with  the 
perpendicular ;  at  what  angle  must  a  lance  be  thrown  to  strike  the  fish  ? 

190.  If  a  pool  of  water  appears  to  be  5  feet  deep,  what  should  we  consider  its 
real  depth  ? 

191.  A  small  pencil  of  solar  rays,  incident  upon  the  surface  of  a  refracting 
sphere,  is  brought  to  a  focus  upon  the  opposite  surface;  what  is  the  refractive 
index  of  the  material  of  which  the  sphere  is  made  ? 

192.  A  small  pencil  of  light  falls  upon  a  concave  spherical  surface  of  glass 
(n  =  1£),  the  radius  of  which  is  2  feet.    Supposing  the  radiant  point  distant  3  feet 
from  the  refracting  surface,  where  will  the  focus  of  the  refracted  rays  be  found/ 

86 


394  PHYSICS   OF   IMPONDERABLE   AGENTS. 

193.  When  divergent  rays  are  incident  from  a  certain  point  upon  a  spherhal 
surface  of  glass,  the  refracted  rays  are  found  to  converge  to  a  focus  at  exactly 
the  same  distance  on  the  opposite  side  of  the  surface ;  is  the  surface  convex  or 
concave  ?  and  if  the  position  of  the  point  of  incidence  be  3  feet  from  the  refract- 
ing surface,  and  n  =  1-5,  what  is  the  radius  of  the  refracting  surface? 

194.  A  double  convex  lens  of  glass  (•»  =  1*534),  whose  radii  are  respectively 
2  inches  and  4£  inches,  is  placed  15  inches  before  a  luminous  point;  what  is  the 
position  of  the  focus  of  refracted  rays  ? 

195.  What  is  the  form  of  a  double  convex  lens,  having  the  least  spherical 
aberration,  when  the  glass  of  which   it  is   made  has  an  index  of  refraction 
m=  1-635? 

196.  What  is  the  distance  of  the  principal  focus  from  a  lens  of  flint  glass 
(n  =  1-635)  whose  radii  a*re,  r  =  2£,  and  «  =  —  5  ? 

197.  What  single  lens  is  equivalent  to  a  combination  of  a  double  convex  lens 
of  focal  length  2  inches  with  a  double  concave  lens  of  focal  length  4  inches  ? 

198.  Determine  the  form  of  two  lenses  of  flint  and  crown  glass,  that  may  be 
cemented  together  so  as  to  constitute  a  plano-convex  achromatic  combination 
of  7  inches  focal  length,  using  flint-glass  in  which  m  =  1'635,  and  the  disper- 
sive power/)  =  1000,  and  crown-glass  n  =  1-534,  and p'  =  625. 

199.  Two  convex  lenses,  whose  focal  lengths  are  3/and/,  are  separated  by  an 
interval  of  2/;  how  must  a  pencil  of  rays  be  incident  upon  the  first  lens,  so  as 
to  emerge  parallel  after  refraction  through  the  second  lens  ? 

Optical  Instruments. 

200.  Considering  the  distance  of  distinct  vision  8  inches,  what  will  be  the 
magnifying  power  of  a  lens  whose  solar  focus  is  3  inches,  when  it  is  placed  at  a 
distance  of  5  inches  from  the  eye  ? 

201.  Calculate  the  radii  of  the  two   surfaces  of  a  meniscus  of  crown-glass 
(n  =  1-5)  to  be  used  as  the  field-lens  of  Prof.  Airy's  eye-piece  (500),  when  the 
eye-lens  has  a  solar  focus  of  half  an  inch,  and  the  field-lens  is  2  feet  from  the 
object-glass. 

202.  Calculate  the  illuminating  power  of  Herschel's  great  telescope,  allowing 
fo  of  the  incident  light  to  be  reflected  by  the  speculum. 

203.  On  the  same  conditions  calculate  the  illuminating  and  penetrating  powers 
of  Lord  Rosse's  great  telescope  (503). 

204.  Estimate  the  illuminating  and  penetrating  powers  of  the  Cambridge 
refracting  telescope  (506).     A  =  15  inches,  a  =  0-1  inch,  x  =  0-9,  n  =  2. 

205.  Compare  the  illuminating  and  penetrating  powers  of  two  achromatic 
objectives  for  the  microscope,  one  of  which  has  an  angular  aperture  of  100°, 
and  the  other  150°,  calling  n  =  6  in  both  cases,  and  x  =  0-8. 

Polarization  of  Light. 

206.  Calculate  the  angles  of  most  perfect  polarization  by  reflection  from  the 
three  kinds  of  glass  whose  index  of  refraction  is  given  in  g  407. 

207.  What  proportion  of  the  incident  light  is  reflected  in  each  of  the  cases 
considered  in  the  last  problem,  supposing   the  increase  of  reflection   uniform 
between  any  two  angles  whose    amount  of  reflection   is   given    in    the   table, 
page  299  ? 

208.  What  is  the  index  of  refraction  for  the  extraordinary  ray  in  Iceland 
spai,  when  it  makes  an  angle  of  54°  with  the  principal  axis  of  the  prism  ? 


HEAT  395 


CHAPTER  II. 

HEAT. 

|  1.  Nature  of  Heat. 

564.  Heat. — Its    nature. — The    sensations,    which    we    call    heat 
or   cold,  are   produced  by  an   agent   or   cause  whose   real   nature   is 
unknown.     Whatever  this  agent  may  be,  it  influences  matter  of  all 
kinds   without   changing   its   nature.     Scientific   opinion   is   divided, 
chiefly,   between   two  views  of  the   nature  of  heat.     These   are,  the 
corpuscular  theory,  or  theory  of  emission,  and  the  undulatory  theory. 

According  to  the  corpuscular  theory,  heat  is  attributed  to  a  peculiar  imponder- 
able fluid,  existing  in  all  bodies  in  combination  with  their  atoms.  The  parti- 
cles of  this  supposed  fluid  are  self-repellent,  and  thus  the  atoms  of  bodies  are 
prevented  from  coming  into  absolute  contact  with  each  other.  This  fluid  is  thrown 
off  from  all  hot  bodies  with  inconceivable  velocity,  and  upon  its  absorption  by 
other  bodies  the  effects  of  heat  are  manifested.  Thus  hot  bodies  lose  what 
colder  bodies  gain. 

By  the  undulatory  theory,  heat  is  attributed  to  the  vibratory  movements  of 
the  molecules  of  a  hot  body,  communicated  to  those  of  other  bodies,  by  means 
of  a  highly  elastic  fluid  called  ether.  This  ether  pervades  all  space,  and  in  it 
the  undulations  of  heat  are  propagated  with  inconceivable  rapidity,  in  a  manner 
analogous  to  the  slower  progress  of  sonorous  waves  in  air,  as  already  explained. 
This  same  medium,  by  another  kind  of  motion,  is  supposed  to  produce  light 
and  electricity. 

565.  Temperature. — Heat  and  cold. — All  bodies  receive  or  part 
with  heat,  as  their  conditions  change  from  time  to  time ;  the  relations 
which  they  sustain  to  heat  at  a  given  moment  are  distinguished  by  the 
word  temperature,  which  term  implies  nothing  as  to  the  quantity  of  heat 
present  in  a  body,  but  only  its  relation  at  a  specific  time  to  an  arbitrary 
standard. 

Heat  and  cold  are  relative  terms ;  cold  implying  not  a  quality  antago- 
nistic to  heat,  but  merely  the  absence  of  heat  in  a  greater  or  less  degree. 
There  are  no  bodies  so  cold  that  they  will  not  be  warm  to  bodies  colder 
than  themselves.  Our  sensations  give  us  but  little  evidence  respecting 
actual  changes  of  temperature. 

If  we  place  one  hand  in  hot  and  the  other  in  cold  water,  and  then  suddenly 
transfer  both  to  water  having  an  intermediate  temperature,  our  sensations  are 


396  PHYSICS    OF   IMPONDERABLE   AGENTS. 

at  once  reversed;  one  hand  will  feel  cold,  and  the  other  warm,  although  both 
are  exposed  to  the  same  temperature. 

566.  Action  of  heat  on  matter. — Assuming  that  cohesion   and 
heat  are  counteracting  forces,  it  follows  that  the  three  states  of  matter 
are  effects  of  the  relative  intensities  of  these  two  agencies ;  and  heat 
being  a  repellent  force,  its  increase  must  be  accompanied  with  an 
enlargement  of  volume  in  either  of  the  three  states  of  matter,  while  a, 
loss  of  volume  must  accompany  an  increase  of  molecular  force,  or  a 
loss  of  heat. 

Many  familiar  facts  of  daily  experience  confirm  this  statement.  All 
bodies  (with  few  exceptions)  expand  with  an  increase,  and  contract 
with  a  loss  of  heat.  The  expansion  may  be  measured  by  an  increase 
of  length ;  in  which  case  it  is  called  linear  expansion,  or  by  an  increase 
of  volume,  and  then  it  is  called  cubic  expansion.  The  first  measure  is 
commonly  used  for  solids,  the  second  for  liquids  and  gases,  but  the  first 
is  easily  converted  into  the  second  by  cubing.  Substances  vary  very 
much  in  their  degree  of  expansion  for  the  same  increase  of  temperature : 
solids  expand  less  than  fluids,  and  liquids  less  than  gases. 

But  the  laws  of  expansion  will  be  better  studied  after  some  acquaint- 
ance is  obtained  with  the  means  of  measuring  differences  of  temperature. 

\  2.  Measurement  of  Temperature. 

I.     THERMOMETERS. 

567.  Thermometers. — The  measurement  of  temperature  is  accom- 
plished by  observing  the  amount  of  expansion  or  contraction  in  any 
substance  arbitrarily  assumed  as  a  standard  for  the  purpose.     Such  an 
instrument,  whether  the  substance  selected  is  a  solid,  a  liquid,  or  a 
gas,  is  called  a  thermometer,  or  measure  of  temperature.     For  special 
purposes,  thermometers  are  constructed  with  either  solids,  liquids,  or 
gases.     In  much  the  greater  number  of  cases,  however,  mercury  is  the 
only  substance  employed,  not  only  because  of  its  great  range  of  tem- 
perature between  freezing  and  boiling,  but  also  because  its  changes  of 
volume  for  equal  changes  of  temperature  are  more  nearly  proportional 
to  the  temperature  than  those  of  any  other  liquid. 

568.  Construction  of  mercurial  thermometers. — Thermometer 
tubes. — A  capillary  glass  tube  of  which  a  thermometer  is  to  be  made, 
should  be  one  whose  bore,  throughout,  is  of  the  same  calibre,  so  that 
equal  lengths  within  it  will  contain  equal  quantities  of  mercury.     The 
equality  of  the  bore  is  ascertained  by  causing  a  short  cylinder  of  mer- 
cury (say  one  inch)  to  pass  from  end  to  end  of  the  tube,  and  if  it 
measures  an  equal  length  throughout,  then  the  calibre  is  equal ;  other- 
wise the  tube  is  rejected.     Only  about  one  in  six  of  thermometer  tubes 


HEAT. 


397* 


441 


are  found  to  possess  a  canal  of  equal  bore.  A  proper  tube  having  been 
selected,  a  bulb  (cylindrical  or  spherical)  is  blown  upon  it  by  means 
of  a  gum  elastic  bag  fitted  to  the  open  end.  The  breath  would  fill  the 
tube  with  moisture.  The  form  of  the  bulb  is  conventional.  A  cylin- 
drical bulb  will  be  more  readily  affected  by  the  temperature  of  the 
surrounding  medium  than  a  spherical  one,  because  it  exposes  a  larger 
surface. 

Filling  the  tube  with  mercury  is  facilitated  by  tying  a  paper 
funnel  on  the  open  end  of  the  tube,  or  a  glass  reservoir,  C,  fig.  441, 
is  employed  to  hold  a  portion  of  pure  mercury. 
As  so  dense  a  fluid  could  not  enter  a  capillary 
opening,  the  air  in -the  bulb,  D,  is  expanded  by 
the  flame  of  a  spirit  lamp,  holding  the  tube 
as  seen  in  the  figure.  As  the  air  expands,  a 
portion  of  it  escapes,  passing  the  mercury  in 
C.  Allowing  the  bulb  D  to  cool,  the  pressure 
of  the  air  soon  forces  a  portion  of  the  mercury 
from  C  through  the  capillary  tube  into  the 
lower  reservoir,  exhibiting  in  its  progress  the 
successive  stages  of  the  capillary  surfaces 
explained  in  §  235.  The  lamp  is  again  ap- 
plied to  boil  the  mercury  in  D,  and  after 
several  minutes,  all  the  air  and  moisture 
are  expelled  from  the  tube  by  the  mercurial 
vapor.  The  bulb  is  then  cautiously  cooled 
once  more,  when  it  will  be  found,  as  well  as 
the  stem,  completely  filled  with  mercury.  The 
extremity  of  the  tube,  C,  is  then  drawn  out  to 
a  narrow  neck,  and  broken  off  preparatory  to 
sealing.  A  greater  or  less  portion  of  the 
mercury  remaining  in  the  stem,  must  now  be 
removed,  according  to  the  range  designed  to  be  indicated  by  the  ther- 
mometer. This  is  accomplished  by  gently  heating  the  bulb.  When 
about  two-thirds  of  the  mercury  contained  in  the  stem  has  been  driven 
out,  and  while  the  stem  is  yet  full,  the  flame  of  a  blow-pipe  is  directed 
upon  the  end  of  the  stem,  the  glass  melts,  and  the  tube  becomes  her- 
metically sealed. 

569.  Standard  points  in  the  thermometer. — Graduation. — As 
variations  in  the  height  of  the  mercurial  column  in  the  thermometer 
depend  upon  the  changes  of  temperature  to  which  it  is  subjected,  it  is 
necessary  to  graduate  the  instrument,  or  construct  a  scale,  whereby 
these  variations  may  be  indicated,  and  the  temperatures  indicated  by 
36* 


398 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


one  thermometer  compared  with  those  shown  by  anotner.  If  there 
existed  a  natural  zero,  or  absolute  limit  to  temperature,  the  thermo- 
metric  scale  might  be  numbered  upwards  from  it.  But  there  is  no 
natural  zero,  and  therefore  the  thermometric  scale  must  be  arbitrary, 
although  based  upon  certain  well-determined  physical  phenomena. 
Experiment  has  determined  that  the  melting  point  of  ice,  and  the  boil- 
ing point  of  pure  water,  under  certain  given  conditions,  are  always  the 
same,  and  these  points  (called,  respectively,  the  freezing  and  boiling 
points)  have  been  adopted  in  all  countries  as  the  two  temperatures,  with 
reference  to  which  thermometric  scales  are  constructed. 

Freezing  point. — To  fix  the  freezing  point  in  a  thermometer,  a  tin  vessel, 
like  fig.  442,  is  filled  with  pounded  ice  or  snow ;  a  hole  in  the  bottom  of  the 
vessel  allows  the  water  from  the  melted  ice  to  escape.  Into  this  vessel  the  bulb 
of  the  thermometer  is  thrust,  with  part  of  the  stein. 

When  the  mercurial  column  becomes  stationary,  that  is,  when  the  mercury 
contained  in  the  bulb  has  attained  the  temperature  of  the  melting  ice,  its  level 
is  marked  with  a  diamond  point,  upon  the  glass,  or  with  a  pencil  upon  a  paper 
previously  attached  to  the  tube.  This  indicates  the  melting  point  of  ice,  and 
consequently  the  freezing  of  water.  This  point  may  be  indicated  by  the  expres- 
sion n0  for  the  centigrade  scale,  or  n^  for  the  Fahrenheit  scale. 

Boiling  point. — This  point  is  accurately  fixed  by  immersing  the  whole 
thermometer  in  vapor  of  boiling  water.  For  this  purpose  Regnault  has  contrived 
the  apparatus,  a  section  of  which  is  seen  in  fig.  443.  The  course  of  the  steam 
442  443 


rising  through  A,  and  descending  in  the  outer  vessel,  is  shown  by  the  arrows, 
and  the  drawing  is  so  easily  understood  as  to  need  no  description.  An  equally 
efficacious  apparatus  may  be  made  by  using  a  chemical  flask,  in  the  elongated 


HEAT.  399 

neck  of  which  the  thermometer  is  suspended  by  a  cork,  thr  ugh  which  a  small 
glass  tube  allows  also  the  escape  of  the  steam.  The  stem  of  the  thermometer  (t) 
is  adjusted  so  that  the  point  a,  to  which  the  mercury  rises  when  heated  to  the 
temperature  of  boiling  water,  is  just  visible  above  the  cork.  This  point  is 
definitely  marked  when  the  level  of  the  mercury  becomes  stationary,  thus  indi- 
cating the  boiling  of  water.  Let  this  point  be  indicated  by  the  expression  nT, 
which  corresponds  to  the  temperature  T,  at  which  the  observation  was  made. 

This  temperature  T  is  equal  to  100°  C.  or  212°  F.,  when  the  barometric  pres- 
sure is  30  inches  (or  760  millimetres).  But  as  the  temperature  of  ebullition 
varies  with  the  barometric  pressure,  it  is  plain  that  the  value  of  T  will  vary  with 
the  height,  H,  of  the  barometer.  It  is  essential,  therefore,  to  accuracy  in 
graduating  the  thermometer,  that  the  boiling  point  should  be  fixed  when  the 
barometer  is  at  30  inches. 

After  dividing  the  space  between  the  freezing  and  boiling  points  into  as  many 
equal  parts  as  there  are  designed  to  be  degrees  in  the  scale,  the  divisions  are 
continued  both  above  and  below  the  fixed  points.  This  mode  of  graduation 
involves,  however,  serious  errors,  some  notice  of  which  '13  taken  in  §  576. 

570.  Different  thermometric  scales. — Having  fixed  these  two 
standard  points  in  a  thermometer,  the  space  between  them  is  next  to 
be  subdivided  into  a  certain  number  of  equal  parts,  called  degrees. 
Unfortunately,  in  different  countries,  this  interval  has  been  differently 
subdivided.  In  scientific  researches,  the  Centigrade  scale  is  almost 
exclusively  in  use,  while  in  common  life,  in  the  United  States,  England, 
and  Holland,  Fahrenheit's  scale  alone  is  used. 

Fahrenheit's  scale. — In  the  Fahrenheit  scale,  the  interval  between 
the  boiling  and  freezing  points  is  divided  into  180  equal  parts,  which 
are  called  degrees.  The  zero,  or  0°,  of  this  scale,  is  32  of  these  degrees 
below  the  freezing  point. 

Fahrenheit  adopted,  as  the  zero  of  his  thermometer,  the  temperature  which 
had  been  observed  at  Dantzic,  Holland,  in  1709,  and  which  he  found  he  could 
always  reproduce,  by  using  a  mixture  of  ice  and  salt.  At  that  temperature 
(which  he  believed  to  be  an  absolute  zero  of  cold)  he  computed  that  his  instru- 
ment contained  11,124  equal  parts  of  mercury,  which,  when  plunged  into  melting 
snow,  were  increased  to  11,156  parts.  Hence  the  space  included  between  these 
two  points  (viz.,  11,156  —  11,124  =  32)  was  divided  into  32  equal  parts,  and 
32°  indicates,  therefore,  the  freezing  point  of  water.  When  his  thermometer 
was  plunged  into  boiling  water,  Fahrenheit  estimated  that  the  mercury  was 
expanded  to  11,336  parts,  or  212  parts  above  his  zero,  and  therefore  212° 
(11,336  —  11,124=212)  was  marked  as  the  boiling  point  of  that  fluid.  In 
practice,  Fahrenheit  determined  the  boiling  point  of  water,  and  the  melting  point 
of  ice,  and  then  graduated  the  tube  by  equal  divisions  to  his  zero.  To  Fahren- 
heit belongs  the  merit  of  having  introduced  the  use  of  mercury  in  thermometers, 
which  had  previously  been  made  only  with  alcohol,  water,  or  air,  and  his 
graduation  of  the  thermometric  scale,  although  unscientific,  is  not  irrational  as  it 
is  often  represented. 

Centigrade  scale. — In  the  year  1742,  the  Swedish  philosopher 
Celsius,  professor  at  Upsal,  introduced  the  Centigrade  scale  (from 


400  PHYSICS    OF   IMPONDERABLE    AGENTS 

centum,  one  hundred,  and  gradus,  degree).  It  is  adopted  universally 
in  France,  and  in  the  north  and  middle  of  Europe.  The  interval  be- 
tween the  freezing  and  boiling  points  in  this  scale,  is  divided  into  100 
equal  parts  or  degrees  ;  the  degrees  being  counted  upwards  and  down- 
wards, from  the  freezing  point  of  water,  which  is  zero.  The  tempera- 
tures below  zero  in  this,  as  in  all  thermometers,  are  indicated  bv  the 
negative  algebraic  sign  — ;  those  above,  by  the  positive  algebraic 
sign  -f- ;  thus  —  20°  signifies  20  degrees  below  zero,  but  -j-  20°  signifies 
20  degrees  above  zero. 

Reaumur's  scale. — Reaumur,  a  French  philosopher,  introduced  his  scale 
in  1731.  He  proposed  to  use  spirits  of  wine,  of  such  a  strength,  that  between 
the  two  standard  points,  1000  parts  should  become  1080.  He  divided  the 
interval  between  these  points  into  80  equal  parts;  the  zero  being  placed  at  the 
freezing  point  of  water.  Reaumur's  thermometer  was  the  only  one  used  in 
Prance  before  the  Great  Revolution  (A.  D.  1789);  it  is  still  best  known  in  Spain, 
and  in  some  of  the  older  European  states. 

All  thermometric  scales  are  purely  arbitrary.  We  know  only  a 
small  part  probably  of  the  vast  possible  range  of  temperature,  and  we 
select  the  two  great  natural  phenomena  adopted  for  the  fixed  points 
of  our  scales  because  they  can  be  readily  verified,  and  because  the 
range  between  them  includes  the  temperatures  which  we  have  most 
occasion  to  measure  in  the  common  experience  of  life. 

571.  Comparison  and  conversion  of  thermometric  scales. — 
The  scale  employed  in  a  thermometer  is  indicated  by  the  name,  or  by 
one  of  the  initial  letters,  F.,  C.,  K.     The  degrees  of  one  thermometric 
scale  are  readily  converted  into  those  of  another.    Since  180°  F.  =  100° 
C.  =  80°  R,  therefore  1°  F.  =  f  °  C.  =  f  °  R 

As  the  value  of  a  degree  in  Fahrenheit's  thermometer  is  greater  by  32  than 
the  number  of  divisions  from  the  freezing  point,  32  must  always  be  subtracted 
before  the  -f-  degrees  of  Fahrenheit  are  converted  into  those  of  the  other  scales, 
and  added  upon  the  conversion  of  other  degrees  into  Fahrenheit. 

Easy  rules  for  mental  calculation  are : — 1st,  to  convert  Centigrade  to 
Fahrenheit  degrees,  double  the  number  of  Centigrade  degrees,  subtract  one- 
tenth,  and  add  thirty-two  ;  or,  multiply  the  Centigrade  degrees  by  T8  and 
add  32°.  And  concisely,  to  reduce  Fahrenheit  degrees  to  Centigrade, 
subtract  32°  from  the  Fahrenheit  degrees,  and  divide  the  remainder  byl'8. 

572.  House  thermometers. — For  common  use,  the  thermometer  is 
mounted  on  a  plate  of  brass,  ivory,  porcelain,  or  wood,  on  which   the 
degrees  are  marked,  as  in  fig.  444.     The  words  summer  heat,  blood  heat, 
And.  fever  heat,  are  often  placed  opposite  the  points  68°,  98°,  108°  F. 

House  thermometers  are  usually  graduated  by  comparison  with  a  standard, 
and  not  by  determining  the  two  fixed  points.  For  this  purpose  the  standard 
is  immersed  in  a  water  bath  with  the  tube  to  be  graduated,  and  a  number  of 


HEAT. 


401 


points  are  thus  fixed,  at  different  temperatures,  as  the  bath  slowly  cools  from  boil- 
ing. The  distances  between  the  marked  points  are  divided  into  equal  parts. 
This  mode  of  graduation  is  capable  of  giving  results  accurate  . 

enough  for  common  use,  between  boiling  and  freezing,  say  within  a 
degree  on  Fahrenheit's  scale.  But  above  and  below  these  points 
little  reliance  can  be  placed  on  it,  and  at  low  and  high  temperatures 
common  thermometers  will  be  observed  to  vary  often  several 
degrees,  even  when  made  by  the  best  makers. 

Some  thermometers  have  their  graduated  wooden  support  divided 
near  i/he  lower  end  into  two  parts,  connected  together  by  a  hinge, 
so  that  the  lower  part  may  be  turned  back,  and  the  bulb  thrust 
into  any  liquid  whose  temperature  it  is  desired  to  ascertain. 

Other  thermometers  have  their  stem  very  small,  and  completely 
surrounded  by  a  larger  tube,-  the  scale  being  marked  upon  a 
porcelain  strip,  or  a  roll  of  paper,  inserted  between  the  two 
tubes. 

In  very  accurate  thermometers,  the  degrees  are  marked  on  the 
glass  tube  with  fluohydric  acid  in  a  manner  described  in  $  577. 

Tests  of  a  good  thermometer. — In  order  to  ascertain 
whether  a  thermometer  is  correct  or  not,  it  is  first  plunged 
into  melting  ice,  and  then  into  boiling  water ;  the  level  of 
the  mercury  should  indicate  upon  the  scale  exactly  32°,  and 
212°  F.  When  inverted,  the  mercury  should  fall  with  a 
sudden  click,  and  fill  the  tube,  thus  showing  the  perfect 
exclusion  of  air. 

To  determine  whether  the  value  of  the  degrees  is  uniform,  a 
slight  jerk  is  given  to  the  thermometer,  by  which  a  little  cylinder 
of  mercury  is  detached  from  the  column.  On  moving  the  little 
column  through  the  tube,  it  should  occupy  equal  spaces  in  all 
parts,  if  the  bore  is  perfectly  accurate,  and  the  scale  is  properly 
graduated. 

Sensibility  of  thermometers. — The  sensibility  of  a 
thermometer  is  of  two  kinds ;  it  may  indicate  very  small 
differences,  or  it  may  be  very  sensitive  to  sudden  changes 
of  temperature. 

If  the  capacity  of  the  reservoir  is  large,  compared  with  the  bore  of  the  tube, 
a  slight  change  of  temperature  will  affect,  considerably,  the  height  of  the  mer- 
curial column.  If  the  capacity  of  the  reservoir  is  small,  and  the  glass  bulb 
thin,  the  mercury  contained  in  it  will  be  more  rapidly  affected  than  if  a  larger 
amount  were  to  be  acted  upon.  A  cylindrical  reservoir  is,  therefore,  better  than 
a  spherical  one,  because  it  exposes  a  larger  surface. 

The  two  kinds  of  sensibility  indicated,  are  obtained  in  a  thermometer  which 
has  a  small  cylindrical  reservoir  and  a  very  capillary  tube. 

573.  Displacement  of  the  zero  point.— One  source  of  error  in  the 
mercurial  thermometer  is  found  in  the  displacement  of  the  zero  point 
by  changes  subsequent  to  graduation.  If  a  thermometer  which  has 


402  PHYSICS    OF    IMPONDERABLE   AGENTS. 

been  made  some  time  is  thrust  into  melting  ice,  the  column  of  mercury 
will  not  sink  to  the  original  freezing  point,  but  will  remain  at  a  distance 
above  it,  sometimes  as  much  as  two  or  three  degrees,  and  even  more. 

Mr.  Legrand  has  found  that  the  cause  of  this  change  is,  that  the  capacity  of 
the  reservoir  is  enlarged  at  a  high  temperature  (as  during  the  construction  of 
the  thermometer),  and  that  it  does  not  return  to  its  original  dimensions  until 
after  a  long  time,  sometimes  not  until  after  two  or  three  years. 

The  effect  is  also  supposed  to  arise  from  the  pressure  of  the  atmosphere  upon 
the  bulb,  which,  when  not  truly  spherical,  seems  to  yield  slightly  and  in  a  gradual 
manner. 

This  defect  may  be  avoided  by  giving  the  bulb  a  certain  thickness.  Mr. 
Crichton's  thermometers,  of  which  the  freezing  point  has  not  altered  in  forty 
years,  were  all  made  of  unusually  thick  glass. 

Before  making  important  observations,  therefore,  thermometers  should  be 
examined  as  to  the  position  of  their  freezing  point. 

574.  Limits  of  the  mercurial  thermometer. — Mercury  is  by  far 
the  most  available  thermometric  fluid.    It  may  easily  be  obtained  pure  ; 
it  does  not  adhere  to  the  sides  of  the  tube,  and  above  all,  it  has  a  greater 
range  of  temperature,  between  its  freezing  and  boiling  points,  than  any 
other  liquid ;   freezing  at  —  39°-2,  and   boiling  at  662°  F.     Between 
these  two  points,  its  expansion  for  equal  increments  of  heat  is  very 
regular,  excepting  near  its  freezing  point.     Owing  to  this  last  irregu- 
larity, mercurial  thermometers  cannot  be  accurately  used  for  tempera- 
tures lower  than  —  31°,  or  —  35°  C.     Above   the  boiling  point  of 
mercury,  heat  is  measured  by  instruments  called  pyrometers.    For  very 
low  temperatures,  spirit  of  wine  thermometers  are  usually  employed. 

575.  Spirit  thermometers;  other  liquid  thermometers.— Alcohol 
has  never  been  frozen,  and  is,  therefore,  generally  employed  for  the 
estimation  of  low  temperatures. 

Thermometer  tubes  are  filled  with  alcohol  (which  is  generally  colored  red) 
by  heating  the  bulb,  with  the  open  end  of  the  tube  thrust  into  alcohol,  and  com- 
pleting the  process  in  the  manner  already  indicated  (568).  The  tube  is  graduated 
by  comparison  with  an  accurate  mercurial  thermometer,  exposing  both  to  the 
same  temperature,  and  marking,  successively,  upon  the  alcoholic  thermometer, 
the  temperatures  indicated  by  the  mercurial  thermometer  as  they  are  gradually 
heated.  The  alcoholic  thermometer  should  not  be  divided  into  equal  parts 
between  the  freezing  point  of  water  and  its  boiling  point,  because  it  expands 
unequally  for  equal  increments  of  heat.  Alcoholic  thermometers  often  differ 
much  from  each  other,  because  there  is  great  difficulty  in  obtaining  alcohol  per- 
fectly pure,  or  of  exactly  the  same  degree  of  concentration. 

Capt.  Parry,  in  his  arctic  voyages  (whose  experience  was  confirmed  by  Dr. 
Kane,  Arct.  Exp.  II.,  405),  found  a  difference  of  18°  F.  between  alcoholic 
thermometers  constructed  by  the  most  celebrated  makers ;  and  a  difference  of 
14°  F.  has  been  observed  even  at  a  temperature  of  only  15°  or  20°  F.  In  con- 
lequence  of  this,  other  liquids  have  been  proposed  for  thermometers,  intended  to 
indicate  low  temperatures.  From  the  experiments  of  M.  Pierre,  of  all  liquids, 


HEAT.  403 

ordinary  sulphuric  ether,  chlorid  of  ethyle,  and  bromid  of  methyle,  were  found  to 
be  best  adapted  for  such  instruments. 

It  is  plain  from  these  statements  that  a  more  accurate  mode  of  measuring  lo\l 
temperatures  is  one  of  the  desiderata  of  science. 

576.  Defects  inherent  in  mercurial  thermometers. — Besides 
those  sources  of  error  in  this  instrument  already  noticed,  there  are 
others  inherent  in  the  nature  of  the  materials  employed. 

As  glass  and  mercury  expand  unequally  by  heat,  it  is  plain  that  we 
read  in  the  mercurial  column  not  th&  absolute  expansion  of  the 
mercury,  but  the  difference  between  its  expansion  and  that  of  the  glass. 
If  they  expanded  equally,  no  movement  of  the  mercurial  column  would 
be  perceived,  and  if  the  glass  expanded  more  than  the  mercury,  the 
latter  would  appear  to  fall  when  the  temperature  rose.  But  as  in  fact 
the  mercury  expands  about  seven  times  as  much  as  glass,  the  apparent 
expansion  of  the  metal  in  glass  is  about  one-seventh  less  than  its 
absolute  expansion. 

Again,  it  is  proved  that  the  expansion  of  mercury  for  equal  incre- 
ments of  heat  is  not  absolutely  equal,  but  increases  slightly  with  the 
temperature.  At  temperatures  between  freezing  and  boiling,  this 
increase  is  very  slight,  and  may  be  disregarded,  since  the  division  of  this 
distance  into  parts  of  equal  length  gives  the  degrees  a  mean  length, 
slightly  in  excess  for  the  degrees  near  freezing,  and  as  much  too  short 
for  those  near  the  boiling  point,  but  exact  for  the  intermediate  degrees. 
But  above  the  boiling  point  the  error  is  more  serious,  since  while  the 
degrees  have  the  same  length,  the  spa^e  occupied  by  a  unit  of  mer- 
cury is  constantly  increasing,  consequently  the  degrees  become  too 
short,  and  the  thermometer  reads  too  high  a  temperature.  For  the 
same  reason,  below  the  freezing  point,  the  thermometer  constantly 
indicates  a  temperature  higher  than  the  true  temperature. 

The  error  here  pointed  out  could  be  easily  allowed  for  in  the  gradua- 
tion ;  the  coefficient  of  expansion  of  mercury  for  various  temperatures 
being  known.  But  this  correction  is  rendered  almost  impossible,  from 
the  fact  that  the  rate  of  expansion  of  the  glass  is  found  not  only  to 
increase  about  as  rapidly  as  that  of  the  mercury  (and  sometimes  even 
more  so),  but  to  render  the  case  yet  more  difficult,  it  is  found  that  glass  of 
different  kinds  varies  in  its  rate  of  expansion,  and  the  same  glass  under 
different  conditions  may  also  vary. 

Regnault,  to  whom  we  are  indebted  for  these  data,  has  illustrated 
the  facts  by  a  series  of  observations,  the  results  of  which  are  shown 
in  the  following  table. 

He  has  shown  that  the  air  thermometer  may  be  relied  on  as 
giving  results  almost  invariable  and  exact.  His  form  of  this  instru- 
ment is  described  at  length  in  his  memoir  before  quoted  (p.  220). 


404 


PHYSICS    OP   IMPONDERABLE    AGENTS. 


COMPARISON  OF  DIFFERENT  THERMOMETERS   (CENTIGRADE  DEGREES). 


Air  Thermometer. 
True  Tempera- 
ture. 

Thermometer 
•without  Glass. 

Thermometer, 
Fliut-glass. 

Thermometer,      '   Coefficient  of  Ex- 
Crown-glass,       pansion  of  Mercury. 

0 

o 

o 

0 

0 

0 

0 

0                    0-000  1790 

50-00 

49-65 

50-20               0-000  1815 

100-00 

100-00 

100-00 

100-00               0-000  1830 

120-00 

120-33 

120-12 

119-95               0-000  1850 

140-00 

140-78 

140-29 

139-85               0-000  1860 

160-00 

161-33 

160-52 

159-74              0-000  1870 

180-00 

182-00 

180-80 

179-63               0-000  1880 

200-00 

202-78 

201-25 

199-70               0-000  1890 

220-00 

223-67 

221-82 

219-80               0-000  1901 

240-00 

244-67 

242-55 

239-90               0-000  1911 

246-30 

246-30 

260-00 

265-78 

263-44 

260-20               0-000  1921 

280-00 

287-00 

284-48 

280-52               0-000  1931 

300-00 

308-34 

305-72 

301-08               0-000  194] 

320-00 

329-79 

327-25 

321-80               0-000  1951 

340-00 

351-34 

349-30 

343-00               0-000  1962 

The  temperatures  indicated  by  an  air  thermometer,  recorded  in  the  first 
column,  were  taken  as  a  standard,  and  are  very  near  the  truth.  The  second 
column  gives  the  temperatures  which  would  be  shown  by  a  mercurial  column 
graduated  in  the  ordinary  way,  assuming  the  glass  to  be  without  expansion, 
thus  showing  the  errors  attributable  only  to  the  varying  rate  of  expansion  in  that 
metal.  In  the  third  and  fourth  columns  are  given  the  comparative  tempera- 
tures shown  by  thermometers  of  flint  and  crown  glass  respectively,  showing  the 
discrepancies  due  to  differences  of  material.  The  rapidity  with  which  the  rate 
of  expansion  in  the  mercury  increases  with  the  temperature  is  shown  by  column 
fifth. 

At  and  between  the  fixed  points  of  0°  and  100°  a  perfect  accord  was  observed, 
the  small  differences  there  existing  being  distributed  among  all  the  degrees. 
Above  100°,  however,  it  will  be  seen  the  differences  between  the  true  tempera- 
tures and  the  several  thermometers  are  more  and  more  sensible;  and  most 
conspicuous  in  the  thermometer  without  glass.  The  effect  of  the  expansion  of 
the  flint-glass  is  seen  to  be  approximately  to  correct  the  expansion  of  the 
mercury.  The  crown-glass  thermometer,  owing  to  the  peculiar  rate  of  expan- 
sion in  crown-glass,  is  seen  to  march  very  closely  with  the  true  temperature 
up  to  246°-30,  where  the  coincidence  is  perfect.  Above  that  point  the  differences 
increase,  until  at  340°,  the  error  is  three  degrees.  A  thermometer  of  crown-glass 
is  plainly  to  be  preferred  for  accuracy  over  one  of  flint-glass. 

The  facts  embodied  in  this  table  are  made  conspicuous  by  a  geometrical 
construction,*  fig.  445,  in  which  the  figures  on  the  horizontal  line  (or  axis  of 
ordinates)  stand  for  the  temperatures  of  an  air  thermometer  assumed  as  invaria- 
ble, and  those  on  the  vertical  line  (or  axis  of  abscissas),  for  the  differences  found 
between  the  air  thermometer  and  various  mercurial  thermometers.  The  variation 
of  the  theoretical  thermometer,  without  glass,  from  the  true  temperature,  is  seen 


*  Cook's  Chemical  Physics. 


HEAT. 


405 


in  the  curve  0  n  a  m  ;   while  the  curves  0  n  a  c,  0  n  a  v,  0  n  a  s,   0  n  a  o,  show 
respectively  the  variation  of  thermometers  made  with  flint-glass,  green  glass, 

445 


Swedish  glass,  and  "verre  ordinaire"  of  Paris.  The  last  curve  (corresponding 
to  column  fourth  in  the  table)  is  a  beautiful  illustration  of  the  anomalies  indi- 
cated by  observation.  446 

577.  Standard  thermometer. — The  unavoidable  defects  in 
the  mercurial  thermometer,  just  pointed  out,  are  in  common 
instruments  greatly  exaggerated  by  errors  of  construction. 
Standard  thermometers  for  scientific  purposes  are  constructed 
with  a  scale  engraved  in  the  glass,  as  in  fig.  446.  The  divisions 
of  this  scale  are  marked  by  a  dividing  engine  on  the  surface  of 
a  covering  of  varnish,  with  which  the  tube  is  coated  preparatory 
to  etching.  As  no  calibre  is  absolutely  uniform  in  any  glass 
tube  for  a  considerable  length,  the  value  of  the  calibre  for  every 
part  of  the  tube  is  exactly  measured  by  a  cylinder  of  mercury 
drawn  in  at  one  end  of  the  open  tube,  and  taken  so  short  that 
the  error  in  the  length  chosen  may  be  disregarded.  This  cylinder 
of  mercury  is  then  gradually  moved  from  end  to  end  of  the  tube 
by  the  force  of  air  from  a  gum  elastic  bottle,  dividing  the  tube 
into  lengths  equal  to  the  successive  lengths  of  the  mercury 
column.  The  position  of  these  successive  points  is  marked,  and 
each  of  these  divisions  is  then  subdivided  by  the  engine  into  an 
equal  number  of  degrees ;  varying  in  length,  of  course,  in  propor- 
tion to  the  lengths  of  the  several  cardinal  divisions.  These  gra- 
duations are  then  etched  into  the  glass  by  exposing  it  to  the 
vapor  of  fluohydric  acid.  This  graduated  tube  is  then  soldered 
to  a  cylindrical  reservoir  prepared  of  a  size  proportioned  to  the 
diameter  of  the  tube,  and  the  destined  range  of  the  thermometer. 

The  mode  of  determining  the  required  size  of  this  reservoir  is  as  fol- 
lows : — 

We  wish  to  know  what  size  to  give  the  reservoir  for  a  given  graduated  tube 
ih&t  N  divisions  of  the  thermometer  may  correspond  to  100°  C.    Weigh  the  tube 
37 


406  PHYSICS    OF    IMPONDERABLE   AGENTS. 

empty,  and  also  when  containing  a  column  of  mercury  of  an  observed  length.  We 
thus  learn  the  weight  of  mercury,  10,  occupying  n  degrees  of  the  tube.  From  this 

we  obtain  N-,  the  weight  of  mercury  which  will  fill  N  divisions  of  th,e  tube, 
n 

w 
and  by  (99),  we  know  the  corresponding  volume  =  Ar—  ————-.     But  this 

volume  represents  the  expansion  which  the  mercury  in  the  reservoir  of  the  pro- 
posed thermometer  must  undergo  when  heated  from  0°  to  100°  C.  Now  the 
apparent  expansion  of  mercury  under  these  conditions  is  known  to  be  ^  of  its 
volume  at  0°.  Representing,  then,  by  Fthe  unknown  volume  of  the  reservoir, 

V  w  w 

we  shall  have  :     -  =  N  ,  and  V  =  65  N  •     If  the  reser- 

65  n(tip.Gr.)  n  (bp.  Crr.) 


voir  is  spherical,  V  =  nD3,  from  which  we  can  calculate  the  required 
diameter.  If  it  is  cylindrical,  V=  {r(D2h,  from  which  the  approximate  length 
of  h  is  calculated  when  the  diameter  is  given. 

The  thermometer  thus  graduated  is  filled,  and  the  fixed  points  marked  as  already 
described  (568).  Its  scale,  of  course,  is  arbitrary,  and  may  be  reduced  by  calcu- 
lation to  the  Centigrade  or  any  other  scale.  Observation  determines  the  number 
of  divisions  between  freezing  and  boiling,  which  we  call  JV,  and  also  the  point  on 
the  arbitrary  scale,  corresponding  to  the  freezing  point  (0°  C).  Call  the  number  of 
divisions  below  this  point  d°,  the  degrees  centigrade  C°,  and  those  of  the  arbitrary 

100 
scale  A°.     We  then  have,  N=  100,  and  C=—  (Ay  —  d°).   Suppose  there  are 

379  divisions  on  the  arbitrary  scale  between  the  fixed  points,  and  the  freezing 
point  is  the  147th  division  from  the  bottom,  and  it  is  required  to  know  to  what 
temperature  the  303d  division  corresponds  in  Centigrade  degrees,  we  shall  have 
C  =  ^a§  (303  —  147)  =  41-16.  Every  such  thermometer  has,  of  course,  its 
own  equation  ;  a  table  is  readily  calculated  for  its  convenient  use. 

Every  good  standard  has  both  the  boiling  and  freezing  points  included  in  its 
range.  The  cavity  a,  fig.  446,  is  designed  to  allow  for  any  sudden  expansion 
of  the  mercury  above  the  limit  of  the  scale,  to  avoid  the  fracture  of  the  instru- 
ment. Similar  expansions  are  often  introduced  at  particular  points  on  the  stem, 
to  avoid  undue  length  in  the  stem  when  a  long  range  is  required.  The  whole 
scale  in  this  case  is  distributed  between  several  thermometers,  and  the  swellings 
so  placed  as  to  cover  in  each  case  the  range  of  the  preceding  instrument.  It  is 
thus  possible  to  divide  each  Centigrade  degree  into  twenty  or  more  parts. 

In  accurate  observation,  the  whole  instrument  should  be  immersed  in  the 
medium  whose  temperature  we  seek,  but  when  this  is  not  possible,  a  correction 
may  be  calculated  by  a  formula  which  our  space  requires  us  to  omit.  (See 
Cooke's  Chemical  Physics,  p.  444.) 

II.     SELF-REGISTERING  THERMOMETERS. 

578.  Maximum  and  minimum  thermometers.  —  It  is  often  desir 
able  to  ascertain,  in  the  absence  of  an  observer,  the  highest  and  lowest 
temperature  of  the  night,  or  of  any  other  interval  of  time.  This  may 
be  done  by  the  employment  of  what  are  called  maximum  and  minimum, 
or  self-registering  thermometers.  One  of  the  most  simple  instruments 
of  this  kind  was  invented  by  Rutherford,  and  is  represented  in  fig. 
447. 


HEAT. 


407 


(a.)  Rutherford's  maximum  and  minimum  thermometer  consists 
of  two  thermometers  attached  to  a  plate  of  glass,  or  to  wood ;  their  tubes  are 


bent  at  right  angles,  near  the  bulbs.  The  maximum  thermometer,  A,  contains 
mercury ;  the  minimum  thermometer,  B,  contains  alcohol.  In  the  tube  of  the 
former  is  a  small  piece  of  steel  (seen  at  A) ;  when  the  mercury  expands,  it 
pushes  the  steel  before  it,  but  when  the  fluid  recedes  toward  the  bulb,  the  wire 
does  not  follow  it.  The  steel  is  thus  left  at  the  extreme  point  to  which  the 
mercury  may  have  moved  it,  and  indicates  the  highest,  or  maximum  tempera- 
ture, to  which  it  has  been  exposed.  The  alcoholic  thermometer  contains  a  small 
piece  of  enamel  (seen  at  B),  sunk  below  the  surface  of  the  liquid.  The  position 
of  the  enamel  is  not  affected  by  expansion,  because  the  alcohol  readily  passes  it ; 
but  by  contraction  it  is  drawn  back  with  the  column  of  alcohol,  by  the  cohesive 
attraction  of  the  particles  of  liquid  at  the  surface  of  the  column.  Thus  the 
enamel  is  left  at  the  lowest  point  to  which  the  column  has  retreated,  and  repre- 
sents, therefore,  the  minimum  temperature  which  has  occurred. 

(6.)  Negretti  and  Zambia's  maximum  thermometer. — A  slight 
agitation  given  to  Rutherford's  maximum  thermometer  will  often  cause 
the  steel  index  to  become  immersed  in  the  mercury,  which,  upon  ex- 
pansion, will  pass  by  the  steel,  and  thus  the  instrument  will  fail  to 
fulfill  the  purpose  for  which  it  was  designed.  This  source  of  error  is 
avoided  in  the  use  of*ffegretti  and  Zambra's  instrument,  fig.  448. 

448 


A  small  rod  of  glass,  a  b,  is  introduced  into  the  thermometer  tube,  which  ia 


408 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


then  bent  just  above  the  point  where  the  rod  is  placed ;  the  rod  nearly  fills  the 
bore  of  the  tube.  When  in  use,  the  instrument  is  suspended  horizontally.  The 
mercury,  by  expanding,  will  force  its  way  past  the  obstruction,  to  the  point  c  for 
example;  when  the  temperature  falls,  and  the  mercury  contracts,  the  cohesion 
of  the  particles  of  mercury  to  each  other  will  prevent  the  column  from  passing 
the  rod.  The  extremity  of  the  column,  c,  will  therefore  indicate  the  highest 
temperature  to  which  the  instrument  has  been  exposed.  It  has  been  observed 
that  in  this  form  of  instrument  the  mercury  does  not  move  steadily,  but  by  jerks. 

(c.)  Walferdin's  maximum  thermometer. — The  upper  part  of 
the  tube  of  this  instrument,  fig.  449,  terminating  with  a  small   449 
orifice,  is  surrounded   by  a  reservoir  which  contains  mercury. 
When  the  instrument  is  to  be  used,  it  is  first  heated,  whereby  the 
mercury  rises  in  the  tube  and  flows  over  into  the  reservoir ;    450 
it  is  then  inverted.     The  elongated  point  of  the  tube  thus 
dips  into  the  mercury  of  the  reservoir.     It  is  now  exposed, 
while  inverted,  to  a  lower  temperature  than  the  one  to  be 
determined.    During  this  cooling,  the  tube  will  remain  full 
because  its  point  dips  into  the  reservoir  of  mercury.     The 
instrument  is  now  placed  in  its  proper  position,  and  it  is 
evident  that  as  the  temperature  rises,  a  portion  of  mercury 
will  pass  out  of  the  full  tube  into  the  reservoir  ;  and  this 
portion  will  be  greater  as  the  temperature  is  higher. 

To  determine  afterwards  the  highest  temperature  to 
which  it  has  been  exposed,  it  is  compared  with  a  stand- 
ard thermometer.  Both  being  placed  in  a  water  bath, 
gradually  heated,  the  temperature  indicated  by  the  standard 
thermometer  is  observed  when  the  mercurial  column  has 
risen  to  the  top  of  the  tube  of  the  maximum  thermometer. 

579.  Metastatic  thermometer. — Walferdin  has  ap- 
plied the  same  principle  to  the  construction  of  a  ther- 
mometer designed  to  indicate  very  small  differences  of 
temperature.  In  this  instrument,  fig.  450,  the  reservoir, 
and  calibre  of  the  tube  are  very  small,  so  that  the  instru- 
ment is  extremely  sensitive  to  small  changes  of  tempera- 
ture. 

The  bulb,  B,  corresponds  to  the  reservoir  in  fig.  449.  Just 
below  this  bulb,  the  capillary  tube  suddenly  contracts  at  C.  The  stem  ia 
graduated  into^arts  of  equal  capacity,  each  of  which  represents  a  very  small 
fraction  of  a  degree.  In  using  this  thermometer,  it  is  first  heated  to  a  tem- 
perature somewhat  higher  than  the  one/ it  is  desired  to  estimate.  The  mercury 
rises  in  the  tube  and  partially  fills  the  bulb.  A  slight  jar  given  to  the  instru- 
ment while  cooling,  causes  the  mercurial  column  to  break  at  the  point  of  con- 
traction, and  while  a  portion  of  mercury  remains  in  the  bulb,  the  mercurial 
column  sinks  down  to  a  point  somewhere  above  the  reservoir.  The  thermometer 


HEAT.  409 

must  now  be  exposed  to  a  known  temperature,  very  near  to  that  we  wish  to 
estimate  :  the  position  of  the  level  of  the  mercury  in  the  tube  is  then  noted.  The 
thermometer  is  next  subjected  to  the  medium,  whose  temperature  is  to  be  esti- 
mated. Suppose  there  is  a  difference  in  the  level  of  the  mercurial  column  in  the 
two  cases,  of  18  divisions  of  the  arbitrary  scale,  and  if  300  of  these  divisions  are 
equal  to  one  degree,  then  the  difference  in  temperature  must  be  ^^  of  a  degree. 
Walferdin  has  employed  thermometers  of  this  kind  which  indicated  one  one- 
hundredth  (y£ff)  and  even  one  one-thousandth  (y^^-)  of  a  degree,  Centigrade. 
{J-g  and  -j-^  of  a  degree  F.).  By  causing  more  or  less  mercury  to  flow  into  the 
upper  bulb,  differences  in  temperature  may  be  estimated  for  different  points  on 
the  scale.  A  single  thermometer  of  this  description  may  take  the  place  of  a 
series  of  thermometers  with  a  fractional  scale. 

III.     METALLIC  THERMOMETERS  AND  PYROMETERS. 

580.  Breguet's  metallic  thermometer. — This  instrument,  remark- 
able for  the  extreme  sensitiveness  of  its  indications,  depends  upon  the 
unequal  expansion  of  different  metals ;  it  is  represented  in  fig.  451. 

Strips  of  platinum,  gold,  and  silver,  after  being  soldered  together  through- 
out their  whole  length,  are  rolled  into  a  thin  ribbon,  451 
which  is  then  formed  into  a  spiral,  or  a  helix.  The 
upper  extremity  of  this  helix  is  fixed  to  a  support, 
and  to  the  lower  end,  at  right  angles  to  it,  is  attached 
a  needle,  moving  over  a  graduated  circle,  resembling 
the  dial  of  a  watch.  The  silver,  which  is  the  most  ex- 
pansible of  the  three  metals,  forms  the  inner  face  of  the 
helix ;  the  platinum,  which  is  the  least  expansible, 
.  forms  the  outer  face,  and  the  gold,  which  has  an  inter- 
mediate expansibility,  is  included  be- 
tween them,  and  moderates  their  effects. 
When  the  temperature  rises,  the  silver, 
expanding  more  than  the  other  metals, 
unrolls  the  helix ;  the  contrary  effect 
takes  place  when  the  temperature  is 
lowered.  This  thermometer  is  gradu- 
ated by  comparison  with  a  standard 
mercurial  thermometer.  The  instru- 
ment is  particularly  useful  when  very 
rapid  variations  of  temperature  are  to  be  determined.  Another  form  is  some- 
times given  to  it.  The  compound  ribbon  being  bent  into  the  form  of  a  letter 
U,  one  of  the  extremities  is  fixed,  and  the  other  is  left  free  to  move.  By  means 
of  a  lever  and  toothed  wheels,  the  movements  which  changes  of  temperature 
cause  in  the  free  end  are  communicated  to  a  pointer,  moving  over  a  dial. 

581.  Saxton's    deep   sea   metallic    thermometer. — Mr.  Joseph 
Saxton,  of  the  United  States  Coast  Survey,  has  adapted  the  principle 
of  Breguet's  metallic  thermometer,  to  the  construction  of  an  instrument 
by  which  numerous  very  accurate  observations  have  been  made  upon 
the  temperature  of  the  sea  in  deep  soundings.     Silver  and  platinum 
form  the  compound  spiral,  and  its  torsion  is  registered  by  an  index, 
moved  by  multiplying  wheels,  and  carrying  forward  a  tell-tale,  or  stop- 


410  PHYSICS    OP   IMPONDERABLE    AGENTS. 

hand,  to  the  lowest  temperature  attained.  This  instrument  has  been 
some  years  in  use  for  deep  sea  soundings,  with  the  best  results.  A 
email  correction  in  the  readings  is  made  (not  exceeding  one  degree 
for  600  fathoms)  proportionate  to  the  depth  of  the  sounding. 

The  term  pyrometer  is  sometimes  applied  to  instruments  intended  to 
measure  changes  of  dimensions  in  bodies  at  low  temperatures  by  the 
expansion  of  solid  rods  ;  such  is  : — 

582.  Saxton's  reflecting  pyrometer. — In  the  measurement  of  the 
base  lines  of  the  larger  triangles,  in  the  survey  of  the  coast  of  the  U.  S., 
the  greatest  accuracy  is  required.   These  lines  are  sometimes  forty  or  fifty 
miles  in  length.   An  instrument  constructed  by  Saxton,  under  the  direc- 
tion of  Prof.  Bache,  accomplishes  this  object  perfectly. 

The  measuring  rods  are  compound  bars  of  iron  and  brass,  so  proportioned  in 
their  cross  section  as  to  equalize  their  differences  of  specific  heat  and  conduct! - 
bility,  while  their  unequal  expansions  compensate  for  each  other,  and  preserve 
an  invariable  length.  To  verify  these  bars,  the  ends  are  brought  into  contact 
with  two  blunt  knife  edges ;  one  immovable,  the  other  forming  the  shorter  end 
of  a  compound  lever ;  having  at  the  other  end  a  rotating  mirror.  Any  variation 
of  length  in  the  bar,  by  changing  the  angular  position  of  the  mirror,  gives  evi- 
dence of  the  change  to  an  observer,  whose  eye  is  placed  at  a  telescope  directed 
towards  the  mirror,  in  which  the  one  twenty-five  thousandth  of  an  inch  on  a 
scale  is  magnified  into  a  unit  of  graduation,  about  one-fourth  of  an  inch  long, 
from  which  the  one  hundred-thousandth  of  an  inch,  or  about  one  four-millionth 
of  a  metre  is  easily  read.  If  desirable,  this  degree  of  minuteness  might  be 
greatly  increased.  This  simple  and  beautiful  contrivance  has  superseded  all 
methods  previously  known  for  verifying  rods  of  any  length.  It  is  sensibly 
affected  in  bars  six  metres  long,  by  changes  of  temperature  otherwise  quite 
inappreciable,  and  it  then  becomes  the  most  sensitive  of  thermometers.  This 
method  is  good  only  for  end  measurement. 

583.  Wedgewood's  pyrometer. — The  range  of  the  mercurial  ther- 
mometer is  limited  by  the  boiling  point  of  mercury ;  higher  tempera- 
tures are  measured  by  the  effects  of  heat  upon  solids  with  instruments 
called  pyrometers. 

The  celebrated  English  potter,  Wedgewood,  invented  the  first  pyrometer  used, 
founded  upon  the  contraction  which  clay  undergoes  when  exposed  to  high 
temperatures.  He  assumed  this  contraction  to  be  as  much  greater  as  the 
temperature  was  higher.  The  results  obtained  with  this  instrument  are,  how- 
ever, inaccurate,  as  it  is  now  known  that  the  contraction  which  clay  undergoes 
depends  rather  on  the  duration  than  on  the  intensity  of  the  heat,  and  is  much 
modified  by  the  particular  sort  of  clay  employed. 

584.  Darnell's  pyrometer  is  an  instrument  capable  of  exact  mea- 
surements of  high  temperatures  by  the  expansion  of  a  bar  of  platinum 
encased  in  a  sheath  of  black  lead.     The  bar  and  its  case  are  adjusted 
both  before  and  after  the  experiment  to  a  measure  which  indicates  on 
a  graduated  arc  the  degree  of  expansion.     The  degrees  of  temperature 
are  then  calculated  from  the  known  rate  of  expansion  of  platinum. 


HEAT. 


411 


585.  Draper's  pyrometer. — This  instrument  registers  its  results  by 
the  expansion  of  a  little  strip  of  platinum,  heated  (in  free  air)  by  a 
measured  current  of  voltaic 'electricity. 

The  platinum  strip  is  connected  with  the  short  end  of  a  lever,  whose  longer 
limb  marks  upon  a  graduated  arc  the  degree  of  expansion.  With  this  delicate 
instrument,  Prof.  Draper  conducted  a  series  of  experiments  upon  the  tempera- 
tures at  which  bodies  become  visibly  red,  in  the  dark  and  in  diffused  light,  the 
temperatures  being  determined  from  the  coefficient  of  expansion  in  the  several 
metals.  (Am.  Jour.  Sci.  [2]  IV.  388.) 

586.  Estimation  of  very  high  temperatures. — According  to  Bun- 
sen's  calculations  (Gasometry,  p.  236-243),  the  temperature  of  a  hydrogen 
flame  burning  in  free  air  is  3259°  C.  (=  5898°  F.),  and  of  olefiant  gas 
5413°  C.  (=  9775°  F.).     Since  it  is  probable  that  at  high  temperatures 
the  radiating  power  of  a  body  for  heat  is  proportional  to  its  radiating 
power  for  light,  we  are  in  possession  of  the  means  of  comparing  the 
intensity  of  glow  of  a  coil  of  platinum  heated  in  a  furnace,  or  in  a 
stream  of  lava,  with  the  glow  from  a  like  coil  heated  in  a  flame  of 
known  temperature,  and  thus  approximately  of  estimating  the  tern 
perature  of  a  furnace  or  of  a  volcano. 

IV.     THERMOSCOPES. 

587.  Thermoscopes. — This  name  (from  6lp/j.rj,  temperature,  and 
ffxox£a),  to  see)  is  applied  to  a  class  of  instruments  designed  to  indicate 
small  differences  of  temperature,  and  not  to  measure  them  in  degrees. 

Air  thermometers. — As  air  contracts  and  expands  uniformly  and 
quickly,  it  is  often  used  where  slight  and  sudden  452  453 

variations  of  temperature  are  to  be  observed.  The 
contractions  and  expansions  which  it  undergoes, 
are  rendered  visible  by  the  movements  that  it 
causes  in  liquids.  Such  instruments  are  often 
called  air  thermometers,  but  are  not  to  be  con- 
founded with  the  form  of  air  thermometer  described 
by  Regnault,  which  is  the  most  accurate  measure 
of  temperature  yet  made  known.  The  results  in 
the  first  column  in  the  table  on  p.  404  were 
obtained  by  the  air  thermometer  here  alluded  to, 
some  notice  of  which  will  be  found  in  the  section 
on  expansion. 

The  simplest  air  thermometer  is  that  represented  by 
fig.  452,  and  is  often  called  the  thermometer  of  Sanc- 
torius,  an  Italian  philosopher  of  the  17th  century.  It  is  a  bulbed  tube,  filled 
with  air,  having  for  an  index  a  drop  of  colored  liquid  in  the  stem  at  A.  The 
movements  of  the  index  show  the  variations  of  temperature.  Another  form  of 
the  same  instrument  is  represented  by  fig.  453.  The  extremity  of  the  tube  rests 


412 


PHYSICS  OF  IMPONDERABLE  AGENTS. 


in  the  colored  liquid  contained  in  the  open  vessel.     If  the  bulb  is  heated,  the 
liquid  falls  in  the  tube,  and  rises  if  the  bulb  is  cooled. 

Amontons'  thermometer,  fig.  454,  is  essentially  the  same  as  the  last;  the 
bulb,  C,  is  partially  filled  with  colored  liquid.  Expansion  of  the  air  contained 
in  the  upper  part  of  the  bulb,  C,  causes  the  liquid  to 
rise  in  the  tube  A  B. 

These  instruments  are  necessarily  imperfect,  owing  to 
the  varying  pressure  of  the  atmosphere,  and  they  serve 
only  as  means  for  the  illustration  of  principles  in  the 


455 


454 


class-room. 

(a.)  Leslie's  differential  thermo- 
meter.— This  instrument,  fig.  455, 
avoids  the  objection  to  the  open  air 
thermometer.  It  was  used  by  Leslie 
in  his  experiments  on  radiant  heat, 
and  consists  of  a  .two-bulbed  tube  filled 
with  air,  bent  twice  at  right  angles.  It 
contains  a  column  of  sulphuric  acid  in 
the  stem,  which  stands  at  the  same 
height,  if  both  bulbs  are  equally  heated,  but  if  one  is  heated  more  than 
the  other,  the  difference  is  seen  in  the  unequal  height  of  the  two  columns 
as  shown  in  the  figure. 

(6.)  Howard's  differential  thermometer,  fig.  456,  contains  ether, 


456 


457 


and  the  vapor  of  ether,  in 
place  of  common  air.  It 
is  by  far  the  most  sensitive 
instrument  of  its  class.  It 
was  invented  by  Professor 
Howard,  of  Baltimore,  in 
1819. 

(c.)  Rumford's  thermo- 
scope,  fig.  457,  is  an  instru- 
ment resembling  Leslie's, 
and  like  it,  contains  air.  The  horizontal  tube  is  longer,  and  the  bulbs 
larger,  than  in  Leslie's,  and  a  short  column  of  sulphuric  acid,  n,  sepa- 
rates the  two  masses  of  air,  and  by  its  motion  over  a  scale  of  equal 
parts,  serves  to  indicate  differences  of  temperature. 

588.  Thermo-multiplier. — By  far  the  most  delicate  of  all  means  of 
measuring  small  variations  in  temperature,  is  the  thermo-multiplier,  or 
thermo-electric  pile  of  Nobili  and  Melloni.  Its  indications  depend  on 
the  production  of  electric  currents  by  small  changes  of  temperature. 
It  was  with  this  instrument  that  Melloni  conducted  the  remarkable 
series  of  researches  on  the  transmission  and  radiation  of  heat  which 
are  noticed  in  their  appropriate  place,  farther  on. 


HEAT. 


413 


§  3.  Expansion. 

I.     EXPANSION    OF    SOLIDS. 

589.  Linear  expansion. — Pyrometers. — The  general  fact  of  the 
expansion  of  bodies  by  heat,  has  already  been  stated  in  §  566.  Linear 
expansion,  or  expansion  in  a  single  direction,  is  illustrated  by  the 
;•.;  jiaratus  seen  in  fig.  458.  A  metallic  rod,  A,  securely  held  by  a  screw 

458 


at  the  end,  B,  is  heated  by  the  flame  of  an  alcohol  lamp.  The  expan- 
sion is  shown  by  the  movement  of  the  index,  K,  over  the  graduated 
arc,  occasioned  by  the  pressure  of  the  fore  end  of  the  rod  against  the 
short  end  of  the  index.  At  the  beginning  of  the  experiment,  the  rod 
A  is  adjusted  by  the  screw  B,  so  that  the  index  stands  at  zero;  as  the 
rod  cools  the  index  returns.  Rods  of  various  metals  and  alloys  may  be 
used  for  comparison.  Such  an  instrument  is  called  a  pyrometer  ;  but 
it  has  no  scientific  value,  being  replaced  by  instruments  of  far  greater 
delicacy.  Those  named  in  §§  582,  584,  and  585  are  examples  of  the 
accurate  application  of  linear  expansion  of  solids  for  the  exact  admeas- 
urement of  changes  of  temperature. 

590.  Cubical  expansion  in  solids  may  be  shown  by  the  apparatus, 
fig.  459.  The  ring  of  metal,  m,  allows  the 
ball  of  copper,  a,  merely  to  pass  through 
it  at  the  ordinary  temperature.  If  the 
ball  is  heated,  it  expands  in  all  direc- 
tions, and  will  then  no  longer  pass 
through  the  ring,  but  rests  upon  it,  as  is 
shown  in  the  figure.  As  the  ball  cools, 
it  gradually  returns  to  its  original  dimen- 
sions, and  again  passes  through  the  ring 
as  before. 

Different  solids  expand  unequally,  but, 
for  the  most  part,  uniformly,  in  all  directions,  and  return  to  their  origi- 
nal dimensions  on  cooling. 


414  PHYSICS    OF    IMPONDERABLE    AGENTS. 

There  are  some  exceptions  to  this  general  statement.  Wood  expands  and 
contracts  more  in  the  breadth  of  its  fibres  than  in  their  length ;  and,  when  it 
is  considerably  heated,  it  contracts  permanently.  Clay  also  contracts  perma- 
nently by  heating,  and  becomes  vitrified;  new  chemical  compounds  being 
formed.  The  particles  of  lead  slide  over  each  other  during  expansion,  and  do 
not  return  again  on  cooling  to  their  original  position.  Lead  pipes,  which  con- 
vey hot  water  or  steam,  become  permanently  elongated ;  and  the  leaden  linings 
of  bath-tubs  and  cisterns,  which  receive  hot  water,  become  gathered  into  ridges 
from  this  cause. 

Relation  between  cubical  and  linear  expansion. — The  linear 
and  cubical  expansion  in  any  homogeneous  solid,  is  so  related,  that, 
by  the  same  elevation  of  temperature,  its  length,  breadth,  and  depth 
will  be  increased  in  the  same  proportion.  Thus: — 

If  a  solid,  heated  to  a  certain  temperature,  increases  in  length  one  one-thou- 
sandth of  its  original  length,  its  surface  increases  two  one-thousandths  of  its 
original  area,  and  its  volume,  three  one-thousandths  of  its  original  bulk. 

This  theoretical  view  is  found  to  be  nearly,  but  not  quite,  true,  in  fact. 

Expansion  of  crystals.  —  Crystals  of  the  monometric  system 
(154,  a),  like  common  salt,  fluor  spar,  &c.,  expand  equally  in  all  direc- 
tions. In  this  system,  all  the  crystallogenic  axes  are  equal,  and  at 
right  angles  to  each  other.  In  crystals  of  all  other  systems,  the 
expansion  is  the  same  in  only  two  directions  (dimetric  system,  154,  &), 
or  it  is  different  in  all  three,  depending  upon  the  position  of  the 
crystallogenic  axes  to  each  other.  The  amount  of  expansion  in  some 
crystalline  compound  bodies,  e.  g.,  fluor  spar,  aragonite,  sulphate  of 
barytes,  quartz,  &c.,  is  found  to  be  greater  than  in  metals,  contrary  to 
the  generally-received  opinion. 

591.  Coefficient  of  expansion. — The  small  gain  in  length  in  a  rod 
1  foot  or  1  metre  long,  when  heated  from  32°  to  33°  F.,  or  from  0°  to  1° 
C.,  is  called  its  coefficient  of  linear  expansion. 

1.  Coefficient  of  linear  expansion.    If  the  length  of  the  bar  is  I,  at  the 
temperature  of  32°,  its  length  at  33°  is  I  -f  Z2T>  composed  of  its  original 
length,  Z,  and  a  small  fraction,  IK,  variable  with  the  substance  experi- 
mented on. 

If  the  rod  is  carried  successively  through  the  scale  of  temperatures,  it  gains, 
at  each  degree,  a  new  elongation,  which  experiments  show  to  be  nearly  constant, 
and  equal  to  IK,  so  that  if  the  rod  is  elevated  from  32°  F.,  to  t  degrees  above 
32°  F.,  its  total  gain  in  length  is  expressed  by  IKt,  and  its  new  length,  lt,  is 

I  -f  IKt,     or,  lt  =  l(i-\-  Kt). 

At  any  other  temperature,  I', — this  expression  becomes,  lt'  b  — _  1(1  -f-  Kt'},  and 
if  the  value  of  lt'  (any  temperature  above  32°),  is  sought  in  terms  of  It,  we  write 
approximately,  lt'  —  lt  [1  -f  K  (t'  —  <)]. 

The  coefficients  of  expansion  for  some  of  the  most  frequently  occur- 
ring solids  is  given  in  Table  III.,  in  terms  of  the  decimal  system. 

2.  The   coefficient    of  superficial   expansion,    is    obtained    from    the    expres- 
sions  for  linear  expansion,  by  substituting   S  and   St  for  I  and  lt ;   thus  :— 
St    =     S    (1  -f-  2  Kt),  where  2  K  replaces  K  in  the  formula  for  linear  expansion. 


HEAT.  415 

3.  The  coefficient  of  cubic  expansion,  is  the  small  fraction  of  its  volume, 
by  which  a  solid,  liquid,  or  gas  is  increased  when  heated  from  32°  to  33°  F. 
Assuming  the  expansion  to  be  proportional  to  temperature,  we  must  admit  the 
volume  V  at  t  degrees  and  at  32  degrees  to  be  proportional  to  the  cubes  of  their 
homologous  dimensions.  By  the  same  reasoning  as  before,  we  have,  therefore, 
the  formula;  V  =  V  (1  -\-  3Kt'),  by  which  the  increased  volume  (  V)  of  any 
mass  of  matter  may  be  calculated  when  the  value  of  V,  t,  and  K  £J-e  known. 

The  coefficient  of  cubic  expansion  may  also  be  determined  accurately  from 
the  specific  gravity  of  the  solid  taken  at  different  temperatures,  thus  :  — 

Let  (Sp.  Gr.)  and  (Sp  Gr.)'  represent  the  specific  gravities  of  any  solid  at  the 
two  temperatures,  t  and  t'  ;  let  W  be  the  weight  of  the  solid  under  trial,  V  its 
volume  at  32°,  and  K  the  co-efficient  to  be  found  j  then,  since  by  the  last 
expression,  we  know  the  value  of  the  solid  at  t°  and  t'°,  F  (1  +  3^)»  and 


F(l  -f  3£it',)  we  have  from  §  99  (Sp.  Gr.)  =  ,  and 

r   (L  ~T~ 


(Sp.    Gr.')  =  -  :  --  •      The  value  of  the  co-efficient  of  cubic  expansion, 
K  (1  —  j—  o  /L£  j 

is  obtained  from  the  reduction  and  combination  of  these  two  equations 

Thus.  x=     a.ar.-s.a 


Gr.)t 

This  coefficient  may  also  be  obtained  from  the  apparent  expansion  of  mercury. 

It  is  plain  that  all  questions  relating  to  the  expansion  of  solids,  may  be  solved 
by  these  expressions,  when  the  value  of  K  is  known  ;  and  that  this  quantity 
must  be  the  subject  of  exact  experimental  determination  in  each  solid.  Our 
limits  do  not  permit  the  description  of  the  various  means  by  which  the  linear 
expansion  of  solids  has  been  measured.  In  the  researches  of  Lavoisier  and 
Laplace,  a  bar  of  the  substance  under  examination  was  heated  in  a  water-bath. 
One  end  was  fixed,  the  other  free,  and  touched  the  end  of  a  lever,  acting  by  any 
expansion  of  the  bar,  and  causing  a  movement  observed  in  a  telescope  attached 
to  the  lever,  as  already  described  in  §  582.  The  expansions,  from  32°  to  212°, 
were  thus  'read  off  upon  a  scale  placed  at  a  proper  distance. 

The  capacity  of  hollow  vessels  is  increased  by  the  expan- 
sion of  their  walls,  to  the  same  amount  which  a  solid  mass  of  the 
same  material  and  volume  would  expand  by  a  like  change  of  tempera- 
ture. Hence  it  is  easy  to  calculate  from  the  known  co-efficient  of  glass, 
or  any  other  substance,  the  changes  of  capacity  of  hollow  vessels. 

The  amount  of  expansion  in  solids,  between  freezing  and  boiling, 
is,  after  all,  but  a  very  small  fraction,  being,  for  zinc,  which  is  the  most 
expansible  of  all  metals,  only  one  three-hundred  and  fortieth  of  its 
length  ;  while  glass  expands  only  about  one-third  of  this  quantity,  for 
a  like  change  in  temperature  (1  in  1248).  The  order  of  the  expansi- 
bility of  metals  and  glass  is  as  follows,  commencing  with  the  most  and 
ending  with  the  least  expansible:  —  zinc,  lead,  tin,  silver,  brass,  gold, 
copper,  bismuth,  iron,  steel,  antimony,  platinum,  glass. 

*  In  all  these  formulae,  t  is  taken  to  represent  the  number  of  degrees  above 
the  freezing  point. 


416  PHYSICS    OF    IMPONDERABLE    AGENTS. 

This,  it  is  worth  while  to  remark,  is  also  very  nearly  the  order  of 
compressibility  of  the  same  substances. 

Ice  is  more  dilatable  than  zinc,  in  the  ratio  of  j£T  to  ^^.  The  con- 
traction of  ice  by  cold  has  been  observed  for  30°  or  40°  below  the 
freezing  point. 

The  most  expansible  solids  are,  in  general,  the  most  fusible,  e.  g., 
ice,  zinc,  &c. ;  while  the  least  expansible  metal,  platinum,  is  also  the 
least  fusible ;  but  in  other  cases  this  comparison  fails. 

The  hardness,  ductility,  and  other  physical  properties  of  the  metals, 
appear  to  sustain  no  relation  to  their  expansibility. 

592.  The  ratio  of  expansion  increases  with  the  temperature. — 
Between  32°  and  212°  F.,  the  increase  in  the  coefficient  of  expansion 
in  solids,  is  hardly  appreciable  ;  but  for  high  temperatures,  the  increase 
becomes  a  considerable  quantity.     Regnault  has  determined  the  mean 
coefficients  for  glass,  when  blown  in  hollow  vessels  between  zero  C.  and 
the  following  temperatures — the  coefficients  being  in  each  case  ten-mil- 
lionths  of  the  whole : — 

Coefficients.      K.  =  276      284      291      298      306      313 
Temperatures,  C.       100°     150°    200°    250°    300°    350° 
This  increase  in  the  coefficients  of  expansion  of  bodies  by  rise  in 
temperature,  is  probably  due  to  the  distance  between  the  particles  aug- 
menting with  the  heat.     Their  mutual  cohesion  is  thus  more  readily 
overcome. 

In  the  case  of  glass,  which  has  been  more  carefully  studied  than  any  other 
solid,  it  appears  from  the  results  of  Regnault,  not  only  that  glasses  of  different 
composition  differ  in  their  coefficient  of  expansion,  but  the  same  glass,  in  solid 
rods,  expands  more  than  in  the  form  of  tubes ;  and  that  great  and  sudden 
changes  of  temperature,  as  in  making  a  thermometer  (573),  may  vary  the  co- 
efficient of  expansion,  owing  probably  to  slow  molecular  changes  in  the  glass. 

593.  Amount  of  force  exerted  by  expansion. — The  enormous 
force  exerted  by  an  expanding  or  contracting  solid,  may  be  conceived 
by  estimating  (from  the  coefficient  of  elasticity,  §  161)  the  power  requi- 
site to  produce  an  equal  change  of  length  by  compression  or  by  traction. 

Assuming,  in  round  numbers,  the  coefficient  of  elasticity  of  iron  at 
212°  =  21,000  kilogrammes,  a  bar  of  iron,  one  metre  long,  expands 
0*0012  m.,  if  heated  from  32°  to  212°  F.  Therefore  a  bar  of  iron,  one 
square  inch  in  section,  raised  from  the  temperature  of  freezing  to 
boiling  water,  expands  with  a  force  of  35,847  pounds ;  or  it  exerts  a 
force  of  199-15  pounds  for  every  degree  Fahrenheit  that  its  tempera- 
ture is  elevated. 

When  a  bar  of  iron  one  inch  square  has  its  temperature  changed 
12°  F.,  its  expansion  or  contraction  exerts  a  strain  equal  to  one  tor 


HEAT.  417 

weight ;  and  if  varied  from  10°  to  90°,  a  common  change  from  winter 
to  summer,  it  expands  with  a  force  of  about  seven  tons. 

The  force  of  contraction  in  a  cooling  solid,  is  equal  to  the  force  of  expansion 
when  it  is  heated.  This  force  is  constantly  used  in  the  arts. 

The  walls  of  an  arched  gallery  in  the  Museum  of  Arts  and  Trades  in  Paris, 
having  bulged  outwards  by  the  weight  of  the  arch,  460 

Molard  placed  a  series  of  iron  bars,  fig.  460,  through 
the  wall,  secured  by  nuts  on  the  outside.  The  alter- 
nate bars  were  first  heated  by  charcoal  furnaces, 
and,  when  they  were  expanded,  the  nuts  were 
screwed  firmly  up  to  the  walls.  As  the  bars  cooled, 
they  drew  up  the  walls  to  an  extent  equal  to  their 
contraction.  The  other  half  of  the  bars  were  in 
like  manner  heated  and  cooled ;  and,  by  a  series 
of  such  operations,  the  walls  were  gradually  brought 
to  an  erect  position.  A  similar  proceeding  was 
adopted  in  the  Cathedral  at  Armagh,  and  in  a  store- 
house in  Providence,  R.  I. 

Wheelwrights  and  coopers  make  iron  tires  and  hoops  a  little  smaller  than 
the  wheel  or  barrel  for  which  they  are  designed ;  these  are  applied  in  a  heated 
state,  and  quenched;  as  they  contract,  they  bind  the  parts  firmly  together.  The 
heavy  wrought-iron  rims  of  the  driving-wheels  of  locomotive  engines,  are  shrunk 
on  in  the  same  way.  Rail  car  wheels  are  often  cast  with  split  hubs,  to  allow 
play  for  the  unequal  contraction  of  the  heavy  rims  and  lighter  arms,  or  the  latter 
would  be  broken  at  the  hub,  or  rim,  on  cooling.  The  same  precaution  is  requi- 
site in  all  castings  where  heavy  and  light  parts  are  united.  Boiler-plates  are 
riveted  together  with  red  hot  rivets,  which,  on  cooling,  draw  the  plates  together 
more  firmly  than  any  other  means  could  do.  When  the  stopper  of  a  bottle 
sticks,  it  may  usually  be  withdrawn  by  heating  the  neck  of  the  bottle  with  a 
spirit-lamp,  or  with  a  cloth  dipped  in  warm  water.  The  neck  is  thus  expanded, 
and  the  stopper  is  released. 

594.  Common  phenomena  produced  by  the  expansion  of 
solids. — In  every-day  life  may  be  seen  numerous  phenomena,  caused 
by  the  expansion  and  contraction  of  substances  by  variations  in  tem- 
perature. 

A  stove  snaps  and  crackles  when  the  fire  is  lighted,  and  again  when  it  is 
extinguished,  because  of  the  unequal  expansion  and  contraction  of  the  different 
parts.  The  pitch  of  a  piano-forte,  or  harp,  is  lowered  in  a  warm  room,  owing  to 
the  expansion  of  the  strings  being  greater  than  that  of  the  wooden  frame  which 
supports  them ;  and  for  the  reverse  reason,  the  pitch  is  raised,  if  the  room  is 
cooled. 

Nails  driven  into  wood  often  become  loose;  the  expansion  and  contraction  of 
the  nails,  through  variations  of  temperature,  gradually  enlarging  the  holes. 
A  gate  in  an  iron  railing  may  be  easily  shut,  or  opened,  in  a  cold  day,  but  only 
with  difficulty  in  a  warm  day,  because  the  gate  itself,  and  the  surrounding  rail- 
ings, have  become  expanded  by  the  heat. 

Astronomical  instruments, placed  on  elevated  buildings,  are  sometimes  sensibly 

deranged  by  the  expansion  of  the  walls  exposed  to  the  sun.     Iron  and  platinum 

wires  may  be  successfully  soldered  into  glass,  because  their  mutual  expansibility 

differs  very  little,  while  silver,  gold,  and  copper,  similarly  treated,  crack  out  aa 

38 


418  PHYSICS    OF    IMPONDERABLE    AGENTS. 

the  joint  co«ls,  because  their  expansibility  is  much  greater  than   that  of  t\ie 
glass. 

Glass  and  earthen  vessels,  with  thick  walls,  are  liable  to  break  when  hvt 
liquids  are  suddenly  poured  into  them.  The  surfaces  in  contact  with  the  tot 
liquid,  expanding  before  the  other  parts  are  affected,  have  a  tendency  to  warp, 
or  bend  the  sides  unequally,  and  the  brittle  material  breaks.  We  use  this  pecu- 
liarity of  glass  to  convert  broken  vessels  in  the  laboratory  to  useful  purposes. 
Since,  by  a  red-hot  iron,  or  the  point  of  a  burning  coal,  we  can  lead  a  crack  in 
any  direction,  and  thus  safely  divide  the  thickest  glass. 

Bunker  Hill  Monument,  an  obelisk  of  granite,  two  hundred  and  twenty-one 
feet  high,  moves  £as  observed  by  Horsford),  at  top,  with  the  sun's  rays,  so  as  to 
describe  an  irregular  ellipse  with  the  sun's  motion.  This  movement  commences 
about  7  A.  M.,  of  a  sunny  day,  and  has  its  maximum  in  the  afternoon.  In  a  cloudy 
day,  no  motion  exists,  and  a  shower  restores  the  shaft  to  its  position ;  showing 
that  the  heat  which  produces  the  deflection  penetrates  but  a  short  distance. 

Railroad  bars  must  be  laid  with  open  joints,  or  their  expansion  and  contrac- 
tion between  the  extremes  of  natural  temperature  would  destroy  the  road. 
Between  4°  F.,  and  100°  F.,  the  expansion  of  one  mile  of  rails  (5280  feet)  is  5 
feet  7  inches. 

The  two  tubes  of  the  Britannia  Bridge  (172),  are  secured  at  the  centre  to  the 
main  pier,  called  the  Britannia  Tower  ;  but  the  other  points  of  support  rest  on 
friction  rollers,  admitting  of  free  motion  with  changes  of  temperature.  An 
increase  of  26°  F.,  from  32°  to  58°,  gives  a  total  increase  of  3£  inches  in  the 
whole  length  of  each  tube,  or  one-half  that  amount  at  each  end.  The  daily 
change  of  dimensions  varies  from  half  an  inch  to  three  inches ;  the  maximum 
and  minimum  effects  being  about  3  p.  M.,  and  3  A.  M.,  respectively.  The  same 
changes  noticed  by  Horsford  in  Bunker  Hill  Monument,  are  produced  in  this 
bridge  by  the  sun's  rays.  The  heated  portions  of  the  tube  expand,  warping  the 
free  ends  to  the  cooler  side  about  two  and  a  half  inches,  both  vertically  and 
laterally. 

The  Victoria  Bridge,  at  Montreal,  shows  the  same  phenomena,  but  not  so  re- 
markably, as  the  several  tubes  are  much  shorter  (page  137). 

Fire  regulators. — The  expansion  of  solid  bodies  is  often  used  to 
regulate  the  temperature  of  stoves. 

A  metallic  bar,  usually  of  copper,  is  placed  within,  or  beside  the  stove  or 
furnace,  and  as  it  becomes  heated  it  expands,  and  moving  a  lever,  turns  a 
damper,  or  valve,  thus  regulating  or  arresting  the  draught,  with  perfect 
fidelity  and  accuracy. 

595.  Unequal  expansion  of  solids. — Breguet's  thermometer, 
already  described  (580),  is  a  beautiful  example  of  the  application  of 
unequal  expansion  to  measurement  of -temperatures. 

If  a  compound  bar  of  iron  and  copper,  secured  together  by  rivets, 
fig.  461,  is  heated,  the  copper  ex-  461 

panding  more  than  the  iron,  the  ^ — ^—> :~  -i^n^— J^i 
bar  is  thereby  curved,  as  seen  in  451 

fig.  4616,  to  accommodate  the  ir- 
regularity of  length  resulting.    If 
this  compound  bar  is  cooled  below  the  temperature  at  which  the  two 
metals  were  united,  it  curves  in  the  opposite  direction. 


HEAT. 


419 


596.  Compensating  pendulums. — The  length  of  a  pendulum 
alone  determines  its  times  of  oscillation  (82).  A  difference  of  one 
one-hundredth  of  an  inch  in  a  seconds  pendulum  would  cause  a  clock 
to  vary  eleven  seconds  in  twenty-four  hours,  and  a  difference  of  60°  F. 
produces  this  effect. 

In  ordinary  clocks,  this  defect  in  the  length  of  the  pendulum  is 
remedied,  by  raising  or  depressing  the  ball  at  the  end  of  the  rod  by 
means  of  a  screw.  Pendulums  in  which  this  defect  is  remedied  by  a 
self-adjusting  arrangement,  are  called  compensating  pendulums.  The 
compensation  is  effected  by  the  unequal  expansion  either  of  mercury 
and  glass,  or  of  different  metals. 

Harrison's  gridiron  compensating  pendulum,  fig.  462,  is  one 
of  those  most  commonly  employed.  The  large  weight  at  the  bottom 
of  this  pendulum  is  supported  by  a  series  of  rods  of  452 

brass  and  steel  arranged  in  alternate  pairs.  The  middle 
rod  is  of  steel,  and,  like  all  the  other  steel  rods,  is  shaded 
in  our  figure.  The  cross-pieces  connect  the  two  systems 
of  rods,  alternately  at  top  and  bottom,  in  such  a  way 
that  while  the  expansion  of  the  steel  rods  lengthens  the 
pendulum  the  expansion  of  the  brass  rods  shortens  it. 
The  length  of  the  pendulum  is  plainly  the  sum  of  the 
length  of  the  steel  rods  less  the  sum  of  the  brass  rods  (the 
supporting  crotchet  being  added  to  the  length  of  the 
steel  rods),  each  pair  of  rods  being  reckoned  as  only 
one  rod.  In  order  that  the  length  of  the  pendulum 
should  remain  invariable  with  changes  of  temperature, 
it  is  obvious  that  the  expansion  of  the  two  systems  of 
rods  must  exactly  balance  each  other. 

To  determine  the  length  of  rods  required  to  effect  this,  let 
L  and  I  be  the  sum  of  the  lengths  of  the  steel  and  brass  rods 
respectively,*  and  K  and  K'  their  respective  coefficients  of 
expansion.  Then,  if  the  amount  of  expansion  in  both  systems  is  equal,  L  K 
will  equal  IK'.  But  since,  at  London,  the  length  of  the  seconds  pendulum  is 
39-14056  inches  (82),  it  follows  that  L  —  I  =  39-14056  inches. 

If,  therefore,  we  take  from  Table  III.,  the  values  of  K  and  K',  and  combine 
these  two  equations,  we  shall  find  the  respective  lengths  of  L  and  I. 


L  = 


K' 


K'  —  K 


•r  X  39-14056  inches,    I  = 


K 


K'—K 


X  3914056  inches. 


But  the  position  of  the  centre  of  oscillation,  which  determines  the  virtual 
length  of  the  pendulum  (83),  may  vary,  although  the  sensible  length  remains 
unchanged.  Hence  the  necessity  of  adjusting  the  position  and  mass  of  the 
suspended  weight  after  the  length  of  the  rods  is  approximately  accurate. 

In  Graham's  compensating  pendulum,  fig.  463,  the  rod,  a,  J>,  is  of 


420 


PHYSICS  OF  IMPONDERABLE  AGENTS 


glass,  and  the  ordinary  weight  is  replaced  by  a  glass  vessel  containing  mercury 
sustained  in  a  metallic  stirrup.  When  the  temperature  rises,  the  pendulum 
lengthens,  and  the  mercury  also  expanding,  rises  in  the  glass. 

The  compensation  in  this  instrument  is  not  quite  perfect,  since  the  position  of 
the  centre  of  gravity  (which  remains  unchanged  by  the  construc- 
tion) does  not  entirely  coincide  with  the  centre  of  oscillation,  on 
which  the  virtual  length  of  the  pendulum  depends. 

Mr.  Henri  Roberts'  compensating  pendulum  is 
remarkable  for  its  extreme  simplicity.  The  rod  of  the  pendulum, 
fig.  464,  is  of  platinum,  and  supports  at  its  lower  end  a  disk  of 
zinc.  The  centre  of  gravity  of  this  disk  will  465 

always  be  preserved  at  the  same  distance  from 
the  point  of  suspension,  if  the  expansion  of  the 
platinum  rod  is  equal  to  that  454 

of  the  zinc  disk ;  this  condition 
is  obtained  when  the  radius  of 
the  disk  is  equal  to  one-third 
of  the  length  of  the  rod. 

Martin's  compensa- 
ting pendulum  is  a  com- 
pound bar  of  iron  and  copper 
soldered  together  throughout 
•their  length,  and  fixed  trans- 
versely upon  the  pendulum 
rod,  fig.  465.  The  copper, 
being  the  most  expansible,  is 
placed  below  the  iron.  When  the  temperature  rises,  and  the  centre  of  oscilla- 
tion is,  by  the  expansion  of  the  pendulum,  removed  to  a  greater  distance  from 
the  point  of  suspension,  the  copper,  expanding  more  than  the  iron,  bends  the 
rod  into  the  curve,  mfnt,  whereby  the  metallic  balls,  m  m,  at  the  extremities  of 
the  rods,  are  raised,  and  being  brought  closer  to  the  point  of  suspension,  compen- 
sate for  the  increased  distance  of  the  weight  of  the  pendulum  from  that  point. 
If  the  temperature  is  lowered,  the  rod  bends  into  the  curve,  m'  c  m',  and  the 
balls  are  lowered.  These  balls  are  of  such  a  size,  and  placed  at  such  a  position 
upon  the  compound  bar,  that  the  centre  of  oscillation  is  not  displaced  by  varia- 
tions in  temperature,  and  thus  perfect  compensation  is  produced. 

Compensating  balance  wheels  of  watches  and  chronometers 

are  constructed  precisely  on  the  plan  of  Martin's  pendulum.  The  balance  wheel 
of  a  watch  varies  with  changes  of  temperature, — the  duration  of  an  oscillation 
depending  on  the  radius  of  the  wheel,  the  strength  of  466 

the  spring,  and  the  mass  of  its  rim.  The  expansion 
of  the  wheel,  by  enlarging  the  radius,  retards  the  time- 
piece, and,  conversely,  cold  accelerates  it.  The  three 
metallic  arcs,  a  a  a,  fig.  466,  are  designed  to  counteract 
and  correct  the  effect  of  expansion  on  the  wheel.  Each 
arc  is  composed  of  two  strips  of  metal,  the  most  expan- 
sible being  placed  outside.  Heat,  therefore,  carries  the 
masses,  71  n  n,  inward  and  nearer  to  the  axle  of  the  wheel, 
while  cold  throws  them  outward,  thus  preserving  the  vir- 
tual length  of  the  radius  under  all  changes  of  temperature.  Any  errors  of  com- 
pensation are  adjusted  by  turning  the  masses,  nn«,  on  the  screws  at  the  ends 
of  the  arcs. 


HEAT.  421 

II.     EXPANSION  OF  LIQUIDS. 

597.  General  statement. — All  liquids  expand  by  heat  more  than 
solids ;  thus  mercury,  the  least  expansible  of  all  liquids,  expands  more 
than  zinc,  the  most  expansible  of  all  solids. 

The  rate  of  expansion  in  liquids  is  not  so  uniform  as  it  is  in  solids, 
and  especially  near  their  points  of  solidification  and  vaporization  they 
are  subject  to  great  irregularities. 

598.  Apparent  and  absolute  expansion. — We  have  already  (576) 
noticed  the  fact  that  it  is  only  the  apparent,  and  not  the  absolute,  expan- 
sion of  mercury  which  is  read  in  the  thermometer.     It  is  plain  that 
in  any  case  the  absolute  expansion  of  a  liquid  must  be  the  sum  of  its 
apparent  expansion,  and  of  the  increased  capacity  of  the  containing 
vessel  (591)  at  the  given  temperature.     Either  two  of  these  quantities 
being  known,  the  third  can  be  calculated. 

The  absolute  expansion  of  mercury,  being  one  of  the  most  important 
constants  in  physics,  and  one  on  which  many  others  depend,  has  been 
determined  with  the  greatest  accuracy.  This  'determination  was  origi- 
nally made  by  Dulong  and  Petit,  and  has  been  confirmed  and  corrected 
more  recently  by  Regnault. 

The  method  giving  most  exact  results  depends  on  the  familiar 
principle  of  hydrostatics  (202),  that  the  heights  of  liquid  columns  in 
communicating  vessels  are  in  the  inverse  ratio  of  the  specific  gravities 
of  the  liquids.  What  is  here  true  of  different  liquids  is  of  course  true 
of  the  same  liquid  at  different  temperatures.  To  determine  this  point 
accurately,  a  glass  tube,  bent  into  a  syphon,  is  filled  with  mercury,  and 
so  arranged  that,  while  the  two  legs  are  respectively  exposed  to  the 
required  temperatures,  the  corresponding  heights  may  be  exactly  mea- 
sured by  a  cathetometer.  The  coefficient  of  expansion  for  each  tem- 
perature may  then  be  calculated  from  (591/3)  by  meaijs  of  the  specific 
gravities  thus  determined. 

Let  C  and  C'  represent  the  two  columns;  H  and  (S}).  Gr.)  the  height  and 
specific  gravity  of  C  at  32°,  and  H'  and  (Sp.  Gr.)'  the  height  and  specific 
gravity  of  the  column  C'  at  t°.  Then,  hy  202,  H  (Sp.  Or.)  —  H'  (Sp.  Or.)'..  Let 
K  represent  the  coefficient  of  absolute  expansion  in  mercury,  and  hy  591  and 
99,  we  have  (Sp.  Or.)  =  (Sp.  Or.)'  (1  -f-  Kt.)  Hence  the  value  of  K,  obtained 

H'  —  H 

by  combining  these  equations,  is,  K  =  — 

fit 

The  mean  absolute  expansion  of  mercury  was  by  this  method  found  by  Dulong 
and  Petit  to  be  between  32°  and  212°  F.  for  1°  F.,  K  =  ^ff  =  0*0001001. 
This  number  has  been  corrected  by  the  later  researches  of  Regnault  to 
K=  0-00010085  for  each  degree  of  Fahrenheit's  scale;  or,  K  =  0-00018153  for 
each  degree  Centigrade. 

The  increase  of  the  coefficient  of  expansion  for  mercury,  with  increase  of 
temperature  already  alluded  to  (576),  is  shown  in  the  following  table  copied 
from  Cooke's  Chemical  Physics,  p.  510.  The  degrees  are  Centigrade. 

38* 

f 


422 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


COEFFICIENT  OF  EXPANSION  FOR  MERC  CRY. 


True  Temperature 
ty  Air  Thermo- 
meter. 

Mean  Coefficient  of 
Expansion  of  Mercury 
from  00  to  «o. 

Actual  Coefficient  of 
Expansion  from  <o  to 
(t  +  1)0. 

Volumes  of  Equal 
Weights. 

0° 

0 

0-00017905 

1-0000000 

30 

0-00017976 

0-00018051 

1-0053928 

50 

0-00018027 

0-00018152 

1-0090135 

70 

0-00018078 

0-00018253 

1.0126546 

100 

0-00018153 

0-00018305 

1-0181530 

150 

0-00018279 

0-00018657 

1-0274185 

200 

0-00018405 

0-00018909 

1-0368100 

250 

0-00018531 

0-00019161 

1-0463275 

300 

0-00018658 

0-00019413 

1-0559740 

350 

0-00018784 

0-00019666 

1-0657440 

The  last  column  of  this  table  shows  the  volume  to  which  one  cubic  centimetre 
of  mercury  will  expand  when  heated  to  the  temperatures  given  in  the  first 
column.  Whenever  the  mean  coefficient  between  0°  and  t°  (as  given  in  the 
second  column)  is  known,  the  corresponding  volume  may  be  calculated  by  the 
formula  V  =  V  (I  -\-  Kt)  ;  and,  by  interpolation,  the  volume  can  be  calculated 
for  temperatures  for  which  the  coefficient  has  not  been  determined. 

599.  Correction  of  the  observed  height  of  the  barometer  for 
temperature.  —  As  the  volume  and  density  of  mercury  vary  with  the 
temperature,  the  height  of  the  mercurial  column  in  a  barometer  varies 
not  only  with  changes  of  the  atmospheric  pressure,  but  also  with  changes 
in  temperature.  Before  comparing  barometric  observations,  therefore, 
made  at  different  times,  it  is  necessary  to  reduce  the  observed  heights 
of  the  mercurial  column  to  the  height  they  would  have  at  some  standard 
temperature.  . 

The  principles  enunciated  in  the  last  section  enable  us  to  obtain  the  follow- 
ing value  for  the  height  of  the  barometer^  reduced  to  32°  F. 


H  =  H'  —  H' 


99  1  6 


,  t  being  the  degrees  Fahrenheit  above  freezing  ;    or, 
t 

when  t  is  given  in  degrees  of  the  Centigrade  scale. 


H  =  H'  —  H'  -  •  —  , 
5508  -Jr  t 

The  true  height  of  the  barometer  is  therefore  to  be  obtained  by  subtracting 
the  correction  from  the  observed  height  when  the  temperature  is  above  the 
freezing  point.  There  is  also  a  small  correction  to,be  made  for  the  expansion 
of  the  scale,  which  for  present  purposes  may  be  neglected. 

600.  Apparent  expansion  of  mercury.  —  The  apparent  expansion 
of  mercury  in  glass  is  readily  determined  by  means  of  the  simple 
apparatus,  seen  in  fig.  467,  consisting  only  of  a  glass  tube,  r,  drawn 
out  into  a  narrow  neck,  which  is  recurved  so  as  to  dip  conveniently  into 
the  cup  c.  The  weight  of  the  empty  tube  is  first  taken,  and  it  is  then 
filled  with  mercury  in  the  manner  described  in  $  568  ;  taking  care  to 
expel,  by  continued  boiling,  the  last  traces  of  air  and  moisture.  The 
tube  and  its  contents  are  then  cooled  to  32°  F.  by  immersion  in  melting 


HEAT. 


423 


ice,  the  point  o  being  kept  constantly  beneath  the  mercury  in  c.  It  is 
then  weighed  again,  and  thus  by  deducting  the  weight  of  the  empty 
tube  we  learn  the  weight  ( W]  of  the  mercury  it  contains  4G7 
at  32°.  Lastly,  it  is  exposed  to  a  constant  temperature,  t° 
(say  of  212°  F.,  see  fig.  443),  and  the  weight  of  the  escaping 
mercury  (w]  ascertained.  The  weight  of  the  mercury  which 
fills  the  tube  at  t°  is  therefore  W —  w.  From  these  data  the 
coefficient  of  apparent  expansion  is  calculated. 

The  volume,  V,  of  a  weight  of  mercury,  represented  by  W —  to 
W—w 

at  32°,  is  V  =  .   Now  this  weight  of  mercury  at  t°  filled 

(Sp.  Or.) 

the  same  volume  (i.  e.,  the  whole  apparatus),  not  regarding  the 
expansion  of  the  glass,  which  was  filled  by  the  weight,  W,  at  32°. 

W 

The  volume  of  the  weight  W  —  to  at  t°  is  therefore  V  = . 

(fy.  Gr.) 

Let    the    coefficient   of    apparent    expansion    be    K,    and    then 
V  =  V(l  -f-  Kt);  then  substituting  the  values  of  Fand  V, 

w 

and  reducing,  we  have  K  = =  for  common  French 

W  —  to)  t 

glass  s^. 

A  similar  mode  of  experiment  gives  of  course  the  coefficient 
of  apparent  expansion  for  all  other  liquids.  It  is  also  applicable  for  the  deter- 
mination of  the  coefficient  of  expansion  of  all  solids  not  acted  on  by  mercury, 
since  it  is  true  that  the  coefficient  of  apparent  expansion  for  mercury  is  equal 
to  the  coefficient  of  absolute  expansion  less  the  coefficient  of  expahsion  of  the 
material  for  the  containing  vessel.  As  the  coefficient  of  absolute  expansion  for 
mercury  is  known  with  the  greatest  accuracy,  it  follows  that,  by  an  application 
of  the  reasoning  in  this  section,  we  have  the  means  of  determining  the  coefficient 
of  expansion  in  glass  and  other  solids. 

601.  Amount  of  expansion  of  liquids. — Liquids  expand  very 
unequally  for  equal  increments  of  heat ;  the  law  of  their  expansion 
has  not  been  fully  determined.  Generally  the  most  expansible  liquids 
are  those  whose  boiling  points  are  the  lowest.  Those  whose  boiling 
points  are  high  have  usually  a  small  but  very  regular  expansibility, 
especially  at  temperatures  much  below  their  boiling  points. 

The  rate  of  expansion  in  all  liquids  increases  with  the  temperature, 
but  it  varies  with  each  substance  according  to  laws  not  well  understood. 

Between  32°  and  212°,  mercury  expands  1  in  55,  water  1  in  21*3, 
sulphuric  acid  1  in  17,  alcohol  1  in  9  -f-,  &c.  See  Table  IV. 

The  statement,  in  the  first  edition  of  this  work,  that  in  many  liquids  of  analo- 
gous chemical  constitution,  the  rate  of  expansion  is  nearly  uniform  at  equal 
distances  from  their  respective  boiling  points,  appears,  from  the  observations  of 
Pierre,  not  to  be  sustained. 

The  expansibility  of  liquids  is  not  in  proportion  to  their  density,  but 
is  more  nearly  the  inverse  of  this  than  in  any  other  known  ratio. 


424 


PHYSICS  OP  IMPONDERABLE  AGENTS. 


1000 


468 
960    940   920 


900     880 


602.  Expansion  of  liquids  above  their  boiling  points. — The 

late  researches  of  C.  Drion*  show  that  the  coefficient  of  expansion  in 
liquids,  above  their  boiling  points,  increases  at  an  accelerated  ratio,  and 
even  surpasses  the  coefficient  of  expansion, in  gases.  As  long  since  as 
1835,  Thilorier,  in  his  memoir  on  liquid  carbonic  acid,  states  that  this 
liquid  expands  between  Q°  and  30°  C.  (32°  to  86°  F.),  four  times  as  much 
as  air  expands  for  the  same  range  of  temperature,  being  as  ££f  for  the 
liquid  gas  to  236°7-  f°r  an*-  Twenty  volumes  of  liquid  carbonic  acid, 
between  32°  and  86°  F.,  become  therefore  twenty-nine  volumes. 

Liquid  sulphurous  acid,  and  cyanogen  present  the  same  apparent 
anomaly,  as  well  as  certairi  fluids  found  in  the  minute  cavities  of  topaz 
and  quartz  crystals. 

The  experiments  of  Drion  were  made  on  chlorid  of  ethyl,  sulphur- 
ous acid,  and  hyponitric  acid. 

Curves  of  expansion  of  liquids. — The  variation  in  the  expansion 
of  liquids  may  be  graphically  represented  as  in  fig.  468.  The  diagram 
shows  the  lines  representing  the 
expansion  of  six  liquids.  In  each 
case  1000  parts  of  liquid  are  taken 
at  212°  F.  The  horizontal  lines  30 
(reading  from  above  downwards) 
show  the  bulk  9f  the  liquid  at 
temperatures  below  the  boiling 
point.  These  temperatures  are 
represented  in  degrees  of  Fah-  144 
renheit's  scale  on  the  left  hand 
column,  and  in  Centigrade  de- 
grees on  the  right  hand.  The  line  A  indicates  the  contraction  of  mer- 
cury ;  B,  that  of  water ;  C,  for  alcohol ;  D,  for  wood  spirits ;  E,  for 
formic  ether ;  F,  for  terchlorid  of  silicon  ;  G,  for  ordinary  ether. 

Thus  at  108°  below  the  boiling  point  (at  104°  F.),  1000  parts  water  have 
contracted  into  966  parts ;  alcohol  into  931  parts  j  and  formic  either  into  918 
parts. 

603.  The  amount  of  force  exerted  in  the  expansion  of  liquids 

is  enormous ;  being  equal  to  the  mechanical  force  required  to  compress 
the  expanded  liquid  into  its  primitive  volume. 

Thus  the  expansion  of  mercury  for  10°  F.,  is  -0010085.  Its  compressibility 
for  a  single  atmosphere  is  -0000053.  Therefore  the  amount  of  force  required  to 
restore  the  mercury  to  its  original  bulk,  after  heating  it  10°  F.  is  equal  to  190 
atmospheres  (10085  -r-  53  =  190),  or  2850  pounds  pressure  to  a  square  inch. 
Owing  to  this  enormous  force  exerted  during  expansion,  closed  vessels  filled 
with  liquid,  however  strong  they  may  be  made,  burst  when  heat  is  applied. 


*  Ann.  de  Ch.  et  de  Phys.  1859. 


HEAT. 


425 


604.  Expansion  of  •water. — Water,  which  presents  so  many  re- 
markable exceptions  in  its  physical  history,  does  so  in  no  respect 
more  than  in  the  singular  irregularities  observed  in  its  expansion  for 
equal  increments  of  temperature  between  32°  469 

and  212°.  Its  total  expansion  for  this  range  is 
by  no  means  large,  while  its  coefficient  of  ex- 
pansion is  found,  by  an  examination  of  Table 
IV.,  to  be  smaller  than  that  of  any  liquid 
except  that  of  mercury.  The  expansion  of 
water,  which  is  irregular  through  the  whole 
range,  from  freezing  to  boiling,  is  especially  so 
between  32°  and  40°  F.  While  all  other  liquids 
are  most  dense  at  their  freezing  points,  the 
maximum  density  of  water  occurs  some  degrees 
above  that  point  (39°'2  F.),  and  above  or  below 
this  temperature  it  expands. 

Maximum  density  of  water.— To  illustrate, 
by  experiment,  this  signal  exception  in  water  to  the 
ordinary  laws  of  expansion,  a  water  thermometer,  like 
fig.  469,  may  be  used.  The  flask,  holding  about  a 
quart,  is  filled  with  water,  and  the  tube  passing  into 
it  is  secured  water-tight  by  a  brass  cap  or  well-fitting 
cork,  so  that  at  ordinary  temperatures  the  column 
of  water  stands  at  some  convenient  point  on  the 
scale  of  equal  parts.  It  is  then  set  in  a  cold  room 
(bolow  freezing),  and  the  loss  of  temperature  indi- 
cated by  the  fall  of  the  column  of  water,  is  more 
accurately  noted  by  a  mercurial  thermometer  seen  in 
the  figure  placed  within  the  flask.  When  that  tem- 
perature reaches  about  42°  F.  (6°  C.)  the  fall  of  the 
water  column  ceases — it  comes  -to  rest  for  a  short 
time,  and  at  39°  or  thereabouts  (4°  C.),  it  is  seen  to 
mount  more  and  more  rapidly  as  the  temperature 
falls,  until  it  reaches  32°  (or  even  lower,  if  the  apparatus  is  kept  quite  still). 

If  the  apparatus  is  filled  with  water  near  the  temperature  of  maximum  density, 
and  placed  in  a  warmer  room,  we  have  evidence  of  the  converse,  and  not  less  re- 
markable fact,  that  expansion  equally  occurs,  whether  we  heat  or  cool  the  water. 
These  results  are  somewhat  obscured  by  the  expansion  of  the  glass ;  but  for  a 
few  degrees  above  and  below  38°,  the  density  of  water  is  nearly  uniform. 

At  the  moment  of  freezing,  water  expands  about  ten  per  cent,  of  its  volume, 
and  the  fact  is  often  evidenced  in  the  apparatus  here  figured,  by  &jet  d'eau  from 
the  tube  at  the  moment  of  freezing. 

Owing  to  the  difficulty  of  compensating  ihe  errors  involved  in  the  expansion 
of  the  containing  vessels,  the  point  of  maximum  density  cannot  be  settled  with 
absolute  accuracy.  Hassler  assumed  it  at  39-83  F.  in  his  determination  of  the 
value  of  the  United  States  standards  of  measure.  Gineau  determined  the 
French  unit  of  weight  at  40°  F.  (4-5  C.),  and  Despretz,  in  1839,  fixed  it  at 
39°-2  or  4°  C.  The  later  researches  of  Plucker  and  Geissler  reduced  it  to 


426  PHYSICS    OF    IMPONDERABLE    AGENTS. 

38°-84;  but  it  is  agreed  by  physicists  to  assume  4°  C.,  or  39°-2  F.,  as  represent- 
ing the  true  point  of  maximum  density  for  water. 

The  apparatus  shown  in  fig.  470,  serves  well  to  illustrate  the  effect  of  thi3 
law  in  the  freezing  of  lakes  and  rivers.  A  glass  jar,  around  470 

the  central  part  of  which  is  fitted  a  metallic  vessel,  c,  is  pro- 
vided above  and  below  with  two  delicate  thermometers,  1 1', 
entering  the  sides  of  the  jar  horizontally  by  openings  drilled 
for  that  purpose.  After  filling  the  jar  with  water,  a  freezing 
mixture  of  ice  and  salt  is  placed  in  c,  which  rapidly  cools  the 
water.  The  two  thermometers  continue  to  indicate  nearly  the 
same  temperature  until  the  water  is  cooled  to  39°-2  F.,  when  it 
will  be  observed  that  the  lower  thermometer  remains  at  that 
point,  while  the  upper  one  indicates  a  lower  temperature,  until 
it  finally  reaches  32°  F.,  or  even  lower. 

The  explanation  of  these  phenomena  is,  that  the  water, 
cooled  by  the  freezing  mixture,  becomes  more  dense  and  sinks, 
while  other  and  lighter  portions  rise,  to  be  cooled  and  sink 
in  turn.  Thus  a  system  of  currents  is  established,  by  which 
the  whole  of  the  water  gradually  reaches  the  temperature  of  39°-2.  On  cooling 
below  this  point,  the  water  expands,  and,  thus  becoming  lighter,  the  colder 
portion  remains  at  the  surface,  and  is  further  cooled  by  the  freezing  mix- 
ture, while  the  water  in  the  lower  part  of  the  vessel,  not  coming  in  contact 
with  the  freezing  mixture,  and  being  no  longer  disturbed  by  currents,  remains 
at  the  temperature  of  39° -2. 

Effects  of  the  unequal  expansion  of  water. — Under  the  influ- 
ence of  this  law  of  unequal  expansion  in  water,  the  cold  of  our  most 
severe  winters  produces  only  a  comparatively  thin  covering  of  ice  upon 
the  lakes  and  rivers.  Water  freezes  at  32°,  but,  before  that  tempera- 
ture can  be  reached,  expansion  sets  in  at  the  surface,  and  the  water, 
although  colder,  is  specifically  lighter  than  the  warmer  water  below, 
and,  consequently,  floats  buoyantly  upon  it.  Ice  is  formed  only  on  the 
surface,  but,  being  a  very  bad  conductor,  it  cuts  off  the  escape  of  heat 
from  the  water  below,  and  this  renders  the  freezing  process  a  very  slow 
one.  In  fact,  a  film  of  ice  may  be  likened  to  a  blanket,  which,  although 
of  itself  cold,  becomes  a  means  of  preserving  heat  by  cutting  off  ra- 
diation. 

Lake  Superior  has,  uniformly,  throughout  the  year,  the  temperature  of  about 
40°,  at  a  short  distance  below  the  surface;  and  the  deep  sea  soundings  show,  that 
the  sea,  at  the  bottom  of  the  ocean,  even  under  the  Gulf  Stream,  is  below  the 
temperature  of  maximum  density,  which,  in  saline  solutions,  is  lower  than  in 
pure  water.  The  temperature  of  the  deep  Alpine  lakes  is  39°-2  F.,  at  all 
easons  of  the  year. 

Maximum  density  of  different  aqueous  solutions. — The  solu- 
tion of  various  salts  in  water  has  the  effect  of  lowering  its  point  of 
maximum  density.  Thus,  the  point  of  maximum  density  of  sea-water 
is  25°.70.  The  point  of  maximum  density  of  solutions  falls  more 
rapidly  than  their  point  of  congelation,  and  is  proportional  to  the 
quantity  of  salt  dissolved. 


HEAT. 


427 


The  volume  of  water,  at  different  temperatures,  has  been  de- 
termined by  several  experimenters,  and  the  results,  according  to  Kopp, 
are  given  in  Table  XXIV.,  with  the  corresponding  specific  gravities, 
both  when  taken  at  32°,  for  the  unit  of  volume  and  density,  and  also 
at  4°  C.  (39°-2F.). 

III.     EXPANSION  OF  GASES. 

605.  General   statement. — Gases   and   vapors,    being   under   the 
influence  of  repulsion,   and  having  little  cohesion,  expand,  for  equal 
increments  of  heat,  much  more  than  either  solids  or  ordinary  liquids. 
(Compare  §  602.) 

The  expansion  of  air,  and  of  all  gases,  may  be  shown  by  plunging  the  open 
end  of  a  bulbed  tube  into  water ;  a  slight  elevation  of  temperature,  even  the 
heat  of  tne  hand,  will  expand  the  air  in  the  bulb,  and  cause  a  part  of  it  to  escape 
in  bubbles  through  the  water.  And  when  the  source  of  heat  is  withdrawn,  the 
rise  of  the  water  in  the  tube  indicates  the  amount  of  expansion  (604). 

606.  Gay  Lussac's  laws  for  the  expansion  of  gases  by  heat. — 
Gay  Lussac  was  the  first  to  discover  the  general  laws  of  the  expansion 
of  gases  by  heat.     The  gases  on  which  he  experimented  were  not  freed 
from  moisture  ;  but  the  laws  which  he  deduced  are  remarkable  for  their 
great  simplicity  and  general  accuracy,  considering  the  state  of  experi- 
mental science  at  that  time  (A.  D.  1805).     They  are  as  follows : — 

1st.  All  gases  have  the  same  coefficient  of  expansion  as  common  air. 

2d.  The  coefficient  of  expansion  remains  the  same,  whatever  may  be  the 
pressure  to  which  the  gas  is  subjected. 

These  laws,  like  the  laws  of  Mariotte  (274),  though  sufficiently  accurate  for 
ordinary  purposes,  are  found,  by  the  more  complete  experiments  of  modern 
science,  to  be  not  strictly  correct. 

607.  Results  of  Regnault's  experiments  upon  the  expansion 
of  gases. — Very  valuable  experiments  were  made  by  Dulong   and 
Petit,  but  the  most  recent  and  complete  investigation  of  the  expansion 
of  gases  by  heat,  was  conducted  by  Regnault.     In  all  his  experiments, 
the  different  gases  experimented  upon  were  completely  deprived  of 
moisture,  and  the  results  of  his  experiments  are  contained  in  the  fol- 
lowing tables : — 

EXPANSION  OF  GASES  BETWEEN  32°  AND  212°  F.   (jAMIN). 


Gases. 

Under  Constant  Volume. 

Under  (Constant  Pressure. 

Air  .  ... 

0-3665 

0-3670 

0-3668 

0-3670 

Hydrogen  

0-3667 

0-3661 

Oxyd  of  Carbon  .  .  . 
Carbonic  Acid  .... 
Protoxyd  of  Nitrogen  . 
Sulphurous  Acid  .  .  . 
Cyanogen  

0-3667 
0-3688 
0-3676 
0-3845 
0-3829 

0-3669 
03710 
0  3719 
0-3903 
0-3877 

428          PHYSICS  OF  IMPONDERABLE  AGENTS. 

From  this  table  it  appears  that  the  coefficients  of  expansion  of  those 
gases  which  have  never  been  condensed  to  liquids,  are  very  nearly  the 
same  as  air ;  while  the  coefficients  of  the  condensible  gases,  carbonic 
acid,  sulphurous  acid,  and  cyanogen,  are  considerably  greater,  and  the 
greater  in  proportion  as  they  are  more  readily  condensed  into  liquids. 
Each  gas  has  two  coefficients  of  expansion, — the  coefficient  of  expan- 
sion for  a  constant  volume  being  less  than  for  a  constant  pressure,* 
except  in  the  case  of  hydrogen,  in  which  the  reverse  takes  place.  This 
agrees  in  a  remarkable  manner  with  the  fact  (276)  that  hydrogen  alono 
is  less  compressible  than  the  law  of  Mariotte  would  indicate. 

It  is  further  shown,  by  the  experiments  of  Regnault,  that : — 

1st.  The  coefficients  of  expansion  are  very  nearly,  but  not  absolutely, 
the  same  for  different  gases. 

2d.  The  coefficients  of  expansion,  for  different  gases,  vary  more  from 
each  other  in  proportion  as  the  pressure  to  which  they  are  subjected  is 
increased. 

3d.  The  coefficients  of  expansion  for  all  gases,  except  hydrogen,  increase 
with  the  pressure  to  which  they  are  subjected,  and  this  increase  is  most 
rapid  in  those  gases  which  deviate  most  from  Mariotte's  law  (276). 

4th.  For  ordinary  calculations,  under  the  pressure  of  the  atmosphere, 
the  coefficient  of  expansion  for  all  gases  may  be  considered  as  0*3666 
between  the  freezing  and  boiling  points  of  water,  or  ?^T  of  the  volume  at 
32°,  for  each  degree  of  Fahrenheit's  scale. 

For  accurate  scientific  purposes,  the  coefficient  of  expansion  of  every  gas  con- 
sidered must  be  taken  from  the  tables  given  for  that  purpose. 

Table  V.,  Appendix,  gives  the  coefficients  of  expansion  of  common  gases 
under  varying  pressures. 

608.  Formulae  for  computing  changes  of  volume  in  gases. — In 

physical  researches  it  is  often  desirable  to  ascertain  the  increase  or 
decrease  in  volume  which  a  given  gas  undergoes  by  measured  differ- 
ences in  temperature.  This  is  easily  done  by  the  following  formulae  :— 

Let  V  represent  the  volume  of  the  gas  at  32°  F.,  V  its  volume  at  the  higher 
temperature,  and  t  the  number  of  degrees  between  32°  and  the  higher  tempera- 
ture. The  increase  in  the  volume  will  therefore  be  expressed  by  V  —  V.  And 

V 
since  the  increase  in  volume  for  1°  F.  is  generally  — ,  the  increase  for  the 

V 
higher  temperature  is  —  X  '• 

Therefore,  V  -  V=  ^  X  «,  and  V  =  V  (\  + 

If  the  gas  is  subjected  to  a  lower  temperature,  it  suffers  a  diminution  in  vo- 
lume, expressed  by  V  —  V,  and  if  t  expresses  the  number  of  degrees  below  32° 

*  This  may  be  due  to  the  action  of  cohesion. 


HEAT.  429 

V 
to  which  it  is  reduced,  and  —  its  diminution  for  1°  F.,  then  the  diminution 

V  V 

for  the  lower  temperature  will  be  —  X  f>  an<l  ^ —  V  =  T^\  X  *• 

Therefore,  V  = 


,  V  =  V  /I  — 


If  the  volume  of  a  gas  at  32°  F.  is  known,  its  volume  at  any  other  tempera- 
ture above  or  below  32°  may  be  calculated  by  the  following : — 

RULE. 

Multiply  the  difference  between  the  number  of  degrees  of  temperature 
and  32°,  by  the  coefficient  of  expansion  of  the  gas  (for  ordinary  purposes 
this  coefficient  equals  1  divided  by  491).  Add  the  quotient  to  1,  if  the 
temperature  be  above  32°,  and  subtract  it  from  1,  if  it  be  below  32°. 
Multiply  the  number  thus  found  by  the  volume  of  the  gas  at  32°,  and  the 
product  will  be  the  volume  of  the  gas  at  the  observed  temperature. 

609.  Formulae  expressing  general  relation  between  volume, 
temperature,  and  pressure. — The  volume  which  a  gas  occupies  de- 
pends not  only  on  the  temperature,  but  also  upon  the  pressure  to  which 
it  is  subjected  (274) ;  the  pressure  of  a  gas  being  inversely  as  the 
volume  into  which  it  is  compressed. 

As  the  volume  of  a  gas  at  the  same  temperature  is  inversely  as  the  pressure, 
if  V  and  V  be  two  volumes  under  the  same  temperature,  and  under  the  pres- 
sures P  and  P' ;  then, 

P 
V :  V  =  P'  :  P,   and  F'  =  F  X  — ' 

If  t  and  t'  express  the  number  of  degrees  above  or  below  32°,  at  which 
the  temperature  stands  (-f-  being  used  when  above,  and  —  when  below),  if  a  gas 
be  simultaneously  subjected  to  changes  of  temperature  and  pressure,  the  rela- 
tion between  its  volume,  pressure,  and  temperature,  will  be  expressed  by  the 
general  formula 

V          1  ±Kt          P'  __   491  ±  t         P' 
V  =    1  ±  Kt'   ^  Y  =~    491  HZ  «'  ^  P"' 

610.  Relation  between  expansibility  and  compressibility. — 
It  has  been  found,  generally,  that  the  most  expansible  liquids  are  the 
most  compressible. 

Solids  expand  less  than  liquids,  and  are  likewise  less  compressible, 
while  liquids  have  a  less  expansibility  and  compressibility  than  gases. 
Among  solids,  the  most  expansible  are  generally  the  most  easily  com- 
pressed. 

The  expansibility  of  a  substance  increases  with  the  temperature,  as 
does  also  its  compressibility. 

611.  Density  of  gases. — The  density  of  gases  and  vapors  is  com- 
pared with  atmospheric  air  as  the  standard,  air  being  called  1,  or  1000. 


430  PHYSICS    OP   IMPONDERABLE   AGENTS. 

The  method  for  the  determination  of  the  density  of  gases  is,  in  prin- 
ciple, the  same  as  for  the  density  of  liquids.  The  determinations  are 
made  in  a  glass  globe,  fig.  205  (§  258),  to  which  an  accurately  fitted 
stop-cock  is  attached.  The  globe  is  first  weighed,  when  filled  with 
dry  and  pure  air,  and  again  after  being  exhausted  of  air  by  means  of 
the  air-pump ;  the  difference  in  the  two  weights  gives  the  weight  of  air 
contained  in  the  flask.  The  globe  is  then  filled  with  the  perfectly  dry 
gas  under  examination,  and  again  weighed ;  the  weight  found,  less  the 
weight  of  the  globe,  gives  the  weight  of  the  gas.  The  weight  of  the  gas, 
divided  by  the  weight  of  the  same  bulk  of  air,  gives  the  specific  gravity, 
or  density  of  the  gas,  as  compared  with  air. 

Example :  A  glass  globe  held  28-73  grains  of  atmospheric  air,  and  43-93 
grains  of  carbonic  acid.  The  specific  gravity  of  the  latter  is  therefore  43-93  -f- 
28-73  =  1-529,  or,  28-73  :  43-93  =  1000  :  1-529. 

A  number  of  corrections  must  be  made,  in  order  to  obtain  the  true  density 
of  the  gas  under  examination.  Thus,  the  barometric  height,  and  the  tempera- 
ture of  the  air  at  the  time  of  weighing,  must  be  reduced  to  the  standard  baro- 
metric height,  30  inches,  and  the  standard  temperature,  62°  P.  Corrections 
must  also  be  made  for  the  film  of  hygroscopic  moisture,  always  adhering  to  the 
globe,  and  for  the  buoyancy  of  the  globe  in  the  air. 

Regnault  has  reduced  the  number  of  corrections  ordinarily  necessary,  by 
counterpoising  the  globe  in  which  the  gas  is  weighed  by  a  second  globe  of  equal 
size  made  of  the  same  glass.  Thus,  the  corrections  for  the  film  of  hygroscopic 
moisture,  and  the  buoyancy  of  the  globe  in  the  air,  may  be  dispensed  with,  as 
they  are  equal  in  both  cases. 

The  most  important  applications  of  a  knowledge  of  the  density  of  gases  have 
been  made  in  chemistry.  As  in  demonstrating  and  elucidating  the  discovery 
of  Gay  Lussac,  that  the  volume  of  a  compound  gas  is  either  equal  to,  or  bears 
a  very  simple  relation  to  the  volumes  of  its  constituent  gases.  Also,  in  calcu- 
lating the  atomic  weight  of  numerous  elementary  substances. 

Table  XL  c.,  Appendix,  gives  the  density  of  the  most  important  gases,  as 
obtained  by  distinguished  authorities. 

§  4.    Communication  of  Heat. 

I.    CONDUCTION. 

612.  Modes  in  which  heat  is  communicated. — Heat  is  commu- 
nicated in  three  ways :  1st.  By  conduction  (chiefly  in  solids).     2d.  By 
convection,  or  circulation,  in  liquids  or  gases.     3d.  By  radiation. 

613.  Conduction  of  heat. — Heat  travels  in  solids  slowly,  from 
particle  to  particle.     It  implies  contact  with,  or  close  approach  to,  a 
hotter  body.     The  end  of  a  bar  of  iron  thrust  into  the  fire,  becomes 
red-hot,  while  the  other  end  can  yet  be  handled.     Things  vary  very 
much  in  their  power  to  conduct  heat,  every  substance  having  its  own 
rate  of  conductibility. 

A  metallic  vessel,  filled  with  hot  water,  is  at  once  as  hot  as  its  contents,  while 
an  earthen  vessel  becomes  heated  slowly.  The  metal  is  a  good,  and  the  earthen- 
ware is  a  bad,  conductor.  A  pipe-stem,  vr  glass  tube,  held  in  a  spirit  lamp, 


HEAT . 


431 


may  toe  heated  red-hot  within  a  short  distance  of  the  fingers,  where  a  wire  of 
silver  or  copper  would  become  at  once  too  hot  to  hold. 

The  progress  of  conducted  heat  in  a  solid  is  easily  shown  by  a  metallic  rod, 
to  which  are  stuck  by  wax  several  marbles,  at  equal  distances ;  one  end  is  held 
in  a  lamp,  when  the  marbles  drop  off,  one  by  one,  as  the  heat  melts  the  wax  j 
the  one  nearest  the  lamp  falling  first,  and  so  on.  If  the  rod  is  of  copper,  they 
all  fall  off  very  soon ;  but  if  a  rod  of  leadj  or  platinum,  is  used,  the  heat  is  con- 
ducted much  more  slowly. 

Solids  conduct  heat  better  than  liquids,  and  liquids  better  than  gases,  which 
are  the  poorest  conductors  of  all.  The  metals,  as  a  class,  are  good  conductors, 
and  their  oxyds,  as  a  class,  are  bad  ones.  The  more  matter,  then,  is  present 
in  a  given  body  (i.  e.  the  higher  its  density),  the  greater,  as  a  general  rule,  is 
its  conducting  power,  and  vice  versa'. 

614.  Determination  of  the  conductibility  of  solids. — The  appa- 
ratus of  Ingenhausz,  fig.  471,  may  be  employed  to  determine  the  unequal 
conductibility  of  solids. 

This  is  a  small  copper  box,  one  side  of  which  is  pierced  with  holes,  in  which 
are  fitted,  by  means  of  corks,  small  cylinders  of  different  substances,  of  the 
same  size,  covered  with  wax.  When  the  vessel  is  471 

filled  with  boiling  water  or  hot  sand,  the  wax  will 
be  melted  from  the  rods  in  the  order  of  their  con- 
ductibility, viz.,  copper,  iron,  lead,  porcelain, 
glass,  wood.  Or  small  bits  of  phosphorus  may 
be  placed  at  equal  distances  upon  the  rods,  and 
these  will  be  fired  in  corresponding  succession. 

To  determine  the  relative  conductibility  of 
solids,  the  apparatus  of  Despretz  may  be 
employed,  fig.  472. 

It  is  a  series  of  prismatic  bars,  a  I,  heated  at  one  end,  a,  by  an  argand  lamp. 
Bach  bar  has  a  series  of  small  cavities,  T,  formed  in  it,  at  equal  distances 
(I  c.  m.  =  -39  in.)  throughout  its  length,  and  filled  with  mercury.  In  each 

472 


of  these  cavities  is  placed  a  thermometer,  which  indicates  the  progressive  pro- 
pagation of  the  heat  along  the  bar.  Bars  of  various  metals  are  used.  By  heating 
these  bars  successively  over  a  steady  lamp  flame,  their  relative  conductibility 
will  be  indicated  by  the  times  required  for  them  each  to  attain  the  same  tem- 
perature. 


432 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


615.  Conductibility  of  metals,  &c. — Gold  is  a  better  conductor 
of  heat  than  any  other  metal,  or  other  solid.    Its  conductivity  is  repre- 
sented by  1000.     The  order  of  the  conductibility  of  other  metals  is 
(according  to  Despretz)  platinum,  copper,  silver,  iron,  zinc,  tin,  lead. 
The  conductibility  of  the  last-named  metal  is  only  179'6. 

The  precise  rate  of  the  conductibility  of  these  metals,  according  to  different  au- 
thorities, may  be  seen  in  the  Appendix,  Table  VII.  A.,  and  in  Table  VII.  B  ,  show- 
ing the  conducting  power  of  different  materials  used  in  the  construction  of  houses, 
as  observed  by  Mr.  Hutchinson.  The  substances  are  arranged  in  the  order  in 
which  they  most  resist  the  passage  of  heat,  those  substances  which  are  most 
valuable  in  construction  in  this  respect  (viz.,  the  warmest)  being  placed  first. 
The  substances  marked  H.  P.  are  the  building-stones  employed  in  the  construc- 
tion of  the  new  houses  of  parliament. 

616.  Conductibility  of  crystals. — The  conductibility  of  homoge- 
neous solids,  and  of  crystals  belonging  to  the  monometric  system,  is 
the  same  in  every  direction.     But  in  crystals  of  other   systems,  the 
conductibility  varies  in  different  directions,  according  to  the  relation 
of  the  direction  to  that  of  the  optic  axis  of  the  crystal. 

Senarmont,  in  his  experiments,  took  thin  plates  of  crystals,  some  cut  parallel 
to  the  optic  axis,  and  others  at  right  angles  to  it.  In  the  centre  of  each  plate  a 
small  hole  was  drilled  for  the  reception  of  a  silver  wire,  473 

which  was  heated  by  a  lamp ;  the  surfaces  of  the  crystals 
were  covered  by  a  thin  coating  of  colored  wax.  The  con- 
duction of  the  heat  was  observed  by  the  melting  of  the  wax, 
the  melted  portion  assuming,  with  crystals  of  the  monometric 
system,  the  form  of  a  circle,  1,  fig.  473,  and  in  the  other 
systems,  ellipses  of  different  forms,  2,  fig.  473. 

617.  Couductibility  of  wood. — The  dependence 
of  the  conduction  of  heat  upon  molecular  arrange- 
ment is  shown  as  well  in  organic  structures  as  in 
crystalline  media.    This  subject  was  investigated  most 
carefully  by  Dr.  Tyndall,  who  examined  the  conduct- 
ing power  of  various  organic  substances,  especially 
wood. 

He  found  that  at  all  points  not  situated  in  the  centre 
of  the  tree,  wood  possesses  three  unequal  axes  of  calorific 
conduction.  The  first  and  principal  axis,  is  parallel  to  the 
fibres  of  the  wood ;  the  second,  and  intermediate  axis,  is 
perpendicular  to  the  fibres  and  to  the  ligneous  layers,  and 
the  third,  and  least  axis,  is  perpendicular  to  the  fibres,  and 
parallel  to  the  layers.  It  may  be  stated,  as  a  general  law,  that,  the  axes  of 
calorific  conduction  in  wood  coincide  with  the  axes  of  elasticity,  cohesion,  and 
permeability  to  liquids,  the  greatest  with  the  greatest,  and  the  least  with  the  least. 
The  heat-conducting  power  of  wood  bears  no  definite  relation  to  its  density. 
American  birch,  one  of  the  lightest  of  woods,  conducts  heat  better  than  any 
other.  Oak  wood,  which  is  very  dense,  conducts  nearly  as  well,  but  iron  wood, 


HEAT. 


433 


which  has  the  great  density  of  1-426,  is  very  low  in  the  scale  of  conduction. 
Green  woods  conduct  heat  better  than  dry. 

618.  Vibrations  produced  by  conduction  of  heat. — When   a 
hot  bar  of  metal,  having  a  narrow  base,  is  supported  on  knife  edges 
of  metal  or  crystal,  or  upon  metallic  points,  a  vibratory  motion  of  the 
bar  is  produced,  and  continued  until  the  temperature  of  the  bar  and 
the  supporting  body  become  nearly  the  same.    This  vibration  produces 
a  musical  tone  varying  with  the  nature  of  the  metal  and  the  form  of 
the  bar. 

It  was  formerly  supposed  that  these  vibrations  indicated  that  heat  was  pro- 
duced by  molecular  vibrations.  But  it  has  been  shown  by  Tyndall  (Phil.  Trans. 
1854)  that  these  vibrations  are  caused  by  the  want  of  synchronism  in  the  sudden 
expansion  of  the  points  of  support,  as  heat  is  communicated  from  the  metallic  bar. 

Dr.  Page  produced  similar  vibrations  by  employing  a  rocker  having  a  cylin- 
drical surface  supported  on  two  narrow  bars,  using  voltaic  electricity  as  a  source 
of  heat.  Am.  Jour.  Sci.  [2J  XX.,  p.  165. 

619.  Conductibility  of  liquids. — Count  Rumford  concluded,  from 
his  experiments,  that  liquids  were  absolutely  non-conductors  of  heat, 
but   later   experimenters   have  determined,  that 

liquids  do  conduct  heat,  but  only  to  a  very 
limited  degree.  That  the  conductibility  of  liquids 
for  heat  is  very  slight,  is  shown  by  Rumford's 
apparatus,  fig.  474. 

The  glass  funnel  is  nearly  filled  with  water.  A  ther- 
mometer tube,  with  large  bulb,  is  so  arranged.,  that  the 
bulb  is  just  below  the  surface  of  the  water.  The  stem 
passes  through  a  tight  cork,  and  contains  a  few  drops 
of  colored  liquid  at  A,  which  will  move  with  any 
change  in  bulk  of  the  air  contained  in  the  bulb.  A  little 
ether  poured  upon  the  surface  of  the  water  and  ignited, 
does  not  cause  any  movement  in  the  column  of  fluid  (as 
may  be  found  by  pasting  a  line  of  paper  on  the  stem  at 
one  of  the  drops  of  liquid),  which  would  be  the  case  if 
any  sensible  warmth  was  communicated.  The  warmth 
of  a  finger,  touching  the  bulb,  will  at  once  cause  the 
fluid  to  move  by  expanding  the  air  within.  As  the 
walls  of  the  glass  vessel  gradually  become  hot  by  con 
duction,  the  water  will  slowly  rise  in  temperature.  By 
heating  a  vessel  on  the  top,  therefore,  we  should  never 
succeed  in  creating  anything  more  than  a  superficial  elevation  of  temperature  ; 
at  a  small  depth  the  water  would  remain  cold.  The  heating  of  liquids  is  effected 
by  means  of  currents,  as  will  be  presently  explained  (627). 

620.  Conductibility  of  gases. — Gases   are   more   imperfect   con- 
ductors of  heat  than  liquids.     It  is  difficult  to  make  accurate  experi- 
ments upon  this  subject,  from  the  readiness  with  which  currents  are 
formed,  and  which  thus  diffuse  the  heat,  but  we  know  that  gases,  when 

39* 


434  PHYSICS    OF   IMPONDERABLE    AGENTS. 

confined,  are  almost  non-conductors  of  heat.  Thus,  substances  which 
imprison  large  volumes  of  air  within  their  pores,  as  down,  wool, 
feathers,  &c.,  are  very  poor  conductors  of  heat. 

Air,  loaded  with  moisture,  is  rendered  thereby  a  much  better  con- 
ductor of  heat  than  dry  air,  in  the  proportion  of  230  to  80 ;  hence, 
damp  air  feels  colder  to  the  body  than  dry  air  of  the  same  temperature, 
because  it  conducts  away  the  heat  from  the  body  more  rapidly. 

The  sense  of  oppression  experienced  before  a  thunder  storm  is  due  to 
the  combined  effect  of  the  heat  and  moisture  of  the  atmosphere. 

621.  Relative  conductibility  of  solids,  liquids,  and  gases. — 
If  we  touch  a  rod  of  metal  heated  to  120°  F.,  .we  shall  be  burned ; 
water  at  150°  will  not  scald,  if  the  hand  is  kept  still,  and  the  heat  is 
gradually  raised  ;  while  dry  air  at  300°  has  been  endured  without  injury- 

The  oven-girls  of  Germany,  clad  in  garments  of  woolen  and  thick  socks  to 
protect  their  feet,  enter  ovens  without  inconvenience,  where  all  kinds  of  culi- 
nary operations  are  going  on,  at  a  temperature  above  300°,  although  the  touch 
of  any  metallic  article  while  there  would  severely  burn  them. 

622.  Examples  and  illustrations  of  the  different  conductibi- 
lity of  solids,  are  very  evident  to  common  observation. 

The  crust  of  the  globe  is  composed  of  poor  conducting  materials,  and  not- 
withstanding the  intensity  of  the  central  fires  within,  the  amount  of  heat  which 
escapes  is  so  inconsiderable,  that  it  has  now  no  sensible  influence  on  the  tempe- 
rature of  the  surface.  It  has  been  calculated,  that  the  quantity  of  central  heat 
which  reaches  the  surface  in  a  year  would  not  suffice  to  melt  an  envelope  of  ice 
surrounding  the  earth  one-quarter  of  an  inch  in  thickness. 

Water-pipes  laid  at  a  distance  of  a  few  feet  under  ground,  are  not  frozen 
by  the  winter's  cold,  because  the  soil  is  a  comparatively  poor  conductor. 

Fire-proof  safes  are  boxes  of  iron,  constructed  with  double  or  treble  walls, 
the  intervening  spaces  of  which  are  filled  with  gypsum  (plaster  of  paris),  burnt 
alum,  or  some  other  non-conducting  material.  These  linings  prevent  the  exterior 
heat,  in  case  of  fire,  from  passing  to  the  books  and  papers  within.  Furnaces  are 
lined  with  fire-bricks,  because,  being  of  poor  conducting  and  infusible  material, 
they  prevent  the  waste  of  heat.  Ivory  and  wooden  handles  are  attached  to 
cooking  vessels,  and  to  tea  and  coffee  pots,  because,  being  poor  conductors,  they 
prevent  the  heat  from  passing  to  the  hand  so  rapidly  as  to  burn  it.  Hot  dishes 
are  placed  upon  mats  that  the  table  may  not  be  injured.  Water  is  sooner  heated 
in  a  metallic  vessel  than  in  one  of  glass  or  porcelain,  because  the  first  conducts 
the  heat  more  rapidly  from  the  fire  than  the  others. 

Buildings  constructed  of  wood  and  brick  are  cooler  in  summer  and  warmer  in 
winter  than  those  of  iron,  because  they  are  poorer  conductors  of  heat. 

The  hearth-stone  feels  colder  than  the  wooden  floor,  and  this  than  the  carpet, 
owing  to  the  difference  in  their  conducting  powers,  although  all  are  at  the  same 
temperature. 

623.  Examples  drawn  from  the  animal  and  vegetable  king- 
doms.— The  covering  of  animals   not   only  varies  with   the   climate 
which  the  several  species  inhabit,  but  also  with   the  season.     This 


HEAT.  42,'» 

/overing  is  not  in  itself  a  source  of  warmth,  but  preveuts  the  escape 
of  the  vital  heat  from  within. 

Animals  in  warm  climates  are  generally  naked,  or  are  covered  with  coarse 
and  thin  furs,  which  in  cold  countries  are  fine,  close,  and  thick,  and  are  almost 
perfect  non-conductors  of  heat.  The  plumage  of  birds  is  likewise  formed  of 
substances  which  are  poor  conductors  of  heat,  containing  also  a  large  quantity 
of  air  in  their  interstices.  Besides  this  protection,  the  birds  of  cold  regions  are 
provided  with  a  more  delicate  structure  beneath  the  feathers,  called  down,  which 
intercepts  the  heat  still  more  perfectly.  The  fossil  elephant  of  the  White  River, 
in  Siberia,  was  covered  with  three  sorts  of  hair,  of  different  lengths,  the  shortest 
being  a  fine,  close  wool,  next  the  body,  a  protection  against  the  arctic  cold.  The 
arctic  navigator  and  the  Esquimaux  endure  the  cold  of — 40°,  or  — 60°,  F.  with 
the  aid  of  fur  bags  and  clothes.  Animals  with  warm  blood,  which  live  in  the 
water,  as  the  whale  and  seal,  are  surrounded  with  a  thick  covering  of  oil  and 
fat,  which  acts  in  a  manner  similar  to  the  furs  and  feathers  of  land  animals. 

The  bark  of  trees  is  much  more  porous  than  the  wood,  and,  being  arranged  in 
plates  and  fibres  around  the  body  of  the  tree,  prevents  such  a  loss  of  heat  as 
would  be  injurious  to  its  life. 

624.  The  conducting  power  of  substances  in  a  pulverized  or 
fibrous  state,  is  less  than  that  of  the  same  thing  in  a  compact  mass, 
partly  because  the  continuity  of  the  substances  is  diminished,  and  also 
because  of  the  air  imprisoned  among  the  particles. 

Saw-dust  in  a  loose  state,  is  a  very  poor  conductor  of  heat,  much  poorer 
than  the  wood  of  which  it  was  formed.  Ice-houses  are  built  with  double  walls, 
between  which  dry  straw,  shavings,  or  saw-dust  are  placed,  keeping  the  interior 
cot  1  by  excluding  the  heat.  Ice  wrapped  in  flannel  is  preserved  by  excluding 
the  warm  air.  Refrigerators  are  generally  double-walled  boxes,  the  space 
Votween  the  walls  being  filled  with  powdered  charcoal,  or  some  other  porous 
ion-conducting  substance.  (See  Ventilation.)  Similarly  constructed  vessels 
form  the  ordinary  water-coolers. 

Snow  is  made  up  of  crystalline  particles,  enclosing  a  large  quantity  of  air 
among  their  interstices,  which,  being  a  very  good  non-conductor,  prevents  the 
escape  of  the  heat  from  the  earth  and  limits  the  penetration  of  frost,  which 
always  reaches  a  much  greater  depth  in  winters  without  snow,  than  when  snow 
abounds.  On  the  flanks  of  Mount  JEtna,  the  winter  snows  often  reach  near  to 
the  border  of  the  fertile  regions,  and  it  is  the  practice  of  the  mountaineers  to 
cover  those  parts  of  the  snow  which  they  wish  to  preserve  for  summer  use,  with 
two  or  three  feet  thickness  of  volcanic  sand  -and  powdered  pumice,  everywhere 
abounding.  The  snow,  thus  protected,  remains  all  summer  under  an  almost 
tropical  sun,  and  is  distributed  from  these  natural  ice-houses  over  the  whole 
Island  of  Sicily.  There  exists  even  to  this  day  a  heavy  bed  of  ice  near  the 
summit  of  JEtna,  covered  first  by  an  eruption  of  ashes  and  sand  several  yards 
thick,  and  subsequently  by  a  flow  of  molten  lava,  many  centuries  since.  This 
store  of  ice  has  been  opened  and  used  when  the  supply  below  on  the  mountain 
fell  short.  Straw-matting,  and  other  fibrous  materials,  being  poor  conductors, 
are  used  to  envelop  tender  plants  and  trees  to  protect  them  from  severe  cold. 

625.  Clothing. — The  object  of  clothing,  in  cold  climates,  like  tb 
furs  and  feathers  of  animals,  in  to  prevent  the  escape  of  heat  from  the 


436  PHYSICS    OF    IMPONDERABLE    AGENTS. 

body.  Fibrous  materials,  as  wool  and  furs,  are  best  adapted  for  cloth- 
ing, because  they  are  themselves  very  poor  conductors  of  heat,  and 
likewise  contain  air  in  their  interstices. 

The  order  of  the  conducfcibility  of  the  different  substances  used  for  clothing, 
is  as  follows  : — linen,  cotton,  silk,  wool,  furs.  Hence  a  woolen  garment  is 
warmer  than  one  of  cotton,  or  silk,  or  linen.  The  linen  sheets  of  a  bed  feel  colder 
than  the  woolen  blankets,  because  they  are  better  conductors  of  heat.  Fine  cloths 
are  warmer  than  coarse  ones,  because  they  are  poorer  conductors  of  heat  In 
summer,  coarse  linen  goods  are  used,  because  they  allow  the  escape  of  heat  from 
the  body  more  readily  than  other  materials,  while  a  dress  of  fine,  close  woolen 
goods,  is  a  better  protection  from  the  cold  of  winter  than  anything  else, 
excepting  furs.  A  thick  dress  of  non-conducting  material  is  sometimes  used 
to  exclude  heat,  as  when  workmen  enter  a  hot  furnace  in  certain  manufacturing 
processes. 

II.     CONVECTION. 

626.  Convection. — Although  liquids  and  gases  are  very  poor  con- 
ductors of  heat,  yet  they  admit  of  being  rapidly  heated  by  a  process 
of  circulation  called   convection,   and  which  depends  upon  the  free 
mobility  of  their  particles.     The   particles  of  liquids  and   gases   in 
immediate  contact  with  the  source  of  heat,  becoming  warm,  and  also 
specifically  lighter,  rise,  and,  moving  away,  make  room  for  others  ;  this 
is  continued  until  all  the  particles  attain  the  same  temperature.     Cur- 
rents are  thus  produced  both  in  water  and  air. 

627.  Convection  in  liquids. — The  circulation  just  mentioned  may 
be  rendered  visible  by  heating  in  a  flask,  water  containing  a  little  bran 

475^  or  amber  (or  other  substance  of  about  the  same  density 

as  water),  over  a  spirit  lamp,  as  shown  in  fig.  475. 

The  particles  of  liquid  at  the  bottom  of  the  vessel, 
where  the  heat  is  applied,  becoming  heated,  rise,  and 
other  particles  of  colder  liquid  come  in  below,  and 
supply  their  place.  Thus  two  systems  of  currents  are 
formed.  In  the  centre  of  the  jar,  currents  of  the  hot 
particles  ascend,  and  descending  currents  of  colder 
particles,  flow  down  the  sides;  this  circulation  con- 
tinues until  the  whole  mass  has  attained  the  same 
temperature. 

Anything  that  checks  this  free  circulation,  and  occasions  viscidity,  impedes 
the  heating  of  the  liquid,  and  likewise  prevents  its  rapid  cooling. 

Starch  and  gum,  during  boiling,  require  to  be  constantly  stirred,  for  the  pur- 
pose of  presenting  fresh  surfaces  to  the  action  of  the  heat,  and  preventing  por- 
tions from  adhering  to  the  hot  bottom,  and  thus  being  charred. 

628.  Currents  in  the  ocean. — In  consequence  of  the  unequal  heat 
to  which  the  waters  of  the  ocean  in  different  parts  are  subjected,  cur- 
rents of  great  constancy  and  regularity  are  formed.    Under  the  tropics, 


HEAT.  437 

li- 
the waters  become  highly  heated  and  flow  off  on  either  side  towards  the 

poles,  while  other  colder  currents  flow  from  the  poles  towards  the  equa- 
tor. These  currents  are  modified  in  their  direction  by  the  form  and 
distribution  of  land  and  water  on  the  surface  of  the  earth,  and  the 
rotation  of  the  earth  upon  its  axis. 

One  of  these  currents  (called  for  that  reason  the  Gulf  Stream)  is  directed 
into  the  Gulf  of  Mexico,  around  the  western  end  of  Cuba,  and  sweeping  through 
it,  passes  by  the  narrow  channel  between  Florida  and  the  Bahama  Islands.  It 
has  a  temperature  8°  or  10°  F.  higher  than  that  of  thp  surrounding  ocean. 
This  current  passes  northward,  parallel  to  the  coast  of  the  United  States, 
gradually  widening  and  becoming  less  marked,  and  finally  is  directed  toward 
the  frozen  ocean  and  British  Islands.  It  carries  away  the  excess  of  heat  from 
the  Antilles,  and  warm  regions  near  the  equator,  beyond  the  western  Atlantic, 
ameliorating  the  climate  of  the  British  Islands  and  all  north-western  Europe. 

The  researches  of  the  U.  S.  Coast  Survey  have  greatly  extended  our  know- 
ledge of  this  remarkable  river  of  the  ocean  (or  rather  union  of  many  rivers  of 
warm  water),  first  brought  to  the  notice  of  the  scientific  world  by  the  illustrious 
Franklin  in  1770. 

III.    RADIATION. 

629.  Radiation  of  heat. — Hot  bodies  radiate  heat  equally  in  all 
directions.     Radiant  heat  proceeds  in  straight  lines,  diverging  in  every 
direction  from  the  points  where  it  emanates.     These  diverging  lines 
are  called  thermal  rays,  or  heat  rays.     Heat  rays  continue  to  issue  from 
a  hot  body,  through  the  whole  process  of  its  cooling,  until  it  sinks  to  the 
actual  temperature  of  the  air,  or  surrounding  medium.    It  is  generally 
by  radiation,  that  bodies  become  heated  at  a  distance  from  the  source 
of  heat. 

Standing  before  a  fire,  or  in  the  sun's  light,  we  feel  the  genial  influ- 
ence of  the  heat  radiated  from  these  sources.  A  candle,  or  gas  light, 
gives  off  its  heat  as  it  does  its  light,  in  all  directions.  A  thermometer, 
placed  at  equal  distances  around  the  flame,  indicates  the  same  tempera- 
ture. 

630.  Radiant   heat  is  but  partially  absorbed  by  the  media 
through  which  it  passes,  and  is  not  sensibly  affected  by  any  motion 
of  the  media,  as  of  winds  in  air. 

The  sun's  rays  lose  about  one-fourth  (0'277)  of  their  heat  in  passing 
through  the  atmosphere,  the  remainder  being  absorbed  or  reflected  at 
the  surface  of  the  earth.  The  air  receives,  however,  the  greater  part 
of  its  warmth  by  reflection,  conduction,  and  convection,  from  the  sur- 
face of  the  earth  thus  heated  by  the  sun. 

We  receive  warmth  from  the  fire  upon  our  persons,  although  the  air 
remains  cold,  and  may  be  continually  renewed. 

The  conduction  of  heat  is  probably  internal  radiation  from  particle  to 
particle;  for  the  material  atoms  of  which  any  substance  consists,  are  not 


438  PHYSICS    OF    IMPONDERABLE    AGENTS. 

supposed  to  be  in  absolute  contact,  although  held  near  each  other  by  a  strong 
attraction. 

631.  Intensity  of  radiant  heat. — The  intensity  of  radiant  heat  is 
according  to  the  following  laws  : — 

1st.  It  is  proportional  to  the  temperature  of  the  source. 

2d.  It  is  inversely  as  the  square  of  the  distance  from  the  source. 

3d.  It  is  greater  in  proportion  as  the  rays  are  emitted  in  a  direction 
more  nearly  perpendicular  to  the  radiating  surface. 

1st.  If  a  thermometer  be  exposed  at  the  same  distance  from  different  sources 
of  heat,  having,  for  example,  the  temperatures  of  100°,  150°,  and  200°,  the 
amount  of  radiant  heat  will  be  directly  as  these  numbers. 

2d.  Thus,  the  heating  effect  of  a  body  at  a  distance  of  two  feet  is  only  one- 
fourth,  at  three  feet,  one-ninth,  and  at  four  feet,  one-sixteenth  of  what  it  is  at 
one  foot. 

This  law  may  be  exemplified  by  supposing  two  globes,  one  of  one  foot  diame- 
ter, the  other  of  two  feet  diameter,  having  a  body  equally  heated  in  both.  The 
larger  globe  exposes  four  times  as  much  surface  as  the  smaller  one )  conse- 
quently, each  square  inch  of  the  larger  one  will  receive  only  one-fourth  as 
much  heat  as  each  square  inch  of  the  smaller  one,  while  the  distance  to  this 
surface  is  only  twice  as  great. 

3d.  This  law  may  be  demonstrated  by  the  apparatus,  fig.  476.  In  the  focus 
of  the  mirror,  a  thermoscope,  /,  is  placed.  A  A,  B  B,  are  screens,  pierced  with 

476 


equal  openings.  The  vessel,  a  c,  is  filled  with  hot  water.  The  position  of  the 
index  of  the  thermoscope  will  be  the  same,  whether  a  c  is  perpendicular,  or 
more  or  less  inclined.  And,  as  in  the  latter  case,  there  is  a  greater  surface  ex- 
posed, and  consequently  a  greater  number  of  heat-rays  pass  through  the  screen  ; 
yet,  as  the  same  effect  is  produced,  the  oblique  rays  must  be  less  intense  than 
the  perpendicular  rays,  the  intensity  diminishing  with  their  obliquity. 

632.  Law  of  cooling  by  radiation. — Newton  supposed  that  the 
rapidity  of  cooling  of  a  body  was  proportional  to  the  difference  between 
its  temperature  and  that  of  the  surrounding  medium.  This  law  is  cor- 
rect only  for  those  bodies  differing  in  temperature  not  more  than  15°  or 
20°  C.  (59°  to  68°  F.) 

Dulong  and  Petit  made-  elaborate  investigations  upon  this  subject, 


HEAT.  439 

and  determined  that  where  the  heated  body  was  placed  in  vacuo  at 
temperatures  ascending  according  to  the  terms  of  an  arithmetic  pro- 
gression, the  rapidity  of  cooling  increased  according  to  the  terms  of  a 
geometric  progression,  diminished,  however,  by  a  constant  quantity, 
this  constant  being  the  heat  radiated  back  upon  the  cooling  body  from 
the  walls  of  the  confining  vessel.  If  the  temperature  of  the  vessel, 
and  that  of  the  heated  body,  were  both  raised  according  to  the  terms  of 
an  arithmetic  progression,  so  that  the  difference  between  the  two  was 
always  constant,  the  rate  of  cooling  increased  according  to  the  terms 
of  a  geometric  progression. 

Radiation  is  found  to  take  place  more  freely  in  vacuo  than  in  air. 

633.  Universal   radiation   of  heat. — Heat  is  radiated  from   all 
bodies,  at  all  times,  whether  their  temperature  be  the  same  as,  or 
different  from,  that  of  surrounding  bodies ;  for  it  is  the  tendency  of 
heat  to  place  itself  in  equilibrium. 

In  an  apartment  where  all  the  articles  are  of  the  same  temperature,  each  re- 
ceives as  much  heat  as  it  radiates,  and,  consequently,  their  temperature  remains 
stationary.  Where  some  bodies  are  warmer  than  others,  the  warmer  radiate 
more  than  they  receive,  until  finally  all  attain  the  same  temperature.  Hence 
all  bodies,  however  cold,  will  warm  bodies  colder  than  themselves ;  thus,  frozen 
mercury,  placed  in  a  cavity  of  ice,  will  be  melted  by  the  heat  received  from 
the  ice. 

634.  Apparent  radiation  of  cold  takes  place  when  two  parabolic 
mirrors  are  placed  opposite  to  each  other,  having  a  delicate  thermome- 
ter in  the  focus  of  one,  and  a  mass  of  ice  suspended  in  that  of  the 
other.     The  temperature  of  the  thermometer  will  be  seen  to  fall,  appa- 
rently by  the  radiation  of  cold  from  the  ice.     The  true  explanation  is, 
that  the  thermometer  is  warmer  than  the  ice,  and  radiating  more  heat 
than  it  receives,  thus  loses  heat,  and  the  temperature  falls.   If  the  ther- 
mometer had  been  at  a  lower  temperature  than  the  ice,  the  phenomenon 
would  have  been  reversed. 

The  following  remarkable  instance  of  the  apparent  focalization  of  cold,  is 
explained  in  a  similar  manner.  The  experiment  is  due  to  the  Florentine 
Academician  Porta  in  the  sixteenth  century.  If  a  parabolic  mirror  is  placed 
with  its  axis  pointing  towards  the  sun,  the  heat-rays  will  be  reflected  to  the 
focus  of  the  mirror.  But  if  the  mirror  be  turned  so  as  to  face  the  clear  blue 
sky,  its  focus  becomes  a  focus  of  cold,  and  a  delicate  thermometer  placed  at  that 
point  will  sink,  in  clear  weather,  a  few  degrees  in  the  day  time,  and  as  much 
as  17°  F.  at  night.  This  phenomenon  is  thus  accounted  for : — the  thermometer 
is  constantly  radiating  heat  in  all  directions;  the  mirror,  being  a  paraboloid, 
reflects  to  its  fo«us  only  those  rays  that  come  in  a  direction  parallel  to  its  axis. 
In  that  direction  no  rays  come,  for  there  is  no  source  to  reflect  them,  conse- 
quently the  temperature  of  the  thermometer  falls.  If  a  cloud  passes  over  the 
the  mirror,  the  thermometer  instantly  rises  to  its  usual  height. 


440 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


§  5.   Action  of  different  Bodies  upon  Heat. 

I.     SURFACE  ACTION. 

635.  Reflection   of  heat. — Conjugate   mirrors. — Radiant   heat, 
like  light,  is  reflected  at  the  same  angle  at  which  it  falls  upon  any  re- 
flecting surface.    This  law  in  respect  to  light  has  been  fully  illustrated 
in  the  chapter  on  that  subject. 

If  a  piece  of  bright  tin-plate  is  held  in  such  a  position  as  to  reflect  the  light 
of  a  clear  fire  into  the  face,  the  sensation  of  heat  will  be  felt  the  moment  the 
light  is  seen. 

Conjugate  mirrors. — The  reflection  of  heat  may  be  shown  in  a  still  more 
striking  manner  by  the  apparatus  called  the  conjugate  mirrors,  fig.  477,  con- 
sisting of  two  similar  parabolic  mirrors, 
arranged  exactly  opposite  to  each  other, 
at  a  distance  of  ten  or  twelve  feet.  In 
the  focus  of  one  mirror  is  placed  a  heated 
body,  as  a  mass  of  red-hot  iron,  and  in 
the  other  a  portion  of  an  inflammable 
substance,  as  gunpowder  or  phosphorus. 
Certain  of  the  heat-rays  pass  directly 
from  A  to  B ;  the  greater  part,  however, 
reach  B,  by  being  twice  reflected.  The 
rays  emitted  from  A  are  reflected  by  the 
mirror,  M,  in  a  direction  parallel  to  its 
own  axis ;  these  rays  are  received  by  the 
second  mirror,  M,  and,  by  reflection,  are 
conveyed  to  the  focus  B,  igniting  the  gunpowder  or  phosphorus  placed  at  that 
point. 

The  reflection  of  heat  in  vacuo,  takes  place  according  to  the  same 
laws  as  in  air. 

636.  Determination  of  reflective  power. — Different  bodies  pos- 
sess very  different  powers  of  re- 

flection.  This  is  well  illustrated 
by  the  apparatus,  fig.  478,  de- 
signed by  Leslie. 

The  source  of  heat  is  a  cubical 
tin  canister,  M,  filled  with  boiling 
water.  A  plate,  a,  of  the  substance 
whose  reflective  power  is  to  be  de- 
termined, is  placed  between  the  mir- 
ror and  its  focus.  The  rays  of  heat 
emitted  from  M,  which  are  directed 
upon  the  mirror  N,  are  reflected 
upon  the  plate  a,  and  from  this, 
upon  the  bulb  of  the  thermoscope,  placed  at  the  point  where  the  rays  are 
brought  to  a  focus.  The  temperature  indicated  by  the  thermoscope  is  found  to 
vary  with  the  nature  of  the  plates. 

The  causes  which  modify  the  reflective  power  of  bodies  will  be  given  hereafter. 


HEAT. 


441 


637.  Absorptive  power. — Different  bodies  possess  very  different 
powers  of  absorbing  the  heat  thrown   upon   them.     The   absorptive 
power  of  a  body  is  always  in  the  inverse  ratio  of  its  reflective  power ; 
that  is,  the  best  reflectors  are  the  worst  absorbents,  and  vice  versa. 

The  absorptive  power  of  bodies  may  be  determined  by  a  modification  of  the 
apparatus,  fig.  478.  At  the  focus  of  the  mirror,  N,  is  placed  the  bulb  of  a  ther- 
moscope,  \vhich  is  successively  covered  with  different  substances,  as  with  lamp- 
black, Indian  ink,  gum  lac,  metallic  leaf,  Ac.  Leslie  has  been  the  principal 
experimenter  in  this  department  of  heat.  A  smoke-blackened  surface,  and  a 
surface  covered  with  carbonate  of  lead,  absorb  nearly  all  the  radiant  heat  thrown 
upon  them  :  elass,  T^°5  ;  polished  cast  iron,  y2^  j  tin,  -^fo  ;  silver,  T§^.  Table 
no.  VIIL,  Appendix,  gives  the  results  obtained  by  Messrs,  de  la  Provostaye 
and  Desains. 

All  black  and  dull  surfaces  absorb  heat  very  rapidly  when  exposed  to  its 
action,  and  part  with  it  again  slowly  by  secondary  radiation.  The  different 
powers  of  absorption,  possessed  by  the  different  colors,  may  be  illustrated  by 
repeating  Franklin's  experiment.  Pieces  of  the  same  kind  of  cloth,  of  different 
colors,  were  placed  upon  the  snow ;  the  black  cloth  absorbed  the  most  heat,  so 
that  after  a  time  it  sunk  into  the  melted  snow  beneath  it,  while  the  white  cloth 
produced  but  little  effect ;  the  other  colored  cloths  produced  intermediate  effects. 
Ranged  according  to  their  absorbent  powers,  we  have,  1.  Black  (warmest  of 
all) ;  2.  Violet ;  3.  Indigo  j  4.  Blue  j  5.  Green  ;  6.  Red  j  7.  Yellow ;  and  8.  White 
(coldest  of  all). 

638.  Emissive  or  radiating  power. — The  earliest,  and  some  of  the 
most  valuable,  observations  upon  this  subject,  were  published  by  Sir 
John  Leslie,  in  his  Essay  on  Heat,  in  1804.     Leslie  proved  that  the 
rate  of  cooling  of  a  hot  body  is  more  influenced  by  the  state  of  its 
surface,  than  the  nature  of  its  substance.     It  also  varies  greatly  with 
different  substances,  as  may  be  seen  in  the  table  below. 

Leslie  employed  in  his  experiments  the  apparatus,  fig.  478.  A  bulb  of  a 
thermoscope  was  placed  in  the  focus  of  the  mirror,  the  other  bulb  being  pro- 
tected from  the  radiant  heat  by  a  screen.  The  cubical  vessel  containing  boiling 
water,  has  its  lateral  faces  covered  with  different  substances,  which  are  succes- 
sively turned  toward  the  mirror. 

The  table  below  gives  the  results  as  obtained  by  Leslie.  Lampblack,  pos- 
sessing the  greatest  emissive  power,  is  called  100. 


Lampblack     .     . 
Water  (by  calc'n) 

.  100 
.  100 

Indian  ink 
Ice      .... 

.  .  88 
.  .  85 

Polished  lead  .     .     . 
Mercury       .... 

19 

30 

Writing  paper 

.  98 

Minium  .     . 

.  .  80 

Polished  iron  . 

15 

Sealing  wax 
Crown  glass   .     . 

.  95 
.  90 

Plumbago    .     . 
Tarnished  lead 

.  .  75 
.  .  45 

"      silver,  tin, 
"      copper,  gold, 

12 

Messrs.  De  la  Provostaye  and  Desains,  and  also  Melloni,  have  obtained  results 
differing  somewhat  from  those  of  Leslie.  See  Table  VI.,  Appendix.  Melloni 
found  that  the  radiant  and  absorbent  powers  of  surfaces  were  not  always  pro- 
portional, as  the  following  table  shows  : — 


Lampblaok. 

Carbonate  of  Lead. 

China  Ink. 

Isinglass. 

Lac. 

Metallic  Surface. 

Absorptive  power  .     100 

53 

96 

52 

52 

14 

Radiant  power        .     100 

100 

85 

91 

72 

12 

40 


442  PHYSICS    OP    IMPONDERABLE    AGENTS. 

Mellcai  has  also  found  that  the  absorbent  power  of  surfaces  varied  consider- 
ably, according  to  the  source  of  the  radiation,  and  the  temperature  of  the 
ra<Xant  body.  (See  Table  IX.) 

.Jfrom  Melloni's  experiments  may  be  drawn  the  following  conclusions  :— 

1.  That  bodies  agree  very  nearly,  but   not   exactly,  in  their  emitting  and 
absorbent  powers. 

2.  That  their  absorbent  power  varies  very  remarkably  with  the  origin  a!>d 
intensity  of  the  calorific  rays. 

3.  That  they  approach  each  other  more  and  more  in  their  power  of  emitting 
and  absorbing  rays  of  heat,  when  the  temperature  approaches  that  of  boiling 
water ;  and  that,  when  at  exactly  that  temperature,  the  emitting  and  absorbent 
powers  coincide. 

639.  Causes  which  modify  the  emissive,  absorbent,  and 
reflective  powers  of  bodies. — Not  only  do  different  bodies  possess 
the  powers  of  reflection,  absorption,  and  emission  in  different  degrees, 
but  the  physical  condition  of  the  material  affects  them  in  an  important 
manner.  So  also  the  obliquity  of  the  incident  rays,  the  source  of  heat, 
and  the  thickness  of  the  superficial  layer,  exercise  great  influence. 

The  absorbent  and  emissive  powers  of  metallic  plates  are  diminished  if  they 
are  hammered  or  polished.  The  opposite  effect  is  produced  if  the  plates  are 
scratched  or  roughened.  This  is  doubtless  owing  to  the  change  in  density  which 
the  superficial  layers  of  the  plates  undergo  by  these  operations.  For  the  same 
reason,  the  reflective  power  of  a  substance  is  generally  increased  by  polishing 
or  hammering,  and  diminished  by  roughening  or  scratching  it;  which  latter 
also  causes  a  portion  of  the  heat  to  be  irregularly  reflected.  That  this  is  the 
true  explanation  is  probable  from  the  fact,  that  if  such  materials  as  ivory  or 
coal  are  taken,  whose  density  will  not  be  changed  by  roughening  or  polishing, 
the  reflective  and  absorbent  powers  remain  the  same. 

The  thickness  of  the  superficial  layer  has  an  influence  on  the  reflective  power 
of  bodies.  Leslie  covered  a  mirror  with  successive  coatings  of  varnish  ;  the 
reflection  diminished  as  the  number  of  layers  increased,  until  their  thickness 
amounted  to  twenty-five  thousandths  of  a  millimetre,  when  it  remained  con- 
stant. While  a  vessel  covered  with  layers  of  varnish  or  jelly  had  its  emissive 
power  increased  with  the  number  of  layers,  until  they  reached  sixteen  (with  a 
thickness  of  0-034  m.m.),  when  it  remained  constant,  even  upon  the  addition 
of  other  layers.  The  absorbent  power  of  substances  varies  with  the  nature 
of  the  source  of  heat.  Thus  a  substance  covered  with  white  lead,  absorbs 
nearly  all  the  thermal  rays  from  copper,  heated  to  212°  P. ;  56  of  those  from 
incandescent  platinum ;  and  53  of  those  from  an  oil  lamp.  Lampblack  is  the 
only  substance  which  absorbs  all  the  thermal  rays,  whatever  be  the  source  of 
heat.  This  subject  has  been  ably  treated  by  Prof.  A.  D.  Bache.* 

The  absorp'/ve  power  varies  with  the  inclination  of  the  incident  rays;  the 
smaller  tho  angle  of  incidence  the  greater  is  the  absorption.  This  is  one  of  the 
reasons  why  the  sun  heats  the  earth  more  in  summer  and  less  in  winter. 

The  reflective  power  of  glass  increases  with  the  angle  of  incidence,  but  with 
metallic  surfaces  the  proportion  of  heat  reflected  diminishes  with  the  angle  of 
incidence,  and  is  the  same  as  the  proportion  of  light  reflected,  §  407. 

640.  Applications  of  the    powers  of  reflection,    absorption, 


*  Am.  Jour.  Sci.  [1]  XXX.  16,  1836. 


HEAT.  443 

and  radiation  are  often  made  in  the  economical  use  of  heat.  We 
shall  refer  only  to  the  more  familiar  examples. 

Meat-roasters  and  Dutch-ovens  are  constructed  of  bright  tin,  to  direct  the 
heat  from  the  fire  upon  the  article  cooking. 

Hoar  frost  remains  longer  in  the  presence  of  the  morning  sun  upon  light- 
colored  objects  than  upon  the  dark  soil,  because  the  latter  absorbs  much  of  the 
heat,  while  the  former,  reflecting  it,  remain  too  cold  to  thaw  the  frost.  Water  is 
slowly  heated  in  bright  metallic  vessels,  as  in  a  silver  cup  or  a  clean  bright 
kettle,  because  they  are  poor  absorbents,  but  if  the  sides  and  bottom  of  the 
vessels  become  covered  with  soot,  the  water  is  heated  quickly. 

To  keep  a  liquid  warm  it  should  be  contained  in  a  vessel  composed  of  a  poor 
radiating  material.  Hence  if  tea  and  coffee  pots,  &c.,  are  made  of  polished 
metal,  they  retain  the  heat  much  longer  than  those  which  have  a  dull  sift'faee  or 
are  composed  of  earthenware. 

Stoves  of  polished  sheet-iron  radiate  less  heat,  but  keep  hot  longer  than  those 
made  of  cast-iron  with  a  rough  and  dull  surface. 

Pipes  conveying  steam  should  be  kept  bright  or  thoroughly  covered  with  felt 
or  cloth  until  they  reach  the  apartments  to  be  warmed,  and  there  their  surfaces 
should  be  blackened  in  order  to  favor  the  process  of  radiation. 

II.     DIATHERMANCY. 

641.  Transmission  of  radiant  heat. — Light   passes   through  all 
transparent  bodies  from  whatever  source  it  may  come.     The  rays  of 
heat  from  the  sun  also,  like  the  rays  of  light  from  the  same  luminary, 
pass  through  transparent  substances  with  little  change  or  loss.   Radiant 
heat,  however,  from  terrestrial  sources,  whether  luminous  or  not,  is  in 
a  great  measure  arrested  by  many  transparent  substances  as  well  as  by 
those  which  are  opaque. 

The  glass  of  our  windows  remains  cold,  while  the  heat  of  the  sun,  passing 
through  it,  warms  the  room.  A  plate  of  glass  held  before  the  fire  stops  a  large 
part  of  the  heat,  although  the  light  is  not  sensibly  diminished. 

Melloni  terms  those  bodies  which  transmit  heat  diathermanous,  or 
diathermic  (from  the  Greek,  did,  though,  and  0£pfj.aivu>,  to  heat)  ;  those 
bodies  which  do  not  allow  this  transmission  of  heat  are  termed  alher- 
manous,  or  adiathermanic  (from  alpha,  privative,  and  OepiJLaivtt)}. 

It  appears  that  many  substances  are  eminently  diathermanous,  which 
are  almost  opaque  to  light ;  smoky  quartz  for  example. 

Prevost  of  Geneva,  and  De  la  Roche,  in  France,  in  1811  and 
1812,  discovered  many  of  the  phenomena  of  diathermanous  bodies,  but 
it  is  from  the  beautiful  researches  of  Melloni,  in  1832 — 1848,  that  our 
knowledge  upon  this  subject  has  been  chiefly  derived.  Melloni,  called 
by  De  la  Rive  "  the  Newton  of  heat,"  died  of  cholera  at  Naples,  in 
August,  1854. 

642.  Melloni's  apparatus. — The  apparatus  used  by  Melloni  in  his 
researches   upon   the   transmission  of  heat,  is  represented  in  all  its 
essential  details  in  fig.  479- 


444  PHYSICS    OF   IMPONDERABLE    AGENTS. 

At  one  end  of  the  graduated  metallic  bar,  L  L,  is  placed  the  therino-multiplier, 
m,  and  in  connection  with  it,  by  fine  wires,  A  B,  the  anastatic  galvanometer, 
§  905,  D.  Upon  the  stand,  a,  is  placed  the  source  of  heat;  in  this  case  a  Loca- 
telli  lamp  :  F  is  a  double  screen  to  prevent  the  radiation  of  the  heat  from  the 

479 


source,  and  is  lowered  at  the  moment  of  observation :  E  is  a  perforated  screen 
which  allows  only  a  certain  quantity  of  rays  to  pass  through  it  and  to  fall  upon 
C,  which  represents  the  substance  whose  diathermancy  is  to  be  determined. 

In  experimenting,  the  source  of  heat  is  placed  at  such  a  distance,  that  when 
F  is  removed,  the  heat  directed  upon  m,  will  cause  the  needle  of  the  galvano- 
meter to  move  through  30°.  The  screen,  F,  is  then  raised,  and  the  plate,  C,  to 
be  experimented  upon,  is  placed  upon  the  stand.  When  the  needle  of  the  gal- 
vanometer, D,  has  returned  to  0°  (its  normal  position),  the  screen,  F,  is  removed. 
The  proportion  of  heat  transmitted  through  the  plate,  C,  is  then  indicated  by 
the  arc  of  vibration  of  the  needle,  over  the  dial  plate  of  D.  The  construction 
of  the  galvanometer  and  thermo-multiplier  is  more  particularly  described  in  the 
chapter  on  thermo-electricity. 

643.  Influence  of  the  substance  of  screens. — In  experimenting 
with  liquids,  they  were  placed  in  glass  cells.  The  stratum  of  liquid 
was  9'21  m.  m.  ('362  in.)  in  thickness.  The  source  of  heat  used  was 
an  argand  oil  lamp. 

The  independence  of  transparency  and  diathermancy  was  clearly 
shown  in  these  researches,  for  it  was  found  that  the  bisulphid  of 
carbon  transmitted  three  times  as  many  heat-rays  as  ether,  four  times 
as  many  as  alcohol,  and  more  than  five  times  as  many  as  water, 
although  these  liquids  are  equally  transparent  and  colorless.  Table  X 
gives  the  diathermancy  of  different  liquids. 

It  is  found  that  those  solids  which  are  transparent  to  light  do  not 
necessarily  allow  the  passage  of  heat,  and  vice  versa.  Thus  sulphate 
of  copper  transmits  the  blue  rays  of  light,  but  entirely  arrests  the  rays 


HEAT.  445 

of  heat.  Again,  black  mica,  smoked  rock-salt,  and  opaque  black  glass, 
transmit  a  considerable  portion  of  the  heat-rays,  but  prevent  the 
passage  of  light. 

Rock-salt  is  the  only  substance  that  permits  an  equal  amount  of  heat 
from  all  sources  to  pass  through  it.  Melloni  experimented  with  plates 
of  this  substance  of  a  thickness  varying  from  one-twelfth  of  an  inch  to 
two  or  three  inches,  and  in  all  cases  92*3  of  100  rays  incident  upon 
them  were  transmitted.  The  loss  of  7'7  per  cent,  being  due  to  a 
uniform  quantity  which  is  reflected  at  the  two  surfaces  of  the  plate. 
Rock  salt  is,  therefore,  to  heat,  what  clear  glass  is  to  light,  and  well 
deserves  the  name  which  Melloni  gave  it,  of  the  glass  of  heat. 

The  diathermanic  power  of  different  solids  for  different  sources  of  heat 
may  be  found  in  detail  in  Table  XIII. 

644.  Influence  of  the  material  and  nature  of  the  source. — The 
quantity  of  heat  transmitted  through  different  solids  of  the  same  thick- 
ness is  very  variable.     The  nature  of  the  source  of  heat  exercises  a 
great  influence  on  the  diathermanic  power  of  bodies.     Melloni,  in  his 
experiments,  used  four  sources  of  heat,  viz. :  1.  The  naked  flame  of  a 
lamp  ;  2.  Incandescent  platinum  ;  3.  Copper  heated  to  700°  F. ;  and, 
4.  Copper  heated  to  212°  F. 

645.  Other  causes  which  modify  the  diathermanic  power  of 
bodies   are  the  degree  of  polish,  the  thickness  and  number  of  the 
screens,  and  also  the  nature  of  the  screens  through  which  the  heat  has 
been  previously  transmitted. 

The  quantity  of  heat  which  a  diathermanic  body  transmits,  increases  with  the 
degree  of  polish  of  its  surface.  The  diathermanic  power  of  a  body  diminishes  with 
its  thickness,  although  according  to  a  less  rapid  rate.  Thus  with  four  plates  whose 
thickness  was  as  the  numbers  1,  2,  3,  4;  of  1000  rays,  the  quantity  absorbed  by 
each  was,  respectively,  619,  577,  558,  549  :  so  that  beyond  a  certain  thickness 
of  the  body,  the  quantity  of  heat  it  can  transmit  remains  nearly  constant.  Rock- 
salt  is  the  only  exception  to  this  law  5  it  always  allows  the  same  quantity  of  heat 
to  pass  through  it,  at  least  for  thicknesses  between  2  and  40  m.  m.  (-0787  and  * 
1-575  in.) 

The  increase  of  the  number  of  screens  produces  an  effect  similar  to 
an  increase  of  thickness.  If  many  plates  of  the  same  kind  are  placed 
together,  they  absorb  more  heat  than  one  plate  having  the  combined 
thickness  of  several,  owing  to  the  numerous  surfaces. 

The  thermal  rays  which  have  passed  through  one  or  more  diathermanic  bodies, 
are  so  modified,  that  they  pass  with  more  facility  through  other *diathermanic 
bodies  than  direct  rays  do.  Thus  the  heat  from  an  argand  lamp,  where  the 
flame  is  surrounded  with  a  glass  chimney,  differs  much  in  its  transmissibility 
from  the  heat  of  a  Locatelli  lamp,  where  the  flame  is  free  and  open.  Thus  in 
making  use  of  an  argand  lamp  surrounded  with  a  glass  chimney,  and  a  Loca- 
telli lamp  which  is  not  thus  protected,  Melloni  obtained  the  following  results. 
40* 


446  PHYSICS    OF    IMPONDERABLE    AGENTS. 


TABLE  OF  HEAT  TRANSMITTED  FROM  DIFFERENT  SOURCES. 


Of  100  rays. 

Argand  lamp. 

Locatelli  lamp. 

Rock-salt  transmitted 

92 

92 

Iceland  spar     " 

62 

39 

Quartz  (limpid)  blackened,  transmitted 

57 

34 

Sulphate  of  lime                             " 

20 

19 

Alum                                                 " 

12 

7             ! 

646.  Thermochrosy,  or  heat-coloration  (Osp/tot;,  heat,  and 
color). — As  Newton  has  shown  that  a  pencil  of  white  light  is  composed 
of  different  colored  rays,  which  are  unequally  absorbed  and  transmitted 
by  different  media,  and  which  may  be  combined  together  or  isolated, 
so  Melloni  argues  from  his  results,  that  there  are  different  species  of 
calorific  rays  emitted   simultaneously  in  variable  proportions  by  the 
different  sources  of  heat,  and  possessing  the  property  of  being  trans- 
mitted more  or  less  easily  through  screens  of  various  substances. 

If  a  pencil  of  solar  light  falls  successively  upon  two  plates  of  colored  glass, 
one  red  and  the  other  bluish-green,  it  will  be  wholly  absorbed,  the  second  plate 
-  absorbing  all  the  rays  transmitted  by  the  first.  This  is  precisely  analogous  to 
what  may  happen  with  a  thermal  pencil,  its  entire  absorption  being  caused  by 
passing  it  through  two  media  successively,  each  of  which  absorbs  the  rays 
transmitted  by  the  other.  Viewed  in  this  manner,  it  may  be  said  that  rock-salt 
is  colorless  as  respects  heat,  while  alum,  ice,  and  sugar-candy,  are  almost  black. 
It  is  a  fact  of  common  observation,  that  snow  melts  more  quickly  under  trees 
and  bushes  than  in  those  spots  which  receive  the  direct  rays  of  the  sun.  This 
is  proved  by  Melloni  to  be  owing  to  the  fact,  that  the  rays  emitted  by  the  heated 
branches  are  of  a  different  nature  from  the  direct  rays  of  the  sun,  and  more 
easily  absorbed  by  snow  than  the  latter. 

647.  Applications  of  the  diathermancy  of  bodies. — The  air  is 

undoubtedly  very  diathermanic,  or  else  the  upper  layers  would  be  heated 
by  the  solar  rays  passing  through  them,  while  we  know  that  they  are 
only  slightly  heated  by  this  means. 

In  certain  processes  of  the  arts,  workmen  protect  their  faces  by  a 
glass  mask,  which  allows  the  passage  of  the  light  but  arrests  the  heat 

In  certain  physical  experiments,  where  heat  is  to  be  avoided,  the 
light  is  first  passed  through  a  solution  or  plate  of  alum,  whereby  the 
heat  is  arrested.  On  the  contrary,  if  the  heat  is  directed  upon  rock-salt 
covered  with  lampblack,  the  light  is  arrested  but  the  heat  passes  through 
but  slightly  diminished. 

648.  Refraction  of  heat. — Heat,  like  light,  is  refracted,   or  bent 
out  of  its  course,  in  passing  obliquely  through  diathermanic  bodies,  as 
is  shown  by  the  burning-glass.     A  double  convex  lens,  fig.  480,  con- 


HEAT.  447 

centrates   the  rays  of  heat  from  the  sun,  or  other  heated  body,  m 

the   same   manner   as   it  concentrates  the  rays  of  light.     It  is  only 

with  a  lens  of  rock-salt,  that  the  rays  480 

of  all  our  sources  of  heat  can  be  con. 

densed,  for  a  lens  of  glass  concentrates 

only  the  solar  rays,  and  becomes  itself 

heated  by  artificial  heat,  M 

A  lens  of  ice  was  made  in  England  in 
1763,  having  a  diameter  of  3  metres  (118-112 
in.),  at  whose  focus  gunpowder,  paper,  and 
other  combustibles  were  inflamed.  Burning- 
glasses  have  generally  more  power  than  mirrors  of  equal  diameter.  Both  pro- 
duce their  more  intense  effects  on  high  mountains  after  a  fall  of  snow,  for  then 
the  air  is  free  from  moisture,  and  the  solar  rays  lose  less  of  their  intensity  in 
passing  through  it. 

649.  Polarization  of  heat. — Heat  is  polarized  in  the  same  manner 
as  light.     It  undergoes  double  refraction  by  Iceland  spar,  and  the  two 
beams  are  polarized  in  planes  at  right  angles  to  each  other.     A  pencil 
of  heat,  polarized  by  a  plate  of  tourmaline,  or  by  a  NicoPs  prism,  is 
transmitted   or   intercepted  by  another   tourmaline   plate   or   NicoFs 
prism,  in   the    same   circumstances   that   a   pencil  of  polarized  light 
would  be  transmitted  or  intercepted. 

Heat  also  suffers  a  rotation  of  its  plane  of  polarization,  by  plates  of  right  or 
left-handed  quartz,  in  the  same  direction,  and  to  the  same  extent  as  light  of  the 
same  refrangibility.  Polarization  of  heat  is  also  effected  by  reflection  from 
plates  of  glass,  or  by  repeated  refraction,  also  by  reflection  from  the  atmosphere, 
in  which  points  of  no  polarization  and  of  maximum  polarization  exist  cor- 
responding with  similar  points  in  regard  to  polarized  light.  The  phenomena 
of  magnetic  rotary  polarization  of  heat  have  also  been  observed. 

Prof.  Forbes  of  Edinburgh  first  demonstrated  the  polarization  of  heat. 
Knoblauch  has  obtained  distinct  evidence  of  the  diffraction  and  inter- 
ference of  the  rays  of  heat. 

2  6.  Calorimetry. 

650.  Calorimetry. — The  amount  of  heat  required  to  produce  a  given 
temperature  varies  greatly  for  the  different  bodies  to  which  it  is  applied. 
Calorimetry  (from  calor,  heat,  and  /nerpov,  measure)  is  the  measure- 
ment of  the  quantity  of  heat  which  different  bodies  absorb  or  emit 
during  a  known  change  of  temperature,  or  when  they  change  their 
state.    Water  absorbs  or  emits  a  much  greater  quantity  of  heat  during 
a  change  of  temperature  than  the  same  weight  of  any  other  substance. 
It  is  therefore  selected  as  the  standard  of  comparison. 

Unit  of  Heat. — The  quantity  of  heat  which  is  required  to  raise 
a  pound  of  pure  water  from  32°  to  33°  F.,  is  reckoned  as  the  unit  of 
heat,  or  thermal  unit,  both  in  this  country  and  in  England. 


448  PHYSICS    OF    IMPONDERABLE    AGENTS. 

lii  France,  and  in  Europe  generally,  the  thermal  unit  is  the  quantity 
of  heat  necessary  to  raise  one  kilogramme  (2-20486  Ibs.)  of  water  from 
0°  to  1°  C. 

651.  Specific  heat. — If  equal  weights  of  water  and  mercury  at  the 
same  temperature  be  placed  over  the  same  source  of  heat,  it  will  be 
found,  that  the  mercury  becomes  heated  much  more  quickly  than  the 
water.  That  when  the  water  is  heated  10°  the  mercury  will  have 
become  heated  330° ;  the  capacity  of  water  for  heat  is,  therefore,  33 
times  as  great  as  that  of  mercury.  Each  substance  in  this  regard  has 
its  own  capacity  for  heat.  This  relation  is  called  caloric  capacity,  or 
more  commonly,  specific  heat.  Table  XI.  contains  the  specific  heats  of 
certain  solids  and  liquids  as  determined  by  Regnault. 

Three  methods  have  been  devised  for  determining  the  specific  heat 
of  bodies :  these  are,  1st,  the  method  of  mixture  ;  2d,  by  the  melting  of 
ice ;  3d,  by  cooling. 

Method  of  Mixture. — This  method  is  exceedingly  simple  in  theory, 
and,  with  suitable  care,  exact  in  its  results. 

In  determining  the  specific  heat  of  solids  by  this  method,  a  weighed  mass  of 
each  substance  is  heated  to  the  proper  degree,  and  is  then  plunged  into  a  mea- 
sure of  water  of  known  temperature  and  weight.  The  elevation  of  temperature 
produced  in  each  case  is  carefully  noted. 

If  a  pint  of  water  at  150°  be  mixed  quickly  with  a  pint  at  50°  F.,  the  two 
measures  of  water  will  have  a  temperature  of  100°,  or  the  arithmetical  mean  of 
the  two  temperatures  before  mixture.  If,  however,  a  measure  of  mercury  at  50° 
be  mingled  with  an  equal  measure  of  water  at  150°,  the  temperature  of  the 
mixture  will  be  118°.  The  mercury  has  gained  68°  while  the  water  has  lost 
32°.  Hence  it  is  inferred,  that  the  same  quantity  of  heat  will  raise  the  tempera- 
ture of  mercury  through  twice  as  many  degrees  as  that  of  an  equal  volume  of 
water,  and  that  the  specific  heat  of  water  is  to  that  of  mercury  as  1  :  0-47  when 
compared  by  measure. 

If,  however,  equal  weights  of  these  bodies  be  taken,  the  resulting  temperature 
is  then  still  more  in  contrast.  A  pound  of  mercury  at  40°,  mixed  with  a  pound 
of  water  at  156°,  produces  a  mixture  whose  temperature  is  1520<3.  The  water 
loses  3°-7,  while  the  mercury  gains  112°-3,  and  therefore,  taking  the  specific 
heat  of  water  as  1,  that  of  the  mercury  will  be  0*033,  since, 

112°-3  :  3°-7  =  1  :  x  =  (0-033.) 

Method  by  Fusion  of  Ice. — This  method  is  founded  on  the  quan- 
tity of  ice  melted  by  different  bodies  in  cooling  through  the  same  number 
of  degrees. 

Lavoisier  and  Laplace  contrived  the  apparatus,  fig.  481,  used  for  this  purpose, 
and  called  a  calorimeter.  It  consists  of  three  vessels  made  of  sheet  tin  or 
copper.  In  the  interior  vessel,  c,  pierced  with  holes  and  closed  by  a  double 
cover,  is  placed  the  substance  whose  specific  heat  is  to  be  determined.  This  is 
entirely  surrounded  by  ice  contained  in  the  second  vessel,  b,  and  also  on  the 
cover.  In  order  to  cut  off  the  heat  of  the  surrounding  air,  the  exterior  vessel,  a, 
is  also  filled  with  ice.  The  water  from  the  ice  melted  in  this  outer  vessel,  passes 


HEAT.  449 

off  by  the  stop-cock,  r.  The  body  in  the  interior  vessel,  cooling,  melts  the  ice 
surrounding  it,  and  the  water  from  it  flows  off  through  the  stop-cock,  «,  and  is 
weighed.  481 

The  specific  heat  of  different  substances  is  determined 
in  this  apparatus  by  the  comparative  weights  of  the 
water  produced  during  the  experiments ;  in  which  a 
certain  weight  of  each  body  cools  from  an  agreed 
temperature,  e.  g.  (212°  F.),  to  32°,  the  constant  tem- 
perature of  the  vessel  C. 

The  specific  heat  of  a  liquid  is  determined  by  placing 
it  in  a  vessel,  as  of  glass,  whose  specific  heat  is  known. 
The  amount  of  ice  melted  by  the  liquid,  is  the  whole 
quantity  of  water  produced,  minus  that  which  would 
be  melted  by  the  glass  alone. 

This  method,  though  excellent  in  principle,  is  subject 
to  many  inaccuracies,  and  is  now  seldom  employed. 

The  method  of  cooling  is  founded  on  the  different  rates  of  cooling 
of  equal  masses  of  different  substances;  those  having  the  greatest  specific 
heat  cooling  most  slowly. 

The  application  of  this  method  is  also  attended  with  so  many  sources 
of  error  that  it  is  seldom  employed,  and  need  not  be  described. 

Specific  heat  affected  by  change  of  state. — A  body  in  the  liquid 
state  has  a  greater  specific  heat  than  when  it  is  in  the  solid  form,  as  might  be 
concluded  from  the  fact  that  the  addition  of  heat  is  necessary  to  convert  the 
solid  into  a  liquid. 

Thus  ice  has  a  specific  heat  of  0-505,  water  being  1-000 ;  sulphur  solid,  0-2026, 
fluid,  0-2340;  phosphorus,  between  45°  and  —6°,  0-1887,  at  212°,  0-2045,  &c. 

The  high  specific  heat  of  water  moderates  very  greatly  the  rapidity 
of  natural  transitions  from  heat  to  cold  and  from  cold  to  heat,  owing  to 
the  large  quantity  of  heat  emitted  or  absorbed  by  the  ocean,  and  other 
bodies  of  water,  in  accommodating  themselves  to  variations  in  external 
temperature. 

652.  Specific  heat  of  gases. — If  a  unit  of  weight  of  any  gas, 
allowed  to  expand  freely  without  change  of  pressure,  is  heated  from 
the  freezing  point  one  degree,  the  amount  of  heat  thus  absorbed,  mea- 
sured in  fractions  of  the  unit,  is  called  the  specific  heat  undeit^onstant 
pressure.  If  the  same  gas  is  heated  one  degree,  when  so  confined  that 
its  volume  cannot  be  increased,  the  amount  of  heat  required  to  produce 
the  change  of  temperature  is  called  the  specific  heat  under  a  constant 
volume. 

When  the  heat  required  to  raise  the  temperature  of  equal  volumes 
of  different  gases  one  degree,  is  determined,  the  results  obtained  are 
called  specific  heat  by  volume.  In  these  determinations  the  unit  of 
volume  is  the  volume  of  a  unit  of  weight  of  air  when  the  barometric 
pressure  is  30  inches. 


450  PHYSICS    OF    IMPONDERABLE    AGENTS. 

The  determination  of  the  specific  heat  of  gases  is  a  problem  involved  in 
the  greatest  practical  difficulties,  and  authorities  vary  somewhat  in  the  results 
obtained. 

The  most  valuable  researches  in  regard  to  the  specific  heat  of  ga^es 
have  been  made  by  Regnault.  He  has  established  the  following  very 
important  preliminary  principles  :— 

First.  The  specific  heat  of  gases  is  sensibly  the  same  at  all  tempera- 
tures, 

Second.  The  amount  of  heat  required  to  raise  the  temperature  of  a 
given  weight  of  any  gas  one  degree  does  not  vary  with  the  pressure  to 
which  it  is  subjected,  and  hence  the  specific  heat  of  gases  is  the  same  for 
all  densities. 

Regnault  experimented  on  air  and  other  gases  under  pressures  varied  from 
one  to  ten  atmospheres,  and  found  no  sensible  difference  in  the  quantity  of  heat 
which  the  same  weight  of  a  gas  lost  under  these  different  pressures  in  cooling 
the  same  number  of  degrees.  Nevertheless  he  thinks  it  possible  that  slight  dif- 
ferences may  exist. 

Table  XL  c.  gives  the  specific  heats  of  different  gases  and  vapors  as  determined 
by  Regnault.  The  specific  heat  by  weight  being  determined  under  a  constant 
pressure,  the  gas  being  allowed  to  expand  freely. 

The  specific  heats  by  volume  given  in  the  table  were  obtained  by  multiplying 
the  specific  heat  by  weight,  by  the  specific  gravity  of  the  several  gases  and 
vapors,  as  compared  with  air  taken  as  unity. 

653.  Specific  heat  of  gases  under  a  constant  volume. — It  is 
well  known,  that  the  temperature  of  a  confined  mass  of  air  can  be 
raised  sufficiently  high  to  ignite  tinder  by  mechanical  condensation, 
§  739,  and  it  seems  reasonable  to  suppose  that  the  same  amount  of  heat 
is  expended  in  producing  an  equal  degree  of  expansion  when  a  gas  is 
heated. 

It  has  been  stated  (608)  that  gases  expand  5£T  part  of  their  volume  for  an 
elevation  of  temperature  of  1°  F.  Let  t  represent  the  small  increase  of  tempe- 
rature which  a  mass  of  gas  undergoes  when  compressed  ?£T  of  its  volume,  and 
if  S  represent  the  specific  heat  of  the  gas  under  a  constant  pressure,  and  S'  the 
specific  heat  under  a  constant  volume,  we  shall  have  for  the  specific  heat  under 

* 
a  constant^ volume : —  S'  = 

It  is  obvious  that  if  the  value  of  t  could  be  determined  by  condensing  a  gas, 
and  observing  the  increase  of  temperature  the  value  of  S',  the  specific  heat 
under  a  constant  volume  could  be  readily  calculated.  The  unavoidable  loss  of 
heat  absorbed  by  the  walls  of  the  containing  vessel,  when  a  gas  is  compressed, 
has  rendered  it  hitherto  impossible  to  obtain  accurate  values  of  t  by  this  method, 
and  similar  difficulties  have  attended  the  determination  of  the  specific  heat  under 
a  constant  volume  by  other  direct  methods. 

The  principles  of  acoustics  have  happily  furnished  an  indirect  method 
of  determining  the  specific  heat  of  gases  under  a  constant  volume  with 
jreat  accuracy. 


HEAT. 


451 


Specific  heat  determined  by  the  laws  of  acoustics. — By  con 

sidering  the  conditions  of  an  elastic  fluid  during  the  transmission  of  a 
sonorous  wave,  Newton  obtained  the  following  formula  for  the  velo- 


city of  sound  in  any  gas : 


F  = 


In  this  formula  F  is  the  velocity  of  sound,  g  the  force  of  gravity,  H 
the  height  of  the  barometer,  and  d  the  density  of  the  gas  referred  to 
mercury  as  unity.  This  formula  gives  for  the  velocity  of  sound  in  dry 
air  at  32°  F.,  when  the  barometer  stands  at  30  inches,  F=  883  feet, 
which  is  less  than  the  true  velocity  of  sound  (1086  feet,  §  344)  by  more 
than  one-sixth  of  the  whole. 

Laplace  discovered  that  this  error  resulted  from  the  effect  of  heat 
developed  and  absorbed  by  alternate  compression  and  rarefaction  of 
the  air  in  the  transmission  of  sonorous  waves,  and  he  showed  that  the 
formula  for  the  velocity  of  sound,  taking  into  account  this  effect  of  heat, 

should  be,      V  =  ^lq.  —  .    ->  in  which  S  represents  the  specific  heat 
V      d  S/ 

of  the  gas  under  a  constant  pressure,  and  S/  the  specific  heat  under  a 
constant  volume.  ; 

From  this  formula  we  obtain,  by  transposition,  S'  =  ™-T-,from  which 

we  readily  obtain  the  value  of  the  specific  heat  of  a  gas  under  a  con- 
stant volume,  when  the  velocity  of  sound  in  the  medium,  and  the  other 
constant  quantities,  are  known. 

By  this  method  Dulong  has  obtained  for  the  specific  heat  of  gases, 
under  a  constant  volume,  the  values  given  in  the  following  table  ;  but 
the  results  obtained  are  regarded  only  as  approximations : — 

SPECIFIC  HEAT  OF  EQUAL  VOLUMES.* 


Name  of  Gas. 

Under  Constant 
pressure. 

Under  Constant 
volume. 

Difference 
S—  & 

l  +  t. 

Air,  

0-2377 

0-1678t 

0-0699t 

1  417f 

Oxygen,     .     .     . 

0-2412 

0-1705 

0-0707 

1-415 

Hydrogen,      .     . 

0-2356 

0-1675 

0-0681 

1-407 

Oxyd  of  carbon, 

0-2399 

01681 

0-0718 

1-428 

Carbonic  acid,     . 

0-3308 

0-2472 

0-0836 

1-338 

Olefiant  gas,  . 

0-3572 

0-2880 

0-0692 

1-240 

Comparing  these  results  in  the  case  of  air,  we  see  that  when  air  is  heated 
in  a  situation  where  it  is  free  to  expand,  only  about  f  of  the  heat  applied 
is  expended  in  producing  elevation  of  temperature — as  in  heating  a 


*  Cooke's  Chemical  Physics. 

f  Corrected  according  to  the  most  recent  experiments. 


452  PHYSICS   OF   IMPONDERABLE    AGENTS 

room  — while  about  f  of  the  heat  is  expended  in  producing  expansion 
of  the  air,  to  be  given  out  again  as  the  room  cools. 

Dulong  has  deduced  from  his  experiments  the  following  conclu- 
sions : — 

1.  Equal  volumes  of  all  gases,  measured  at  the  same  temperature  and 
pressure,  set  free  or  absorb  the  same  quantify  of  heat  when  they  are  com- 
pressed or  expanded  the^same  fractional  part  of  their  volume. 

If  all  gases  had  the  same  specific  heat,  the  same  change  of  volume 
would  be  attended  by  the  same  change  of  temperature.  But  this  is 
the  case  only  with  oxygen,  hydrogen,  and  nitrogen.  The  specific  heats 
of  compound  gases  differ  considerably  from  each  other,  and  change  of 
volume  causes  less  change  of  temperature  in  proportion  as  the  specific 
heat  of  the  gas  is  greater. 

2.  The  variations  of  temperature  which  result,  are  in  the  inverse  ratio 
of  the  specific  heats  under  a  constant  volume. 

Whether  these  laws  are  the  exact  expressions  of  the  truth,  or  only 
approximately  correct,  remains  to  be  determined  by  further  investiga- 
tion. 

654.  Relation  between  the  specific  heat  and  atomic  weight  of 
elements  and  compounds. — Dulong  and  Petit,  from  their  researches 
upon  the  elements,  were  led  to  conclude,  that  the  ultimate  atoms  of  all 
elements  possessed  the  same  capacity  for  heat,  and  they  accordingly 
announced  the  law,  that : — 

The  specific  heat  of  elementary  substances  is  in  inverse  ratio  to  their 
atomic  weights. 

This  law  appears  to  be  true  for  most  of  the  elements,  as  will  be  seen  by 
examining  Table  XL  of  Atomic  Weights  and  Specific  Heats.  It  will  be  no- 
ticed, that  the  one  increases  in  almost  the  exact  proportion  in  which  the  other 
diminishes,  and  that  by  multiplying  them  together,  a  very  nearly  constant  pro- 
duct is  obtained.  Some  elements,  as  those  given  in  the  lower  part  of  the  table, 
give  a  product  ( G  X  P)  double  of  the  others.  So  that  equivalent  weights  of 
these  would  contain  twice  as  much  heat  as  equivalent  weights  of  those  first 
given. 

The  relation  between  the  specific  heat  and  atomic  weight  of  compounds  is 
expressed  by  Regnault  in  the  following  law  : — 

In  all  compound  bodies  containing  the  same  number  of  atoms,  and  of 
similar  chemical  constitution,  the  specific  heats  are  in  inverse  ratio  to 
their  atomic  weights. 

§  7.  Liquefaction  and  Solidification. 

655.  Latent  heat. — During  the  conversion  of  a  solid  into  a  liquid, 
or  of  a  liquid  into  a  gas  or  vapor,  a  certain  quantity  of  heat  is  absorbed 
or  disappears.     As  the  thermometer  and  the  senses  give  no  evidence 
of  the  existence  of  this  heat,  it  is  called  latent  heat. 

Let  a  pound  of  ice  and  a  pound  of  water,  each  at  the  temperature  of  32°,  be 


HEAT.  453 

exposed  to  the  same  source  of  heat  in  precisely  similar  vessels  j  it  will  be 
found,  at  the  moment  when  all  the  ice  is  melted,  that  the  water  into  which  it  is 
converted  has  still  the  temperature  of  32° ;  while  the  temperature  of  the  other 
pound  of  water  has  risen  from  32°  to  174°.  As  hoth  have  received  the  same 
amount  of  heat,  it  follows,  that  the  142°  which  have  disappeared,  have  been  used 
in  converting  the  ice  into  water,  and  have  become  latent  or  insensible. 

If  a  pound  of  water  at  212°  be  mixed  with  a  pound  of  powdered  ice  at  32°, 
when  the  ice  is  melted  the  two  pounds  will  have  the  temperature  of  only  52°  ; 
the  ice  gains  only  20°,  while  the  water  loses  160°.  Here  again  142°  have  dis- 
appeared or  have  become  latent. 

656.  Liquefaction  and  congelation  are  always  gradual,  owing 
to  the  absorption  or  evolution  of  heat  during  these  processes. 

If  this  was  not  so,  water  at  32°  would  immediately  become  ice,  upon  losing 
the  smallest  additional  portion  of  its  heat,  and  on  the  other  hand,  ice  would 
suddenly  pass  from  the  solid  to  the  liquid  state  by  the  smallest  addition  of  heat. 

This  fact,  coupled  with  the  law  of  irregular  expansion  of  water,  will  explain 
why  ice  never  acquires  any  very  great  thickness.  The  high  specific  heat  of 
water  acts  to  moderate  the  natural  changes  of  temperatures. 

657.  Freezing  mixtures. — Solids  cannot  pass  into  the  liquid  state 
without  absorbing  and  rendering  latent,  a  certain  amount  of  heat.     If 
the  heat  necessary  for  the  liquefaction  is  not  supplied  from  some  external 
source,  the  body  liquefying  will  absorb  its  own  sensible  heat.   A  know- 
ledge of  this  fact  enables  us  at  pleasure,  in  the  hottest  seasons  and 
climates,  to  produce  extreme  degrees  of  cold. 

The  so-called  freezing  mixtures  are  compounds  of  two  or  more  sub- 
stances, one  of  which  is  a  solid.  These,  when  mixed  together,  enter 
into  combination  and  liquefy.  The  operation  should  be  so  conducted, 
that  no  heat  can  be  absorbed  from  external  sources,  and  hence,  as  the 
substances  liquefy,  a  depression  of  temperature  results  proportional  to 
the  heat  rendered  latent.  (See  Table XII.) 

The  most  convenient  freezing  mixture  is  salt  1  part,  and  ice  or  snow  2  parts, 
universally  used  in  the  freezing  of  ices  and  creams.  With  this  freezing  mixture, 
a  temperature  of  4°  or  5°  below  zero  can  be  maintained  for  many  hours.  A 
solution  of  equal  parts  of  nitre  and  sal-ammoniac  will  reduce  the  temperature 
from  50°  to  10°  F.  Very  well  constructed  ice-cream  freezers  are  now  commonly 
sold  in  the  shops,  in  which  an  adroit  use  has  been  made  of  the  laws  of  radiant 
heat  and  conduction,  to  facilitate  the  rapidity  of  this  operation. 

Thilorier,  with  a  mixture  of  solid  carbonic  acid  and  sulphuric  acid,  or  sulphuric 
ether,  obtained  a  temperature  120°  below  zero.  More  lately,  Mitchell  obtained  by 
the  same  means  a  temperature  of — 130°  and  — 146°  F.  At  the  former  temperature, 
alcohol  (Sp.  Grr.  0-798)  had  the  consistency  of  oil,  and  at  the  latter  temperature 
resembled  melting  wax. 

In  the  liquefaction  of  metallic  alloys,  a  similar  depression  is  observed.  When 
an  alloy  composed  of  207  parts  lead,  118  tin  and  284  bismuth,  is  dissolved  in 
1617  parts  mercury,  the  temperature  will  sink  from  63°  to  14°  F. 

In  producing  extreme  degjrees  of  cold,  the  substance  to  be  operated  upon  is 
first  cooled  to  a  certain  degree  by  a  less  powerful  freezing  mixture,  before  the 
more  energetic  one  is  used ;  the  full  effect  of  the  latter  is  thus  obtained. 
41 


454  PHYSICS    OP    IMPONDERUILE    AGENTS. 

658.  Laws  of  fusion  and  latent  heat  of  fusion. — Expansion  (the 
first  effect  of  heat)  has  a  limit,  at  which  solids  become  liquids.     The 
powers  of  cohesion  are  then  subordinate  to  those  of  repulsion,  and 
fusion  results. 

Fusion  takes  place  in  accordance  with  the  following  laws : — 

1st.  All  solids  enter  into  fusion  at  a  certain  temperature,  invariable 
for  the  same  substance. 

2d.  Whatever  may  be  the  intensity  of  the  source  of  heat  when  the 
fusion  commences,  the  temperature  remains  constant  until  the  whole  mass 
is  fused. 

3d.  The  latent  heat  of  fusion  is  obtained  by  multiplying  the  differ- 
ence between  the  specific  heat  of  the  substance  in  its  liquid  and  solid  form, 
by  the  quantity  obtained  by  adding  the  number  256  (an  experimental  con- 
stant furnished  by  researches  upon  the  latent  heat  of  water]  to  the  melting 
point  of  the  substance  in  question. 

The  fusion  points  and  latent  heat  of  fusion  of  a  number  of  the  more 
important  substances  are  given  in  Table  XV.  of  the  Appendix,  drawn 
from  the  labors  of  Kegnault  and  others. 

659.  Peculiarities  in   the   fusion   of   certain   solids. — Certain 
solids  soften  before  they  become  liquefied ;  such  are  tallow,  wax,  and 
butter,  while  others  never  become  entirely  fluid.     This  is  because  the 
former  are  composed  of  several  substances,  which  melt  at  different  tem- 
peratures.   Metals,  like  iron  and  platinum,  that  are  capable  of  welding, 
soften  before  they  fuse.     Glass,  and  certain  metals,  never  attain  perfect 
fluidity.     The  fusion  of  sulphur  presents  striking  peculiarities.     (See 
Chemistry.} 

660.  Refractory  bodies. — Substances  difficult  of  fusion  are  called 
refractory  bodies. 

Among  the  most  refractory  bodies  are  silica,  the  metallic  oxyds,  lime,  baryta, 
alumina,  &c.  Their  fusion  may  be  effected  by  the  oxy-hydrogen  blow-pipe,  or 
by  the  use  of  the  voltaic  battery.  By  these  means,  also,  the  fusion  of  platinum 
is  effected,  which  resists  the  heat  of  a  powerful  blast-furnace,  although  a  thin 
wire  of  this  metal  can  be  melted  by  the  mouth  blow-pipe. 

Carbon  is  the  most  refractory  of  all  bodies.  Its  fusion  has  .not  yet  been  per  • 
fectly  effected ;  although,  by  means  of  the  voltaic  battery,  Professor  Silliman 
obtained  (in  1822)  unequivocal  evidences  of  the  volatility  and  partial  fusion  of 
this  substance :  and  more  lately  these  results  have  been  verified  by  Despretz, 
with  a  carbon  battery  of  600  cups ;  boron  and  silicon  also  yielding  to  the  same 
power. 

661.  Solution. — Saturation. — When  a  solid  immersed  in  a  liquid 
gradually  disappears,  the  process  is  termed  solution.     Thus,  sugar  and 
salt  dissolve  in  water,  camphor  in  alcohol,  &c.     Solution  is  the  result 
of  an  attraction  existing  between  the  particles  of  a  liquid  and  those  of 


HEAT.  455 

a  solid.  A  liquid  is  said  to  be  saturated  when,  at  a  given  temperature, 
it  has  dissolved  as  much  as  possible  of  a  solid. 

The  causes  which  diminish  cohesion  among  the  particles  of  a  solid,  generally 
facilitate  solution.  Thus,  a  pulverized  body  dissolves  quicker  than  the  same 
quantity  in  large  masses.  Heat  also  facilitates  solution  by  diminishing  the 
cohesive  force  and  producing  currents.  The  solubility  of  some  bodies  is  dimin- 
ished by  heat,  and  the  precipitation  of  bodies  from  solution  is  sometimes 
hastened  by  heat, — sulphate  of  soda  and  hydrate  of  lime  are  examples  of  the 
former. 

662.  Laws   of  solidification. — The  passage  of  a  body  from  the 
liquid  to  the  solid  state,  always  occurs  in  accordance  with  the  following 
laws : — 

1st.  The  solidification  of  a  body  takes  place  at  a  certain  fxed  tempera- 
ture, which  is  also  that  of  its  fusion. 

2d.  The  temperature  of  a  body  remains  constant  from  the  commence- 
ment to  the  end  of  its  solidification. 

663.  Elevation  of  temperature    during  solidification. — When 
liquids  return  to  the   solid  state,  the  heat  which  has  been  absorbed 
during  their  liquefaction,  and  rendered  latent,  is  given  out. 

If  the  solidification  takes  place  suddenly,  the  heat  evolved  is  often  very  appa- 
rent. Thus  water  may  be  cooled  to  22°  or  23°,  and  yet  remain  liquid,  but  if  in 
that  state  it  is  shaken,  it  becomes  at  once  a  confused  mass  of  ice  crystals,  and 
rises  to  32°,  the  freezing  of  a  part  giving  out  heat  enough  to  raise  the  tempera- 
ture of  the  whole  8°  or  10°.  Thus  we  arrive  at  the  seeming  paradox,  that  freezing 
is  a  warming  process  ;  and,  owing  to  the  absorption  of  heat  during  liquefaction, 
it  is  equally  true,  that  melting  is  a  cooling  process.  Hence,  in  part,  the  cooling 
influence  of  an  iceberg,  or  of  a  large  body  of  snow  on  a  distant  mountain. 

664.  Change  of  volume  during  solidification,  and  its  effects.^ — 

Mercury,  and  most  metals,  contract  while  solidifying ;  hence,  the  freez- 
ing of  a  mercurial  thermometer  does  not  burst  its  reservoir.  Water 
expands  during  freezing  to  the  amount  of  one-eleventh  of  its  bulk ; 
hence,  ice  floats  on  the  surface  of  water,  and  close  vessels,  even  of  iron, 
are  burst,  if  frozen  when  full  of  water. 

This  fact  is  familiar  to  housekeepers,  who  prevent  the  bursting  of  their  water- 
casks  during  winter,  by  a  stick  of  wood  placed  in  the  cask,  about  which  the 
bulge  from  expansion  takes  place.  Aqueduct  service-pipes  are  often  saved  from 
the  same  accident  in  cold  weather,  by  allowing  the  water  to  flow  uninterruptedly, 
thus  preventing  the  formation  of  ice  crystals,  both  by  motion  and  the  supply 
of  warmer  water. 

A  brass  globe  filled  with  water  burst  at  32°,  in  the  experiments  of  the  Flo- 
rentine Academicians,  who  estimated  the  force  exerted  as  equal  to  28,000  pounds 
on  the  square  inch.  A  bomb-shell,  filled  with  water,  and  tightly  closed  by  an 
iron  plug,  when  exposed  to  severe  cold  in  Montreal,  discharged  the  plug  to  a 
distance  of  400  feet,  and  a  cylinder  of  ice  eight  inches  in  length  protruded  from 
the  hole.  All  metals  which,  like  water,  assume  the  rhombohedral  form  on 
solidification,  produce  sharp  casts.  Such  are  cast-iron,  antimony,  tin,  zinc,  and 
bismuth.  All  alloys  capable  of  producing  sharp  casts,  must  contain  such  a 


456  PHYSICS    OF    IMPONDERABLE    AGENTS. 

metal.  Type-metal  (3  lead  and  1  antimony),  brass  (2  copper  and  1  zinc),  and 
bell-metal  (7  copper  and  3  tin),  are  familiar  examples.  Copper,  lead,  gold, 
silver,  and  indeed  most  metals,  except  those  above  enumerated,  crystallize  in 
the  monometric  system,  and  occupy  less  space  as  solids  than  as  fluids,  producing 
imperfect  casts.  Hence,  coins  are  stamped,  and  gold,  silver,  and  copper  utensils, 
and  ornamental  wares  are  wrought  by  the  hammer,  or  stamped,  to  secure  sharp- 
ness and  beauty. 

665.  Freezing  of  water. — Water  ordinarily  freezes  at  32° ;  but  it 
has  already  been  stated  (663)  that,  under  certain  circumstances,  it 
may  be  cooled  near  to  22°,  and  remain  liquid.     If,  however,  water  is 
turbid,  or  contains  carbonic  acid,  it  always  freezes  at  32°. 

Certain  experiments  made  in  France  indicate  that  the  temperature  to  which 
water  may  be  exposed  without  freezing,  falls  in  proportion  as  it  is  exposed  in 
tubes  of  smaller  diameter.  This  remarkable  circumstance  seems  to  throw  light 
upon  the  fact,  that  plants,  whose  capillaries  are  full  of  juices,  resist  frost  in  a 
manner  so  noticeable  as  many  of  them  do.  Nevertheless,  in  very  severe  weather, 
the  trunks  of  large  trees  are  sometimes  burst  open  by  frost. 

Water,  containing  salts  in  solution,  freezes  at  a  lower  temperature  than  pure 
water.  Thus,  sea  water  freezes  at  27°.  The  ice  formed  from  salt  water,  and 
from  impure  or  turbid  water,  is  comparatively  fresh  and  pure,  since  it  is  the 
water  which  freezes,  and  not  the  foreign  bodies  it  contains.  Frozen  ink,  and 
other  colored  fluids,  precipitate  the  coloring  matterj  and  are  spoiled  as  colors, 
until,  by  boiling,  the  precipitate  is  again  diffused.  Likewise,  the  watery  portion 
of  cider,  and  other  weak  alcoholic  liquors,  exposed  to  moderate  cold,  congeals ; 
and  the  alcoholic  part  may  thus  be  obtained  in  a  more  condensed  state. 

Some  absorbent  rocks  are  pulverized,  and  gradually  covered  by  a  thick  bed 
of  soil,  by  the  effects  of  freezing  water  in  breaking  down  their  solid  mass.  The 
value  of  building-stones,  in  our  climate,  depends  much  upon  the  resistance  they 
offer  to  the  action  of  frost.  In  hot  climates  the  effect  is  not  seen,  and  the  crags 
and  summits  of  mountains  are  there  generally  more  sharp.  Experiments  to 
determine  the  resistance  of  rocks  to  frost,  are  made  by  saturating  cubes  of  the 
material  with  .water,  and  repeatedly  freezing  them.  But  the  same  result  is  more 
conveniently  obtained  by  using  a  solution  of  sulphate  of  soda.  This  salt,  crys- 
tallizing on  exposure  to  the  air,  effects  the  same  results. 

666.  Absolute  zero. — Since  the  permanent  gases  contract  ¥£T  of 
their  volume  at  32°,  for  each  degree  of  Fahrenheit  below  that  point  (or 
expand  that  quantity  for  each  like  increment  of  heat  above  32°),  it  has 
been  inferred  by  Clement  and  D6sormes  that,  at  the  temperature  of 
— 459°  F.  they  would  cease  to  exist  as  gases,  since  the  amount  of  con- 
traction would  then  be  equal  to  their  initial  volume.     Likewise,  since 
the  volume  of  a  gas  is  doubled  by  heating  from  32°  to  523°,  they  further 
inferred  that  the  quantity  of  heat  added  must  be  equal  to  that  held  by 
the  initial  volume,  and  that  at  — 459°  F.  there  must  be  an  absolute  zero. 

\  8.  Vaporization  and  Condensation. 

667.  Vaporization. — Liquids  become  vapors  upon  receiving  a  cer- 
tain quantity  of  heat.     Thus,  water  at  212°  is  rapidly  converted  into 
steam,  which,  at  or  above  that  temperature,  remains  as  an  invisible 


HEAT. 


457 


vapor.    This  change  of  state  presents  some  of  the  most  interesting  and 
important  phenomena  of  physics. 

"Evaporation  occurs  only  at  the  surface  of  liquids,  quietly,  as  in  the  insensible 
changes  of  water  to  vapor  in  an  open  vessel.  Boiling  or  ebullition,  is  the  rapid 
formation  of  vapor  throughout  the  whole  mass  of  liquid,  producing  more  or  less 
agitation.  Sublimation  is  the  change  of  solids  to  vapors  without  the  interme- 
diate liquid  condition.  Arsenic,  iodine,  and  camphor  are  examples  of  solids 
which  may  be  so  changed. 

The  remarkable  disappearance  of  nearly  one  thousand  degrees  of 
heat  when  water  is  turned  into  steam  (and  correspondingly  for  other 
liquids),  will  be  considered  under  Latent  Heat  of  Steam,  §  683. 

668.  Formation  of  vapors  in  a  vacuum. — Evaporation  takes  place 
slowly  in  the  open  air,  owing  chiefly  to  the  atmospheric  pressure.  In 
a  vacuum,  however,  it  occurs  instantaneously,  because  the  vapor  then 
meets  with  no  resistance.  This  phenomenon  occurs  in  obedience  to 
the  following  laws  : — 

1st.  All  volatile  liquids,  in  a  vacuum,  volatilize  instantly. 

2d.  At  the  same  temperature  the  vapors  of  different  liquids  possess 
unequal  elastic  force. 

These  laws  are  illustrated  in  the  apparatus,  fig. 
482,  where  four  barometer  tubes,  originally  filled 
with,  pure  dry  mercury,  are  supported  by  the  stand 
in  a  mercurial  cistern,  and  will  all  indicate  upon  the 
scale,  C,  the  same  height  of  column.  A  drop  of  ether 
passed  up  to  E,  instantly  flashes  into  vapor,  and  de- 
presses the  column  perhaps  half  its  height  or  more. 
This  illustrates  the  first  law.  A  drop  of  bisulphid  of 
carbon  introduced  into  D  ;  of  alcohol  into  B  ;  and  of 
water  into  A,  will  also  be  respectively  changed  to 
vapor,  wholly,  or  in  part,  and  will  depress  the  mer- 
cury unequally,  in  the  order 'of  their  volatility  as 
enumerated.  This  illustrates  the  second  law.  If  all 
the  ether  introduced  into  B  has  disappeared,  then 
successive  small  portions  may  be  added,  and  with 
each  addition  an  increased  depression  of  the  mercury 
will  be  observed,  until,  finally,  a  point  is  reached 
where  the  ether  remains  liquid.  This  is  the  point 
of  saturation,  or  maximum  tension  of  ether  vapor  for 
that  temperature.  A  change  of  temperature  will,  of 
course,  vary  these  conditions.  If  either  of  the  tubes 
ia  surrounded  by  one  of  larger  diameter  dipping 
under  the  mercury,  and  so  affording  a  cell  into  which 
hot  water  may  be  poured,  the  liquid  ether  in  E,  for 
example,  will  be  vaporized,  still  further  depressing  the  mercury,  according  to 
the  temperature.  If  a  freezing  mixture  were  similarly  used,  the  reverse  would 
be  seen — a  portion  of  vapor  would  be  liquefied,  and  the  mercury  will  rise  in 
proportion. 

41* 


458 


PHYSICS    OF   IMPONDERABLE    AGENTS- 


669.  Saturated  space  or  maximum  tension  of  vapors. — The 

meaning  of  these  terms  may  be  still  further  illustrated  by  the  use  of 
the  apparatus  in  fig.  483,  which  is  provided  with  a  433 

well,  filled  with  mercury,  and  deep  enough  to  allow 
the  tube  to  be  depressed  nearly  its  whole  length. 

Suppose  the  tube  to  have  the  condition  of  E  in  the  last 
paragraph  j  that  is,  the  vapor  of  ether  has  nearly  filled 
the  whole  tube,  and  is  at  its  point  of  saturation  or  maxi- 
mum tension.  If  the  tube  is  now  depressed,  the  contained 
vapor  is  subject  to  increased  tension,  in  proportion  to  the 
amount  of  depression  ;  and  the  result  is,  that  a  portion 
of  it  becomes  liquid,  and  the  mercury  takes  the  place 
of  the  vapor.  If  the  tube  is  raised,  then  the  pressure  is 
again  diminished,  and  a  fresh  portion  of  ether  is  vaporized. 
There  is,  therefore,  a  maximum  tension  or  elasticity  for  the 
vapor  of  different  liquids  at  every  temperature ;  so  that,  in 
a  saturated  space,  at  a  given  temperature,  the  maximum 
tension  is  the  same,  whatever  may  be  the  pressure  to  which 
the  vapor  is  subjected. 

670.  Dalton's  law  of  the  tension  of  vapors  is 

as  follows : — 

The  tension  or  elasticity  of  different  vapors  is  equal, 
if  compared  at  temperatures  the  same  number  of  de- 
grees above  or  below  the  boiling  point  of  their  respective 
liquids. 

This  law  does  not  perfectly  accord  with  the  results 
of  experiment,  but  it  is  nearly  correct  (except  for 
mercury),  at  short  distances  above  and  below  the 
boiling  point.  See  Table  XIV. 

671.  The  tension  of  vapors  in  communicating  vessels  une- 
qually heated  is  the  same,  and  is  equal  to  that  of  the  lower  temperature. 

Thus,  if  a  vessel  containing  water  at  32°,  communicates  by  a  tube  with  a 
vessel  in  which  the  water  is  boiling,  the  pressure  in  both  of  the  vessels  will  bo 
the  same,  as  may  be  ascertained  by  a  manometer.  This  is  explained  by  the 
condensation  which  the  vapor  constantly  suffers  in  the  colder  vessel.  Applica- 
tion is  made  of  this  principle  in  the  condenser  of  the  steam-engine. 

672.  Temperature  and  limits  of  vaporization. — The  evaporation 
of  liquids  takes  place  at  temperatures  much  below  their  boiling  points, 
as  common  experience  testifies.     Even  at  the  ordinary  temperature  of 
the  air,  water,  many  liquids,  and  even  some  solids  vaporize. 

Even  mercury,  whose  boiling  point  is  662°,  evaporates  at  all  temperatures 
above  60°  F.,  as  was  proved  by  Faraday.  He  suspended  from  the  cork  of  a  flask 
containing  mercury,  a  slip  of  gold  leaf.  After  six  months,  the  gold  leaf  was 
found  to  be  whitened  by  the  mercury  which  had  risen  in  vapor.  A  dew  of 
metallic  globules  is  sometimes  seen  in  the  Torricellian  vacuum.  Iodine,  cam- 
phor, and  other  solids,  rapidly  evaporate  at  the  ordinary  temperature.  Snow 


HEAT.  459 

and  ice  disappear  from  the  surface  of  the  earth  during  cold  weather  when  there 
has  been  no  thawing.  Boyle  found  that  two  ounces  of  snow,  in  a  very  cold 
atmosphere,  lost  ten  grains  in  six  hours. 

The  experiments  of  Faraday,  however,  appear  to  show  that  vapori 
zation  does  not  occur  at  all  temperatures. 

Thus,  mercury  gives  off  no  appreciable  vapor  below  60°.  Sulphuric  acid 
undergoes  no  appreciable  evaporation  at  ordinary  temperatures.  Faraday 
proved  that  several  substances  which  are  volatilized  by  heat  at  temperatures 
between  300°  and  400°,  did  not  suffer  the  slightest  evaporation  when  kept  in  a 
confined  space  at  the  ordinary  temperatures  during  four  years. 

The  limit  of  evaporation  is  reached  when  the  cohesive  force  of  the  particles 
of  the  solid  or  liquid  overcomes  the  feeble  tendency  to  evaporation. 

673.  Circumstances  influencing  evaporation. — Evaporation,  as 
has  been  said,  is  the  slow  production  of  vapor  from  the  surface  of  a 
liquid.     The  elastic  force  of  a  vapor  which  saturates  a  space  containing 
a  gas  (like  air)  is  the  same  as  in  a  vacuum.     The  principal  causes 
which  influence  the  amount  and  rapidity  of  evaporation,  are  as  fol- 
lows : — 

1st.  Extent  of  surface.  As  the  evaporation  takes  place  from  the  surface,  an 
increase  of  surface  evidently  facilitates  evaporation. 

2d.  Temperature,  by  increasing  the  elastic  force  of  vapor,  increases  the  rapidity 
of  evaporation ;  therefore,  the  temperature  of  ebullition  marks  the  maximum 
point  of  evaporation. 

3d.  The  quantity  of  the  same  liquid  already  in  the  atmosphere,  exercises  an 
important  influence  on  evaporation.  When  the  air  is  saturated,  evaporation 
ceases  ;  it  is,  therefore,  greatest  when  the  air  is  free  from  vapor. 

4th.  Renewal  of  the  air  facilitates  evaporation,  since  new  portions  of  air, 
capable  of  absorbing  moisture,  are  presented  to  it ;  hence  evaporation  is  more 
rapid  in  a  breeze  than  in  still  air. 

5th.  Pressure  on  the  surface  of  the  liquid  influences  evaporation,  because  of 
the  resistance  thus  offered  to  the  escape  of  the  vapor. 

Prof.  Daniell,  from  a  series  of  researches  on  the  rate  of  evaporation,  deduced 
the  following  law,  viz.  : — 

The  rapidity  of  evaporation  is  inversely  as  the  pressure  upon  the  surface  of  the 
evaporating  liquid. 

674.  Dew-point. — If  air  saturated  with  moisture  is  cooled,  a  por- 
tion of  the  moisture  will  be  precipitated  as  dew.     The  ten  perature  at 
which  this  deposition  of  moisture  commences,  is  called  the  dew-point. 
The  dew-point  is  nearer  the  temperature  of  the  atmosphere,  the  more 
fully  the  air  is  saturated  with  moisture.     The  methods  of  determining 
the  amount  of  moisture  contained  in  the  atmosphere,  will  be  described 
in  the  chapter  on  Meteorology. 

675.  Ebullition. — The  elasticity  of  the  vapor  from  a  boiling  liquid 
is  equal  to  the  pressure  of  the  superincumbent  atmosphere. 

When  water  is  boiled  in  a  glass  vessel,  the  phenomena  of  ebullition  may  be 


460  PHYSICS    OF    IMPONDERABLE    AGENTS. 

distinctly  seen.  On  first  heating  a  liquid,  the  dissolved  air  is  expelled  in 
small  bubbles.  As  the  heat  is  continued,  bubbles  of  transparent  and  invisible 
steam  are  formed  in  the  lower  part  of  the  vessel  where  the  heat  is  applied. 
These  grow  smaller  and  smaller  as  they  rise,  and  finally  condense  in  the  colder 
liquid  with  a  series  of  little  noises,  producing  what  we  call  simmering.  After  a 
time,  when  the  mass  of  liquid  attains  a  nearly  uniform  temperature,  these  bub- 
bles increase  in  size  as  they  rise  to  the  surface,  owing  to  the  evaporation  from 
their  interior  surfaces,  as  well  as  from  the  less  pressure  to  which  they  are  there 
subjected.  As  they  reach  the  external  air,  at  the  surface  of  the  liquid,  they  con- 
dense in  a  cloudy  vapor,  which  is  commonly  called  steam,  but  which,  in  reality, 
is  water  in  exceedingly  minute  globules,  steam  itself  being  invisible. 

When  a  liquid  has  reached  the  boiling  point,  a  comparatively  small  quantity 
of  heat  maintains  it  at  that  temperature.  Water,  or  any  other  liquid,  boiling 
moderately,  has  the  same  temperature  as  when  it  is  in  violent  ebullition ;  the 
excess  of  heat  only  causing  a  more  rapid  evaporation  of  the  water.  The  boiling 
points  of  certain  liquids  are  shown  in  Table  XVII. 

676.  Circumstances  influencing  the  boiling  point. — The  prin- 
cipal of  these  are : — 

1.  Adhesion.     It  is  probably  owing  to  the  different  degrees  of  adhe- 
sion befween  the  liquid  and  the  surfaces  of  the  vessels,  that  the  boiling 
point  of  water  varies  in  vessels  of  different  materials. 

2.  Solids  in  solution  in  liquids  raise  their  boiling  points  in  proportion  to  the 
quantity  dissolved.    Thus,  a  saturated  solution  of  common  salt  boils  at  227°  F. ; 
of  nitre  at  240°;  of  carbonate  of  potash  at  275°;  and  of  carbonate  of  soda  at 
220°.     This  is   probably  owing  to  the  adhesion  existing  between  solids   and 
liquids,  which  opposes  itself  to  the  repulsive  force  of  heat.     The  vapor  rising 
from  boiling  solutions,  Rudburg  says,  has  only  the  temperature  of  steam  from 
pure  water  boiling  in  free  air.     According  to  Regnault,  the  temperature  of  the 
vapor  of  a  "boiling  saline   solution,  appears  very  nearly  equal  to  that  of  the 
liquid.     It  is  extremely  difficult  to  obtain  accurate  results,  because  the  bulb  of 
the  thermometer  becomes  covered  with  a  film  of  condensed  water. 

3.  Pressure.  As  ebullition  consists  in  the  rapid  formation  of  vapor 
of  the  same  elasticity  as  the  superincumbent  atmosphere,  it  is  evident, 
that  if  the  pressure  is  diminished,  the  boiling  48i 

point  will  be  lowered  ;  and  if  it  be  increased,  that 
the  boiling  point  will  be  raised. 

The  influence  of  pressure  on  the  temperature  of  ebul- 
lition, is  strikingly  shown  by  placing  a  vessel  of  water, 
which  has  cooled  considerably  below  the  boiling  point, 
beneath  the  receiver  of  an  air-pump  and  exhausting  the 
air,  fig.  484.  As  the  air  is  removed,  the  water  enters 
into  violent  ebullition,  even  at  a  temperature  of  125°. 
Liquids  generally  boil  in  vacuo  at  a  temperature  of  from 
70°  to  140°  below  their  point  of  ebullition  under  the  ordi- 
nary atmospheric  pressure;  Black  says  140°  for  all  liquids. 

Table  XVI.,  from  Regnault,  shows  the  temperature  at 
which  water  boils  under  different  pressures,  represented  by  the  corresponding 
heights  of  the  barometric  column.  These  results  have  been  confirmed  by  direct 
observation. 


HEAT. 


461 


In  Table  XVIII.  is  given  the  boiling  point  of  water  at  different  places,  with 
their  corresponding  elevation  above  the  level  of  the  sea. 

677.  The  culinary  paradox  is  an  excellent  illustration  of  the  pheno- 
mena of  boiling  under  diminished  pressures.  485 

A  small  quantity  of  water  is  boiled  in  a  glass  flask 
until  the  steam  has  driven  out  the  air.  When  the 
water  is  in  active  ebullition,  a  good  cork  is  firmly 
inserted  in  the  mouth,  and  the  heat  is  removed.  The 
flask  is  then  supported  in  an  inverted  position,  as 
is  shown  in  fig.  485.  The  water  still  continues  to 
boil  more  violently  than  when  over  the  flame.  If  cold 
water  be  poured  upon  the  flask,  the  ebullition  becomes 
still  more  violent,  but  will  be  speedily  arrested  by  the 
application  of  hot  water. 

The  cause  of  this  seeming  paradox  is  plain.  When 
the  flask  was  corked,  there  was  only  the  vapor  of 
water  above  the  liquid,  the  air  being  driven  out  by 
the  previous  boiling.  By  the  application  of  cold 
water,  a  portion  of  this  vapor  becomes  condensed, 
and  the  water  within  being  under  diminished  pres- 
sure, boils  at  a  correspondingly  low  temperature. 
But  hot  water  thrown  upon  the  flask  increases  the 
elasticity  of  the  vapor,  and  the  water  being  thus 
subjected  to  a  greater  pressure,  ceases  to  boil. 

Franklin's   pulse  glass,  a  double   bulbed   glass,  fig.  486,  partly  filled 
with  ether  and  closed  while  boiling ;  boils  from  the  4gg 

heat  of  the  hand,  a  sensible  coolness  being  felt  as 
the  last  portions  of  fluid  rush  out  of  the  empty 
bulb,  the  hand  furnishing  the  heat  needed  to  va- 
porize the  ether. 

678.  Useful  applications  in  the  arts  are  constantly  made  of  the 
facts  just  explained,  to  concentrate  vegetable  extracts,  cane-juice,  &c., 
under  diminished  pressure,  and  consequently  at  a  temperature  below 
the  point  where  there  is  any  danger  of  injury  from  heat.     Sugar  is 
usually  concentrated  thus  in  large  close  copper  vessels,  called  vacuum- 
pans,  at  a  temperature  of  150°  F.,  aided  by  a  powerful  air-pump  and 
condenser  to  remove  the  vapor  rapidly.     There  is  no  economy  of  fuel 
"by  boiling  under  diminished  pressure,  as  will  be  understood  from  what 
is  said  hereafter. 

679.  Measurement  of  heights  by  the  boiling  point. — Hypso- 
meter. — On  ascending  mountains,  the  boiling  point  of  liquids  falls, 
because  the  atmospheric  pressure  is  less,  and  conversely  in  descending 
into  mines,  it  rises.     Accurate  observations  show,  that  a  difference  of 
about  543  feet  in  elevation  produces  a  variation  of  1°  F.  in  the  boiling 
point  of  water.     The  metastatic  thermometer  (579)  is  used  in  these 
observations.     Fahrenheit  first   proposed  determining  the  heights  of 
mountains  by  the  depressed  temperature  cf  boiling  water. 


462 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


488 


Regnault  has  designed  an  apparatus  called  a  hypsometer,  fig.  487,  for 
determining  elevations  by  the  boiling  point  of  water.  It  consists  of  a  copper 
vessel,  C,  containing  water.  This  is  surmounted  by  a  brass  cylinder  which 
supports  and  enclaees  a  thermometer.  The  upper  part  of  this  cylinder  is  formed 
in  pieces,  t,  which  slide  into  each  other  like  the  tubes  of  a  telescope,  and  serve 
to  confine  the  steam  about  the  thermometer  tube,  as  in  fig.  443.  Air  is  supplied 
to  the  lamp,  I,  by  the  holes,  o,  o.  The  steam  escapes  by  a  lateral  487 

orifice  in  the  upper  part  of  the  instrument. 

680.  High    pressure    steam.— The 
boiling  point  rises   as   the   pressure   in- 
creases.    This   fact    is    readily    demon- 
strated  in   a   general  way  by   Marcet's 
apparatus,  fig.  488. 

A  spherical  boiler  is  supported  over  a  lamp 
upon  a  tripod  of  brass.  A  thermometer,  t, 
enters  the  upper  hemisphere,  and  its  bulb  is 
exposed  directly  to  the  steam.  A  stop-cock 
and  safety  valve,  V,  opens  a  communication 
to  the  outer  air.  A  manometer  tube,  A,  with 
confined  air  (280)  descends  into  some  mercury 
placed  in  the  boiler  (whose  lower  hemisphere 
is  for  that  reason  made  of  iron).  The  boiler 
is  filled  with  water  to  the  equator.  When  the 
water  boils  and  the  air  has  been  expelled,  the 
open  stop-cock  is  closed  and  the  steam  com- 
mences to  accumulate.  The  thermometer, 
which  stood  previously  at  212°,  begins  to  rise 
higher  and  higher  as  the  column  of  mercury 
rises  in  the  gauge.  When  the  mercury  has 
risen  in  the  gauge  a  little  less  than  half 
the  height  of  the  tube,  the  thermometer  will 
indicate  249°-5  F.,  when  two-thirds  of  the  way  273°-3,  and  so  on.  Table  XIX. 
gives  the  boiling  point  of  water  at  different  atmospheric  pressures  as  ascer- 
tained by  Regnault. 

Advantage  is  taken  of  the  temperature  of  high  steam  in  the  arts  to  extract 
gelatine  from  bones,  and  to  perform  other  difficult  solutions  and  distillations 
which,  at  212°,  would  be  impossible.  Papin,  a  French  physicist,  who  died  in 
1710,  first  studied  these  effects  of  high  steam  with  an  apparatus  known  as 
Papin's  digester.  It  is  only  a  boiler,  of  great  strength,  provided  with  a  safety 
valve  (then  first  used). 

681.  Production  of  cold  by  evaporation. — A  liquid  grows  sen- 
sibly colder,  if  while  evaporating  it  does  not  receive  as  much  heat  as  it 
loses,  and  the  more  sensibly  so,  as  the  evaporation  is  more  rapid. 

Eau  de  cologne,  bay-rum,  or  ether,  evaporating  from  the  surface  of  the  skin, 
produces  very  sensible  coldness,  due  to  the  rapid  absorption  of  the  bodily  heat 
in  the  evaporation.  Portions  of  body  may  be  thus  benumbed  and  rendered 
insensible  to  pain  during  surgical  operations. 


HEAT. 


463 


489 


A  summer  shower  cools  the  air  by  absorbing  heat  from  the  earth  and  the  air 
during  evaporation.  Curtains  wet  with  water,  called  tatties,  much  used  in  India; 
Leafy  branches  of  trees,  mossy  banks,  and  fountains  draped  by  climbing  plants, 
are  cool  for  the  same  reason.  Fanning  the  surface  produces  coolness  both  from 
conduction  and  evaporation.  Wet  clothes  are  pernicious,  chiefly  from  the  rapid 
loss  they  cause  of  animal  heat  during  evaporation,  thus  impeding  the  circula- 
tion. In  hot  climates,  where  ice  is  rare,  water  is  cooled  to  an  agreeable 
temperature  by  the  use  of  jars  of  porous  earthenware  placed  in  a  draught  of 
air.  The  surface  moisture  is  rapidly  evaporated  by  the  dry  air,  and  the  water 
in  the  vessels  falls  20  or  30  degrees  below  the  exterior  air,  even  at  80  or  90 
degrees.  Water  is  readily  frozen  in  a  thin  narrow  test-tube  by  the  constant 
evaporation  of  ether  from  a  muslin  cover  drawn  over  the  outside  of  the  tube. 
In  the  East  Indies,  water  is  frozen  by  its  own  evaporation,  aided  by  radiation, 
in  cool  serene  nights,  when  the  external  air  is  not  below  40°.  For  this  purpose 
shallow  earthen  pans  are  used,  placed  in  a  slight  pit  or  depression  of  the  earth 
upon  straw  to  cut  off  terrestrial  radiation. 

Water  is  endowed  with  a  remarkable  emissive 
power,  and  will,  as  shown  by  Melloni,  lose  7°  be- 
low the  atmosphere  by  simple  radiation  in  serene 
nights.  Compared  to  this  remarkable  Indian 
result,  Leslie's  experiment  of  freezing  water  in 
the  vacuum  of  an  air-pump  (over  sulphuric  acid 
to  absorb  the  vapor,  fig.  489)  seems  simple;  and  easier  still  is  the  same  effect 
produced  in  the  cryophorus  (or  frost-bearer)  of  Dr.  Wollaston,  fig.  490,  where  a 
portion  of  water  in  one  490 

bulb  of  a  vacuous  glass 
tube  is  frozen  by  its  own 
rapid  evaporation  due  to 
cooling  the  empty  bulb  in 
a  freezing  mixture. 

Twining's  ice  ma- 
chine.— An  apparatus  has  been  successfully  contrived  by  Prof.  Alex.  Twining 
for  producing  ice  upon  a  commercial  scale  in  those  hot  climates  where  it  cannot 
be  carried  from  colder  countries,  by  the  rapid  evaporation  of  a  portion  of  ether 
confined  in  metallic  chambers  contiguous  to  the  water  vessels — the  process,  by 
aid  of  an  air-pump  and  condenser,  being  continuous  and  without  sensible  loss 
of  ether.  This  plan  is  equally  applicable  to  cooling  the  air  of  apartments,  either 
for  the  preservation  of  provisions  or  for  the  comfort  of  the  occupants. 

682.  Latent  heat  of  steam. — A  large  amount  of  heat  disappears 
or  is  rendered  latent  during  evaporation.  According  to  Regnault,  the 
latent  heat  of  steam  is  967°'5.  Its  determination  is  made  in  a  number 

of  ways. 

If  a  vessel  containing  water  at  the  temperature  of  32°  is  placed  over  a  steady 
^•jurce  of  heat,  it  receives  equal  additions  of  heat  in  equal  times.  Let  the  time 
be  noted  that  is  required  to  raise  the  temperature  to  212°.  If  now  the  heat  is 
continued  until  all  the  water  is  converted  into  steam,  it  will  be  found  that  the 
time  occupied  in  the  evaporation  was  5£  times  that  required  to  heat  the  water 
through  the  first  180°,  i.  e.,  from  32°  to  212°.  Consequently  5^  times  as  much 
heat  is  absorbed  during  the  evaporation  of  water  as  is  required  to  bring  it  to 
boiling  point.  The  latent  heat  of  steam  is  therefore  about  (180°  X  5i)  990°. 


464  PHYSICS    OF    IMPONDERABLE   AGENTS. 

Again,  the  latent  heat  of  steam  is  determined  by  distilling  a  certain  amount 
of  water  and  condensing  the  steam  in  a  large  volume  of  the  same  liquid.  If 
the  temperature  be  noted  before  and  after  the  experiment,  it  will  be  found  that 
the  heat  from  the  steam  formed  from  a  pound  of  water,  was  sufficient  to  raise 
the  temperature  of  ten  pounds  of  water  99°.  The  latent  heat  of  steam  is  there- 
fore again  found  to  be  (99°  X  10)  "°°- 

Experiments  conducted  in  the  simple  manner  just  mentioned  cannot  be 
entirely  accurate,  owing  to  a  certain  loss  of  heat  by  vaporization,  conduction, 
and  radiation.  Numerous  precautions  are  therefore  to  be  adopted  to  insure  the 
accuracy  science  demands  in  such  an  investigation,  the  details  of  which  are 
inconsistent  with  our  limited  space. 

The  latent  heat  of  steam  obtained  by  different  experimenters,  varies 
somewhat  as  follows :— Watt,  950° ;  Lavoisier,  1000° ;  Despretz,  955°'8  ; 
Brix,  972° ;  Regnault,  967°'5 ;  Fabre  and  Silbermann,  964°'8. 

683.  Latent  and  sensible  heat  of  steam  at  different  tempera- 
tures.— The  whole  amount  of  heat  in  steam  is  the  latent  heat,  plus  the 
sensible  heat.     Thus  the  heat  of  steam  at  the  temperature  of  ebullition 
is  967°'5  -f  212°  =  1179°'5.     It  has  heretofore  been  generally  stated, 
that  the  heat  absorbed  in  vaporization  is  less  as  the  temperature  of  the 
vaporizing  liquids  is  higher.     So  that  if  the  sensible  heat  of  steam  at 
any  temperature  is  subtracted  from  the  constant  11790>5,  the  remainder 
is  the  latent  heat  of  steam  at  that  temperature.   For  example :  the  latent 
heat  of  steam  at  279°'5,  is  900°,  at  100°,  1079°'5,  &c.     This  statement 
however  is  found  to  be  somewhat  inaccurate,  although  in  practice  it 
may  be  assumed  to  be  nearly  correct. 

From  the  experiments  of  Regnault,  it  appears  that  the  sum  of  the 
latent  and  sensible  heat  increases  with  the  temperature  by  a  constant 
difference  of  0°'305  for  each  degree  F.,  as  is  shown  in  Table  XXII. 

684.  Mechanical  force  developed  during  evaporation. — During 
the  conversion  of  a  liquid  into  vapor,  a  certain  mechanical  force  is  exerted. 
The  amount  of  this  force  depends  on  the  pressure  of  the  vapor  and  the 
increase  in  volume  which  the  liquid  undergoes. 

Equal  volumes  of  different  liquids  produce  unequal  amounts  of  vapor  at  their 
respective  boiling  points. 

1  cubic  inch  of  water  expands  into  1696  cubic  in.  vapor  at  boiling  point. 
1      "         "          alcohol     "          "       528      "       "        "  "  " 

1      "         "          ether         "          "       298      "       "        "  "  " 

1     "        "          turpentine          "       193      "      "       "  "  " 

Now  although  the  latent  heat  of  equal  weights  of  other  vapors  is  less  than 
that  of  steam,  yet  no  advantage  would  arise  in  generating  vapor  from  them  in 
place  of  water  in  the  steam-engine.  For  equal  volumes  of  alcoholic  and  aqueous 
vapor  contain  nearly  the  same  amount  of  latent  heat  at  their  respective  boiling 
points,  and  such  is  the  case  to  a  great  extent  with  other  liquids.  The  cost  of 
the  fuel  in  generating  vapor  would  be  in  proportion  to  the  amount  of  latent 
neat  in  equal  vi  lunaes  of  the  vapor. 


HEAT  465 

685.  Liquefaction  of  vapors,  or  the  conversion  of  vapors  into  liquids, 
is  accomplished  ia  three  ways.     1st,  by  cooling;  2d,  by  compression; 
and  3d,  by  chemical  affinity.     Only  the  first  two  of  these  methods  will 
be  spoken  of.     When  vapors  or  gases  are  condensed  into  liquids,  the 
same  amount  of  heat  is  given  out  as  sensible  heat  which  was  absorbed 
and  rendered  latent  when  they  assumed  the  aeriform  condition. 

686.  Distillation  is  the  successive  evaporation  and  condensation  of 
liquids.     The  process  depends  on  the  rapid  formation  of  vapor  during 
ebullition,  and  the  condensation  of  the  vapor  by  cooling. 

Distillation  is  used,  first,  for  the  separation  of  fluids  from  solids,  as  the  dis- 
tillation of  ordinary  water,  to  separate  the  impurities  contained  in  it;  2d,  for 
the  separation  of  liquids  unequally  volatile,  as  in  the  distillation  of  fermented 
liquors,  to  separate  the  volatile  spirits  from  the  watery  matter. 

687.  Distilling  apparatus  of  various  kinds  is  employed  according 
to  the  special  purpose  to  which  it  is  applied.     The  most  ancient  is 
the  alembic  ;  its  invention  is  attributed  to  the  Arabs.     It  consists  of  a 
boiler  of  copper  or  iron,  furnished  with  a  dome-shaped  head ;  to  the 
upper  part  of  this  is  attached  a  metal  tube  which  passes  through  a 
vessel  of  cold  water,  whereby  the  vapor  (as  it  passes  over  when  heat 
is  applied  to  the  boiler)  is  condensed,  and  flows  into  a  proper  receptacle. 

Where  small  quantities  491 

of  liquid  are  to  be  distilled, 
glass  retorts,  fig.  491,  or 
flasks  are  used.  These  are 
heated  by  alcohol  lamps,  or 
by  small  charcoal  furnaces. 
The  receiver  may  consist 
of  a  small  flask  connected 
with  the  neck  of  the  retort, 
as  represented  by  S.  By 
means  of  water  flowing 
continually  on  it  from  B,  a 
proper  cooling  is  effected. 

688.  Physical  identity  of  gases    and  vapors. — The   difference 
between  gases  and  vapors  is  merely  one  of  degree,  and  their  identity 
in  many  physical  properties  has  already  been  shown.     Thus  the  ratio 
of  their  expansion  by  heat  is  the  same  as  that  of  the  permanent  gases. 
A  permanent  gas  may  be  considered  as  a  super-heated  vapor  ;  the  vapor 
of  a  liquid  which  volatilizes  at  very  low  temperatures. 

Theory  of  the  liquefaction  and  solidification  of  gases. — By 
the  last  section,  if  the  excess  of  heat  is  removed  from  a  gas,  it  is  in  the 
same  condition  as  an  ordinary  vapor,  containing  only  sufficient  heat  to 
42 


466 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


maintain  it  in  the  aeriform  condition.  By  the  compression  of  a  gas, 
heat  is  evolved,  by  rendering  sensible  the  heat  before  latent.  If  the 
compressed  gas  is  then  surrounded  by  a  freezing  mixture,  the  further 
abstraction  of  heat  causes  the  condensation  of  a  corresponding  portion 
of  gas  into  a  liquid.  It  is  thus  by  condensing  and  cooling  gases,  that 
their  liquefaction  and  solidification  have  been  effected. 

689.  Methods  of  reducing  gases  to  liquids. — In  1823,  Faraday 
liquefied  chlorine,  cyanogen,  ammonia,  carbonic  acid,  and  some  other 
gases,  by  the  following  simple  means. 

The  materials  from  which  the  gas  was  to  be  evolved,  provided  they  were  solida, 
were  placed   in   a   strong  glass  tube,  492 

bent  at  an  obtuse  angle  near  the 
middle,  fig.  492,  and  the  open  ends 
hermetically  sealed.  Heat  was  then 
applied  to  the  end  containing  the 
materials  (e.  g.  cyanid  of  mercury), 
while  the  empty  end  was  cooled  in  a 
freezing  mixture.  The  pressure  of  the  gas  evolved  in  so  small  a  space,  united 
with  the  cold,  liquefied  a  portion  of  it.  Otherwise,  if  fluids  were  to  be  employed, 
the  tube  had  the  shape  seen  in  fig.  493.  The  fluids  were  introduced  by  the  small 
funnel  o  n,  into  the  curves  c  and  b,  and  the  ends,  a,  d,  were  then  sealed  by  the 
blow-pipe.  By  a  simple  turn  of  the  tube,  all  the  fluid 
contents  are  transferred  to  the  end,  a,  fig.  494,  and  the 
empty  end,  d,  is  placed  in  a  freezing  mixture  where  the 
liquid  gas  collects.  Any  fluid  which  distils  over  from 
a,  collects  in  the  bottom  of  the  middle  curve.  A  minute 
manometer  was  introduced  by  Faraday  into  these  tubes, 
in  order  to  determine  the  pressure  at  which  liquefaction 
occurred.  The  manometer  was  a  small  glass  tube  sealed 
at  one  end,  and  holding  a  drop  of  mercury ;  the  mode 
of  reading  the  pressure  has  been  before  explained  (280). 

Later  researches  of  Faraday. — In  1845, 
Faraday  published  the  results  of  his  experiments 
on  the  liquefaction  of  gases  by  means  of  solid 
carbonic  acid.  A  mixture  of  this  solid  with  ether, 
in  the  vacuum  of  an  air-pump,  gave  him  a  tempe- 
rature as  low  as  —166°  F. 

In  such  a  bath,  at  the  ordinary  pressure  of  the 
atmosphere,  chlorine,  oxyd  of  chlorine,  cyanogen,  am- 
monia, sulphuretted  hydrogen,  arseniuretted  hydrogen,  hydriodic  acid,  hydro- 
bromic  acid  and  carbonic  acid,  were  obtained  in  the  liquid  form  under  moderate 
pressures.  These  liquids  were  colorless,  with  the  exception  of  those  from  chlo- 
rine and  oxyd  of  chlorine,  which  are  colored  gases  in  the  ordinary  state.  A 
number  of  the  liquefied  gases 'were  solidified.  The  results  obtained  by  Faraday 
on  the  liquefaction  and  solidification  of  gases  may  be  found  in  Table  XX. 

690.  Thilorier's  and  Bianchi's  apparatus  for  condensation  of 


HEAT.  467 

gases.-— To  avoid  the  danger  of  explosion  in  the  use  of  glass  tubes, 
and  at  the  same  time  to  obtain  large  supplies  of  liquid  gases  in  a 
manageable  form,  a  powerful  apparatus  of  iron  has  been  contrived  by 
Thilorier;  and,  more  lately,  another  by  Bianchi  with  mechanical  com- 
pression, for  a  description  of  which  reference  may  be  had  to  the  Author's 
C/iem  istry. 

691.  Properties  of  liquid  and  solid  gases. — Liquid  carbonic  acid 
is  colorless,  like  water,  arid  has  a  density  of  0'83.     Its  coefficient  of 
expansion  is  more  than  four  times  that  of  air.     Twenty  volumes  of  the 

'liquid  at  32°,  becoming  29  volumes  at  86°. 

The  solidified  acid  obtained  by  the  evaporation  of  a  portion  of  the  liquid, 
appears  in  the  form  of  snow;  when  congealed  by  intense  cold  alone,  it  is  clear 
and  transparent  like  ice.  It  melts  at  a  temperature  of  — 70°  F.,  and  is  heavier 
than  the  liquid  bathing  it.  The  solid  acid  may  be  preserved  for  many  hours  if 
it  be  surrounded  with  cotton  or  some  other  poor  conductor  of  heat.  It  gradually 
vaporizes  without  assuming  the  liquid  form.  The  temperature  of  this  solid,  as 
determined  by  Faraday's  experiments,  is  about  106°  below  0°  F.  Although  so 
intensely  cold,  it  may  be  handled  with  impunity,  and  when  thrown  into  water, 
the  latter  is  not  frozen.  By  moistening  it  with  ether,  to  which  it  has  a  strong 
adhesion,  its  low  temperature  is  at  once  manifested.  If  mercury  is  placed  in  a 
wooden  basin  and  covered  with  ether,  and  then  solid  carbonic  acid  be  added, 
the  mercury  will  soon  be  frozen.  The  temperature  required  to  freeze  the  mer- 
cury is  about  — 40°  F.  This  frozen  mercury  may  be  drawn  into  bars,  or  moulded 
into  bullets,  or  beaten  into  thin  plates,  if  the  operations  be  performed  with  wooden 
instruments. 

NATTERER,  with  a  mixture  of  liquid  protoxyd  of  nitrogen  and  bisul- 
phid  of  carbon,  records  a  temperature  of  — 220°  F.  Even  at  this  low 
temperature,  liquid  chlorine  and  bisulphid  of  carbon  preserve  their 
fluidity. 

In  protoxyd  of  nitrogen  gas,  combustibles  burn  with  nearly  as  great  intensity 
as  in  pure  oxygen ;  combustion  also  takes  place  in  liquid  protoxyd  of  nitrogen, 
notwithstanding  the  intense  cold.  A  fragment  of  burning  charcoal,  thrown  into 
this  liquid,  burns  with  brilliant  scintillations,  and  thus  almost  at  the  same  point 
there  is  a  temperature  of  about  3600°  above  and  180°  below  Fahrenheit's  zero. 

692.  Latour's  law. — From  his  experiments  on   the  conversion   of 
liquids  into  vapors,  Caignard  de  Latour  announced  the  following  law : — 

There  is  for  every  vaporizable  liquid  a  certain  temperature  and  pres- 
sure at  which  it  may  be  converted  into  the  aeriform  state,  in  the  same 
space  occupied  by  the  liquid. 

In  these  experiments,  strong  glass  tubes,  furnished  with  interior  manometer 
gauges,  were  partially  filled  with  water,  alcohol,  ether,  and  other  liquids,  and 
hermetically  sealed.  The  temperature  of  the  tubes  was  then  gradually  raised. 
Ether  becomes  a  vapor  at  328°,  in  a  space  equal  to  double  its  original  bulk, 
exerting  a  pressure  of  37'5  atmospheres;  alcohol  at  a  temperature  of  404°-5, 
with  a  pressure  of  119  atmospheres,  and  water  disappeared  in  vapor,  in  a  space 


468  PtifrSICS    OF   IMPONDERABLE   AGENTS. 

four  times  its  own  bulk,  at  the  temperature  of  about  773°.  If  Mario  fcte's  law 
held  good  in  these  cases,  the  pressures  exerted  would  have  been  very  much 
greater  than  were  actually  observed.  Even  before  a  liquid  wholly  disappears, 
the  elasticity  of  the  vapor  is  found  to  increase  in  a  proportion  far  greater  than 
is  the  case  with  air  at  equally  elevated  temperatures.  It  is  not  therefore  sur- 
prising that  mere  pressure  fails  to  liquefy  many  bodies  which  exist  ordinarily 
as  gases.  Compare  the  statements  respecting  Mariotte's  law  in  $$  274-277. 

693.  Density  of  vapors. — The  accurate  determination  of  the  density 
of  vapors,  is  of  much  importance  in  Chemical  Physics.     It  is  accom- 
plished by  filling  a  globe,  or  other  vessel  of  glass,  with  the  vapor  at  a 
given  temperature,  and  weighing  it;  this  weight,  divided  by  the  weight 
of  an  equal  volume  of  air,  under  the  same  circumstances  of  tempera- 
ture and  pressure,  gives  the  density  of  the  vapor.     The  details  of 
the  methods  in  use  for  this   purpose,  belong   more   appropriately  to 
chemistry. 

\  9.   Spheroidal  condition  of  Liquids. 

694.  Spheroidal  state. — Drops  of  water  scattered  on  a  polished 
surface  of.  heated  metal  do  not  immediately  disappear,  but  assume  the 
form  of  flattened  spheres,  rolling  quietly  about,  until  they  gradually 
evaporate. .    If  the  metal  has  not  a  certain  temperature,  it  is  wetted  by 
the  water  with  a  hissing  sound.     This  observation  was  made  in  1746, 
and  ten  years  after,  Liedenfrost  called  particular  attention  to  the  phe- 
nomenon.    Dobereiner,  Laurent  and  others,  also  experimented  upon 
this  subject.     They  found   that   saline   solutions,   as  well  as   simple 
liquids,  would  act  in  the  same  manner  as  water.     It  is,  however,  to 
Boutigny  that  we  are  particularly  indebted  for  the  investigation  of  the 
phenomena  of  the  spheroidal  state  of  liquids. 

Illustration  of  the  spheroidal  state. — The  above  experiment  may 
be  variously  performed,  according  to  the  ingenuity  of  the  experimei  ter. 

A  small  smooth  brass  or  iron  capsule  is  heated  over  a  lamp,  fig.  495,  and  a  few 
drops  of  water  allowed  to  fall  upon  it  from  a  pipette ;  the 
drops  do  not  wet  the  metallic  surface,  but  roll  about  in  495 

spheroidal  globules,  uniting  together  after  a  time  into  a 
single  mass,  which,  it  will  be  seen,  has  the  form  of  an 
oblate  spheroid,  and  evaporates  but  slowly.  This  is  the 
condition  distinguished  by  Boutigny  as  the  spheroidal 
state.  If  the  metal  is  allowed  to  cool  gradually,  when 
the  temperature  falls  to  a  certain  point,  the  liquid  will 
burst  into  violent  ebullition  and  quickly  evaporate. 

The  spheroidal  state  may  be  produced  in  a  vacuum  as  well  as  in  the 
air,  upon  the  smooth  surface  of  most  solids,  and  also  upon  the  surface 
of  liquids. 

Noticeable  phenomena  connected  with  the  spheroidal  state. 
— There  are  several  important  points  to  be  noticed  as  regards  this 
curious  subject.  The  chief  of  these  are,  that,— 


HEAT. 


469 


496 


1.  The  temperature  of  the  plate  must  be  greater  than  the  boiling  point  of  the 
liquids,  in  order  to  produce  the  spheroidal  state,  and  it  varies  with  the  boiling 
point  of  the  liquid  employed. 

Thus,  with  water,  the  spheroidal  state  is  produced  when  the  plate  is  at  a  tem- 
perature of  340°,  and  may  attain  it  even  at  288° ;  with  alcohol 
and  ether,  the  plate  must  have  at  least  the  temperature  of  273° 
and  142°  respectively. 

2.  The  temperature  of  the  spheroids  is   always  lower  than   the 
boiling  points  of  the  liquids.     This  was  determined  by  Boutigny, 
by  immersing  a  delicate  thermometer  in  the  spheroid,  as  shown 
in  fig.  496. 

Thus,  205°-7  is  the  temperature  of  the  spheroid  of  water;  168°-5 
that  of  alcohol;  93°-6  that  of  ether;  13°-1  that  of  sulphurous 
acid. 

The  temperature  of  a  spheroid  is  not  quite  as  definite  as  the 
temperature  of  ebullition  of  the  liquid,  but  rises  somewhat  as  the 
plate  upon  which  it  rests  is  more  intensely  heated. 

3.  The  temperature  of  the  vapor  from  a  spheroid  is  nearly  the 
same  as  that  of  the  plate  upon  which  it  rests,  which  proves  that 
the  vapor  is  not  disengaged  from  the  mass  of  the  liquid. 

4.  The  rapidity  of  evaporation  from  a  spheroid,  increases  with 
the  temperature  of  the  plate  upon  which  it  rests,  as   is   proved   by 
the  following  experiments  of  Boutigny.     The  same  quantity  of 
water  (0-10  gramme,  or  1-534  grs.)  was  evaporated  in  each  case. 

With  the  plate  at  the  temperature  of  392°,  the  water  evaporated  in  207  seconds. 
With  the  plate  at  the  temperature  of  752°,  the  water  evaporated  in  91  seconds. 
With  the  plate  at  dull  red  heat,  the  water  evaporated  in  73  seconds.  With  the 
plate  at  bright  red  heat,  the  water  evaporated  in  50  seconds. 

Water,  in  the  spheroidal  state,  evaporates  much  more  slowly  than  at  the  tem- 
perature of  ordinary  ebullition.  Thus,  when  the  plate  was  at  the  temperature 
of  212°,  O'lO  grins,  of  water  evaporated  in  4  seconds ;  and  when  at  the  tempera- 
ture of  392°,  in  207  seconds,  or  about  one-fiftieth  part  as  rapidly. 

695.  Spheroidal  state  produced  upon  the  surface  of  liquids. — 

A  highly  heated  liquid  may  cause  the  spheroidal  state  in  another  liquid  of  lower 
boiling  point  than  itself. 

Thus,  Pelouze  found  that  water  assumed  the  spheroidal  state  on  very  hot  oil  of 
turpentine,  although  the  water  is  the  denser  liquid.  Boutigny  has  thus  sustained 
water,  alcohol,  and  ether  on  sulphuric  acid,  nearly  at  its  boiling  point.  With 
sufficient  precautions,  a  number  of  liquids  may  be  thus  piled  one  upon  the  other. 

696.  A  liquid  in  a  spheroidal  state  is  not  in  contact  with  the 
heated  surface  beneath. — This  must  appear,  on  reflection  upon  the 
facts  already  stated,  and  may  be  demonstrated  as  follows: — 

A  horizontal  silver  plate  is  surmounted  by  a  tube  of  the  same  metal,  fig.  497, 
whose  lower  edges  have  two  longitudinal  slits  opposite  to  each  other.  The  plate 
is  placed  upon  the  eolipile  (704)  containing  alcohol,  which  is  nicely  adjusted  to 
a  perfect  level  by  the  screws  in  the  triangular  base.  Silver  is  employed  to  avoid 
the  formation  of  scales  of  oxyd  of  copper,  which  would  interfere  with  the  obser- 
vation by  interposing  themselves  to  the  light. 

When  the  plate  heated  over  the  lamp  reaches  the  proper  temperature,  a  por- 
tion of  water  is  placed  upor  its  centre,  and  immediately  assumes  the  spheroidal 
•12* 


•470  PHYSICS    OF    IMPONDERABLE    AGENTS. 

condition.    Placing  the  eye  on  a  level  with  the  surface  of  the  plate,  and  looking 
through  the  apertures  in  the  sides  of  the  tube,  the  flame  of  a  candle  opposite 
497 


may  be  distinctly  seen.  This  could  not  happen  if  the  liquid  was  in  contact 
with  the  plate.  If  a  thick  and  heavy  silver  capsule  is  heated  to  full  whiteness 
over  the  eolipile,  it  may,  by  an  adroit  movement,  be  filled  entirely  with  water, 
and  set  upon  a  stand,  some  seconds  before  the  heat  declines  to  the  point  when 
contact  can  occur  between  the  liquid  and  the  metal.  When  this  happens,  the 
water,  before  quiet,  bursts  into  steam,  with  almost  explosive  violence,  and  is 
projected  in  all  directions,  as  shown  in  fig.  498. 

697.  A  repulsive  action  is  exerted  between  the  spheroid  and 
the  heated  surface. — This  proposition  follows,  indeed,  as  a  conse- 
quence of  the  last.    It  has  already  been  demonstrated,  that  a  liquid  does 
not  wet  a  surface,  when  the  cohesion  which  exists  between  its  particles  is 
double  of  their  adhesion  for  the  solid  (234).     This  adhesion  is  not  only 
diminished  by  heat,  but  a  repulsive  action  is  exerted  between  the  hot 
body  and  the  liquid,  which  becomes  more  intense  as  the  temperature 
is  higher.     This  repulsive  action  is  strikingly  demonstrated  by  the 
following  experiment  of  Boutigny: — 

A  few  drops  of  water  were  let  fall  into  a  basket,  formed  of  a  net-work  of 
platinum  wires,  heated  red-hot.  The  water  did  not  pass  through  the  meshes, 
even  when  the  basket  was  rapidly  rotated.  But  when  the  metal  was  sufficiently 
cooled,  the  water  immediately  ran  through  in  a  shower  of  small  drops,  or  was 
quickly  dissipated  in  vapor.  It  would  also  seem,  that  vapors,  like  liquids,  are 
repelled  from  the  heated  surface,  for  Boutigny  found  that  a  hot  silver  dish  was 
not  attacked  by  nitric  acid,  or  one  of  copper  by  sulphuric  acid  or  ammonia. 
The  latter  substance  had  no  action  upon  either  iron  or  zinc  at  a  high  tempera- 
ture. The  suspension  of  chemical  affinity  under  certain  conditions  of  high 
temperature,  is  a  fact  of  great  interest  in  the  physics  of  the  globe. 

698.  The  causes  which  produce  the  spheroidal  form  in  liquids 
are  at  least  four : — 

1st.  The  repulsive  force  of  heat  exerted  between  the  hot  surface  and 
the  liquid,  and  which  is  more  intense  as  the  temperature  rises. 

2d.  The  temperature  of  the  plate  is  so  high,  that  the  water  in  mo- 
mentary contact  with  it,  is  converted  into  vapor,  upon  which  the  sphe- 
roid rests  as  upon  an  elastic  cushion. 


HEAT.  471 

3d.  The  va^r  is  a  poor  conductor  of  heat,  and  thus  prevents  the  con- 
duction of  heat  from  the  metal  to  the  globule.  Another  cause  which 
prevents  the  liquid  from  becoming  highly  heated  is,  that  the  rays  of 
heat  from  the  metal  are  reflected  from  the  surface  of  the  liquid.  This 
is  shown  by  the  fact,  that,  if  the  water  be  colored  by  lampblack,  heat 
is  absorbed,  and  the  evaporation  is  much  more  rapid. 

4th.  Evaporation  from  the  surface  of  the  metal  carries  off  the  heat  as 
it  is  absorbed,  and  thus  prevents  the  liquid  from  entering  into  ebulli- 
tion. The  form  of  th%  oblate  spheroid,  which  the  liquid  assumes,  is 
the  combined  result  of  the  cohesion  of  the  particles  to  each  other,  and 
the  action  of  gravity  upon  the  mass. 

699.  Freezing  water  and  mercury  in  red-hot  crucibles. — The 
remarkable  phenomena  of  freezing  water,  and  even  mercury  in  red-hot 
crucibles,  are  striking  examples  of  the  production  of  the  spheroidal 
state  of  liquids. 

Boutigny  placed  a  portion  of  liquid  sulphurous  acid  in  a  red-hot  vessel.  It 
assumed  the  spheroidal  state  immediately,  at  a  temperature  below  that  of  its 
ebullition,  that  is,  below  14°  F.  A  little  water  placed  in  the  spheroid  becomes, 
therefore,  cooled  below  32°  F.,  its  freezing  point,  and  is  converted  into  ice. 

Faraday  placed  in  a  heated  crucible  a  mixture  of  solid  carbonic  acid  and 
ether,  which  immediately  assumed  the  spheroidal  state.  Into  it  was  plunged  a 
metal  spoon  containing  mercury ;  almost  immediately  the  mercury  was  frozen 
into  a  solid  mass.  The  temperature  in  this  case  was  probably  as  low  at 
—148°  F. 

700.  Remarkable  phenomena  cpnnected  with  the  spheroidal 
state. — On  the  principle  explained,  the  hand  may  be  bathed  in  a  vase 
of  molten  iron,  or  passed  through  a  stream  of  melted  copper  unharmed, 
or  one  may  stir  fused  glass  under  water  without  danger.     In  all  similar 
cases,  if  the  temperature  be  sufficiently  high,  the  moisture  of  the  hand 
assumes  the  spheroidal  state,  and  does  not  allow  of  contact  with  the 
heated  mass.     If,  however,  the  hand  is  drawn  rapidly  through  the 
melted  metal,  contact  is  mechanically  produced,  and  injury  follows  this 
rashness.     The  finger,   moistened  with  ether,  may  be,  for  the  same 
reason,  plunged  into  boiling  water  without  injury. 

701.  Explosions  produced  by  the  spheroidal  state. — The  ex- 
periment illustrated  by  fig.  499,  may  be  modified  to  illustrate  explo- 
sions, and  some  other  interesting  facts  consequent  on  the  spheroidal 
state. 

A  copper  bottle,  fig.  499,  is  heated  as  hot  as  possible  over  a  double  current 
\arnp,  and  in  this  state  a  few  grammes  of  pure  water  are  introduced  by  a  pipette. 
The  water  at  once  assumes  the  spheroidal  condition,  and  has  a  temperature  (as 
may  be  ascertained  by  a  thermometer)  below  that  of  its  ebullition.  If  the  neck 
of  the  bottle  is  now  tightly  closed  by  a  good  cork,  the  evaporation  is  so  slight, 
that  the  pressure  of  the  vapor  within  is  not  immediately  sufficient  to  drive  out 


472  PHYSICS    OF    IMPONDERABLE    AGENTS. 

the  cork.  If,  however,  the  lamp  is  withdrawn,  the  metal  will  soon  cool  suffi- 
ciently to  allow  contact  of  the  water  with  it.  There  will  then  be  so  sudden  an 
evolution  of  a  large  volume  of  vapor  as  to  drive  the  cork 
from  the  bottle  with  a  loud  explosion. 

Steam  boiler  explosions  may  sometimes  be 
explained  by  a  knowledge  of  the  principles  here 
elucidated.  Thus,  whenever  from  any  cause  a 
deficiency  of  water  occurs  in  a  boiler,  as  when  the 
pumps  fail  of  a  supply,  or  when,  by  careening^a 
part  of  the  flues  are  laid  bare  while  the  fire  is 
undiminished,  a  portion  of  the  boiler  may  become 
heated  even  to  redness.  Water  coming  in  contact 
with  such  over-heated  surfaces,  would  first  assume 
the  spheroidal  state,  and,  almost  at  the  next 
instant,  burst  into  a  volume  of  vapor  so  suddenly 
as  to  rend  the  boiler  with  frightful  violence.  Numerous  accidents  are 
on  record  where  the  explosion  has  been  so  sudden  as  not  to  expel  the 
mercury  from  the  open  gauges.  The  fact  that  explosions  on  our  Ame- 
rican rivers  have  occurred  most  frequently  just  at  or  after  starting  from 
a  landing,  is  explicable  on  the  view  here  presented ;  the  vessel,  while 
landing  and  receiving  freight,  being  careened,  so  as  to  render  the  expo- 
sure of  some  part  of  the  flues  possible. 

702.  Familiar  illustrations  of  the  spheroidal  state,  and  effects 
of  the  spheroidal  state  of  liquids,  are  not  unfrequent  in  common  life 
and  in  manufactures. 

The  most  common  example  of  the  spheroidal  state,  is  that  of  a  drop  of  water 
on  a  heated  stove,  which  moves  around  in  a  spheroidal  mass,  slowly  evaporating. 
The  laundress  determines  whether  her  flat-irons  are  heated  sufficiently  for  her 
purpose  by  touching  the  surface  with  a  drop  of  saliva  on  the  finger.  If  it 
bounds  off,  the  iron  is  judged  to  be  heated  to  a  proper  temperature.  In  the 
manufacture  of  window-glass,  constant  application  is  made  of  the  principles 
here  explained.  The  masses  of  glass  are  first  formed  into  a  rude  hollow  cylin- 
der by  blowing  them  in  wooden  moulds.  In  order  to  prevent  the  charring  of 
the  mould,  its  interior  is  moistened  with  water,  which,  assuming  the  spheroidal 
state,  protects  the  wood,  while  it  does  not  injuriously  cool  the  glass. 

Saline  solutions  are  more  efficacious  for  tempering  steel  than  pure 
water.  Now,  as  the  point  of  ebullition  of  saline  solutions  is  higher 
than  that  of  pure  water,  contact  between  the  liquid  and  the  metal  is 
produced  sooner,  and  thus  the  steel  is  cooled  more  quickly,  and  the 
temper  is  better. 

Melted  metals,  like  iron  or  copper,  allowed  to  fall  into  water,  do  not  throw  the 
water  into  violent  ebullition,  as  might  be  supposed,  but  pass  in  a  brilliant  stream 
to  the  bottom  of  the  vessel,  the  water  in  contact  with  the  metal  assuming  the 
spheroidal  state. 


HEAT.  473 

§  10.  The  Steam-Engine. 

703.  Historical.^-The  principles  involved  in   .he  construction  and 
theory  of  the  steam-engine,  have  already  been  sufficiently  discussed. 
A  few  words  must  suffice  respecting  their  practical  applications  in  the 
discovery  and  perfecting  of  this  remarkable  machine. 

For  the  first  rudiments  of  our  knowledge  of  steam  as  a  motor,  we 
must  go  back,  as  upon  many  other  so-called  modern  inventions,  to 
Egypt,  where,  130  years  B.  c.,  Hero,  or  Heiro,  describes  in  his  "  Spiri- 
talia  seu  Pneumatica,"  among  many  other  curious  contrivances,  what 
he  calLs  the  eolipile. 

704.  The    eolipile  is  a  metallic  vessel,  globular,  or  boiler-shaped, 
containing  water,  and  provided  at  top  with  two  horizontal  jet  pipes, 
bent  into  the  form  of  an  S. 

This  apparatus,  fig.  500,  is  suspended  over  a  flame,  and  being  free  to  move, 
when  the  water  boils,  the  steam  rushing  out,  strikes  against  the  atmosphere, 
and  the  recoil  drives  the  apparatus  around  with  great 
rapidity.  This  is  in  fact  a  direct-action  rotary  steam 
engine,  and  undoubtedly  the  earliest  mechanical  result 
achieved  by  steam  power.  It  has  often  been  re-invented, 
in  numberless  forms,  in  modern  times.  In  another  form 
the  eolopile  is  made  to  blow  by  its  jet  the  flame  of  a  lamp, 
and  in  this  case  the  boiler  is  fixed  and  filled  with  alcohol  in 
place  of  water,  the  jet  descending  through  the  flame  of  the 
lamp  as  in  the  apparatus  seen  in  fig.  497.  Hero  describes 
also  other  devices  where  steam  was  the  moving  power. 

705.  First  steamboat. — Blasco  de  Garay,  a  sea- 
captain  of  Barcelona,  in   Spain,  in  1543,  moved  a 
vessel  of  200  tons  burthen  three  miles  an  hour  by 
paddles  propelled  probably  by  steam,  as  the  moving 
force  came,  it  was   said,   from  a  boiler  containing' 
water,  and  liable  to  burst. 

This  experiment  was  made  on  the  17th  day  of  June,  1543,  in  presence  of 
Commissioners  appointed  by  the  king,  Charles  V.,  whose  report  secured  the  favor 
of  the  crown  to  the  projector.  But  what  is  unaccountable,  nothing  more  ever 
came  from  this  singular  success.  De  Garay  probably  employed  Hero's  eolipile 
on  a  large  scale,  as  Hero's  work  above  named  was  about  that  time  translated 
into  several  languages  and  generally  diffused.  Passing  the  early  efforts  of  Bap- 
tista  Porta  and  De  Caus  (A.  D.  1615),  of  Brancha  (in  1629),  Otto  V.  Guerick 
(1650),  and  the  Marquis  of  Worcester  (1663),  we  come  to  the  first  efficient  steam 
apparatus  (that  of  Savary). 

706.  Savary's  engine. — In  1698,  Capfr.  Thos.  Savary  obtained   a 
patent  "for  raising  water  and  occasioning  motions  to  all  kinds  of  mill 
work  by  the  impellent  force  of  fire."     His  apparatus  can  hardly  be 
called  an  engine,  or  machine,  since  it  has  no  moving  parts. 


474 


PHYSICS    OF    IMPONDERABLE   AGENTS. 


Fig.  501  is  Savary's  engine.  Two  boilers,  L  and  D,  are  connected  together 
by  the  pipe,  H.  Two  "condensers,"  P  and  P',  are  connected  with  the  larger 
boiler,  L,  by  pipes  entering  at  top  of  both,  and  capable  of  being  alternately 
shut  off  from  the  boiler  by  a  valve,  moved  by 
the  lever  Z.  By  two  branch  pipes  beneath  the 
condensers,  communication  is  established  at  plea- 
sure, by  the  aid  of  the  cocks  1,  2,  3,  4,  alternately 
with  the  well  by  T,  and  the  open  air  by  the  outlet 
pipe  S.  The  boiler,  L,  being  in  action,  the  con- 
denser, P,  for  example,  was  filled  with  steam,  the 
cocks  1  and  3  being  closed.  By  moving  Z,  the 
condenser,  P',  was  next  filled  with  steam  also, 
cocks  2  and  4  being  closed,  and  at  the  same 
instant  cock  3  being  opened,  the  water  rushed  up 
through  T,  to  fill  the  vacuum  occasioned  by  the 
condensation  of  the  steam  in  P.  The  lever,  Z, 
was  then  moved  to  close  P'  and  open  P  again  to 
the  boiler.  Cock  4  now  admitted  cold  water  to 
P',  and  cock  1  being  opened,  the  direct  pressure 
of  the  steam  from  the  boiler  forced  the  water 
out  of  P,  in  a  stream  through  the  discharge 
pipe,  S.  The  water  in  P'  was  also  discharged 
in  the  same  manner,  and  so  on,  alternately,  each 
condenser  was  filled  with  cold  water,  and  again 
discharged,  maintaining  a  continuous  stream  of  water  from  S.  To  supply  the 
waste  of  water  in  the  boiler,  L,  the  contents  of  the  smaller  boiler,  D,  wero  from 
time  to  time  forced  by  superior  steam  pressure  into  L,  through  the  pipe  H 
(provided  with  a  valve  for  that  purpose),  reaching  near  the  bottom  of  D,  whose 
capacity  was  such  as  to  fill  L  to  a  suitable  height.  The  boiler,  D,  was  thcu  re- 
filled through  the  pipe,  E,  from  the  supply  box,  X,  attached  to  the  discharge 
pipe. 

All  the  details  of  Savary's  contrivance  show  a  nice  adjustment  of 
means  to  the  end  to  be  accomplished. 

707.  Papin's  steam  cylinder,  Newcomen's  engine. — Denys 
Papin  (Prof,  of  Mathematics  at  Marburg),  whose  name  is  connected 
with  the  high-steam  digester,  suggested  in  1690  the  use  of  steam  to 
produce  a  vacuum  in  lieu  of  the  air-pump  before  used. 

For  this  purpose  he  constructed  the  cylinder  of  sheet  iron,  and  built  a  fire 
beneath  its  bottom,  to  boil  a  portion  of  water  there  placed.  When  the  cylinder 
was  filled  with  steam,  the  piston,  before  held  up  by  a  latch,  descended  as  the 
steam  was  condensed.  No  practical  result  followed  this  clumsy  contrivance,  on 
which  Papin's  countrymen  rest  his  claims  to  be  considered  as  the  inventor  of  the 
steam-engine. 

THOS.  NEWCOMEN,  in  1710,  first  put  in  practice  the  use  of  a  cylinder 
and  piston  in  the  pteam-engine,  in  which  the  steam  was  alternately 
admitted  and  again  condensed  by  a  stream  of  cold  water.  This  engine 
operated  against  the  pressure  of  the  atmosphere,  and  was  effectual  in 
only  one  direction,  i.  e.,  it  was  a  single  acting  engine. 


HEAT. 


475 


708.  The  atmospheric  engine  is  well  illustrated  by  the  apparatus 
shown  in  fig.  502,  which  was  contrived  by  Dr.  Wollaston,  to  show  the 
nature  of  Papin's  cylinder. 

A  glass,  or  metallic  tube,  with  a  bulb  to  hold  water,  is  fitted 
with  a  piston.  This  piston-rod  is  hollow,  and  closed  by  a 
screw  at  a.  This  screw  is  loosened  to  admit  the  escape  of  the 
air,  and  the  water  is  boiled  over  a  lamp :  as  soon  as  the  steam 
issues  freely  from  the  open  end  of  the  rod,  the  screw  is  tight- 
ened, and  the  pressure  of  the  steam  then  raises  the  piston  to 
the  top  of  the  tube,  the  experimenter  withdraws  it  from  the 
lamp,  the  steam  is  condensed,  and  the  air  pressing  on  the  top 
of  the  piston  forces  it  down  again ;  when  the  operation  may  be 
repeated  by  again  bringing  it  over  the  lamp. 

In  all  the  early  steam-engines,  the  steam  was  condensed 
within  the  cylinder,  either  by  water  applied  externally,  or  by  a 
jet  of  water  thrown  directly  into  the  cylinder.  It  is  very  obvi- 
ous, that  a  great  loss  of  fuel  and  time  was  thus  involved  in 
bringing  the  cylinder  up  again  to  212°,  before  a  second  stroke 
could  be  made. 

NEWCOMEX  and  SMEATON  constructed  very  large  engines,  however,  on  this 
principle,  and  applied  their  power  directly  to  the  pumping  of  mines.  Although 
Smeaton  introduced  an  improved  kind  of  mechanical  work  and  many  improve- 
ments in  minor  details,  and  better  boilers,  he  succeeded  only  in  raising  the 
average  duty  of  steam-engines  from  about  five  and  a  half  millions  of  pounds, 
raised  one  foot  by  a  bushel  of  coal  (80  Ibs.)  burned,  to  about  nine  and  a  half 
millions,  in  his  best  engines.  A  good  pumping  engine  now  raises  from  ninety 
to  one  hundred  and  thirty  millions  of  pounds  for  every  bushel  of  coal  burned. 

709.  Watt's  improvements  in  the  steam-engine. — The  steam- 
engine  as  it  was  left  by  Smeaton  was,  as  we  have  seen,  only  a  steam 
pump,  confined  to  the  single  function  of  raising  water,  and  incapable 
of  general  use,  as  well  from  its  imperfections  as  from  the  enormous 
cost  of  fuel  it  required. — "Watt,  in  1763,  was  a  maker  of  philosophical 
instruments  at  Glasgow,  and  had  occasion  to  repair  a  model  of  the 
Newcomen  engine.     The  study  of  this  machine  and  its  defects,  led 
Watt  to  construct  a  new  model,  in  which  the  steam  was  condensed  in 
a  separate  vessel,  in  connection  with  which  he  subsequently  found  it 
advantageous  to  use  an  air-pump — to  aid  in  keeping  the  vacuum  good, 
as  it  was  otherwise  vitiated  by  atmospheric  air  leaking  in,  and  coming 
from  the  water  of  the  boiler.     These  ideas  were  matured  and  realized 
in  1765,  and  in  1769  he  took  out  his  patent,  in  which  all  the  essential 
features  of  our  modern  steam-engines  are  included.    In  connection  first 
with  Mr.  Roebuck,  of  Carron  Iron  Works,  and  subsequently  with  Mr. 
Boulton,  of  Soho,  he  put  his  ideas  in  practice,  and  by  reserving  to  the 
patentees  one-third  part  of  the  saving  of  fuel  effected  by  his  improve- 
ments, his  genius  was  rewarded  by  the  accumulation  of  a   princely 
fortune. 


476 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


Watt's  mention  of  low  pressure  condensing  engines  stands  without  a  parallel 
in  the  history  of  science  for  the  perfect  realization  of  all  the  conditions  of  the 
problems  to  be  solved  —  the  perfect  mastery  of  the  laws  of  nature  —  the  use 
of  matter,  by  which  they  were  accomplished,  and  the  thorough  exhaustion  of 
the  subject  even  in  its  minutest  details,  so  that  to  this  day  we  have  no  improve- 
ments in  this  machine  involving  a  single  principle  unknown  to  Watt.  In  the 
beauty  and  perfection  of  mechanical  work,  in  size  of  parts,  and  the  strength 
of  boilers,  we  have  machines  greatly  superior  to  any  Watt  ever  saw,  but  it  was 
his  genius  that  rendered  those  perfections  possible,  and  supplied  the  very  power 
by  which  they  have  been  worked  out. 

710.  The  low  pressure  or  condensing  engine. — The  low  pres- 
sure engine  is  employed  in  all  situations  where  economy  of  fuel  and 
the  best  mechanical  effect  from  it  are  the  ruling  considerations,  and 
where  lightness  and  simplicity  of  construction  is  unimportant.  This 
machine  now  remains  almost  exactly  as  Watt  left  it.  Owing  to  the 
nearly  perfect  vacuum  obtained  in  it  by  the  condenser  and  air-pump, 
much  less  pressure  of  steam  is  required  to  produce  a  given  mechanical 
result ;  e.  g.,  if  the  vacuum  is  equal  to  fourteen  Ibs.  atmospheric  pres- 
sure, then  a  steam  pressure  of  six  Ibs.  would  give  an  efficient  moving 
force  of  twenty  Ibs.  to  the  machine.  Hence  the  propriety  of  the  term 
"  low  pressure"  engine ;  but  in  practice  it  is  found  advantageous  to  use 
higher  pressures  in  the  condensing  engines  than  Watt  ever  contem- 
plated. 

Fig.  503  is  a  section  of  the  cylinder,  A,  condenser,  e,  air-pump,  hot  and  cold 
well,  and  a  view  of  the  most  important  attached  parts  of  a  modern  condensing 
engine.  The  cylinder,  A,  is  seen  receiving  steam  at  top  through  the  throttle- 

503 


valve,  a,  driving  down  the  piston,  B,  with  its  rod,  C.     A  stream  of  cold  water 
injected  into  the  condenser,  e,  has  completely  condensed  all  the  residual  steam 


HEAT. 


477 


of  the  former  stroke  which  has  found  its  way  from  A  by  the  eduction  j/ipe,  d, 
BO  that  the  piston,  B,  is  descending  into  a  nearly  perfect  vacuum  (671).  The 
hot  water  of  this  condensation  is  constantly  drawn  off  through  the  valve,  k,  by 
the  air-pump  whose  valves,  ii,  rise  to  allow  its  flow  into  the  hot  well,  I,  whence 
it  finds  its  way,  solicited  by  the  plunger  pump,  S,  to  the  boilers  by  the  pipe,  P, 
and  its  valves,  o  o.  The  cold  water  pump,  q,  supplies  a  steady  stream  of  cold 
water  by  the  spout,  r,  to  the  cold  well.  By  the  time  the  piston,  B,  has  reached 
its  lowest  point  of  descent,  the  valve  rod,  V,  and  eccentric  bar,  S,  have  moved 
so  as  to  open  the  lower  steam  ports  and  reverse  the  direction  of  the  piston, 
when  the  steam  above,  B,  is  in  its  turn  taken  into  the  condenser,  e,  by  the 
appropriate  channels,  and  removed  as  already  explained  for  the  downward 
stroke.  The  piston  rod,  C,  and  valve  and  pump  rods,  are  connected  above 
with  the  great  working-beam,  whose  further  extremity  conveys  the  power  of 
the  engine  by  the  pitman,  G,  through  the  crank  pin,  H,  to  the  main  shaft,  K, 
on  which  is  the  fly-wheel,  L,  to  give  steadiness  of  motion  to  the  whole  appa- 
ratus. The  arrows  show  the  motion  of  these  parts  as  the  piston  descends. 
The  governor,  z,  controls  the  throttle-valve,  a,  by  connections  not  shown  in 
this  drawing. 

711.  The  high  pressure  engine. — In  this  machine,  the   escape 
steam  is  driven  out  against  the  pressure  of  the  atmosphere,  and  no 
attempt  is  made  to  utilize  its  capacity  to  form  a  vacuum,  consequently 
this  form  of  apparatus  could  be  used  as  well  with  condensed  air,  or 
any  other  elastic  fluid,  as  with  steam,  if  there  was  any  other  that  could 
compete  in  economy  with  it.     The  lightness,  simplicity,  and  low  cost 
of  the  high  pressure  engine,  make  jt  availa-  504 

ble  in  spite  of  its  uneconomical  use  of  steam, 
in  many  situations  where  a  condensing  en- 
gine would  be  unavailable. 

The  steam  arrives  by  the  pipe,  Z,  fig.  504,  to 
the  steam  chest,  R,  and  is  admitted  alternately 
by  the  ports  e  d,  to  the  top  and  bottom  of  the 
cylinder,  A  A,  as  the  valve  rod,  S,  actuated  by 
the  eccentric,  /,  on  the  main  shaft,  opens  and 
shuts  the  ports  by  the  slide  valve  in  K.  The 
escape  steam  makes  its  exit  through  9  to  the 
atmosphere.  The  pitman,  P,  conveys  the  motion 
of  the  piston,  C,  to  the  crank,  Q,  and  the  main 
shaft,  on  which  is  the  large  fly-wheel,  a;  to 
accumulate  momentum.  The  flow  of  steam  is 
regulated  by  the  governor,  V,  whose  balls  fly 
out  with  the  centrifugal  force  of  a  more  rapid 
motion,  and  by  the  rod,  h  b,  close  more  or  less 
the  throttle-valve,  z,  which  regulates  the  supply 
of  steam ;  the  pump,  o  o,  supplies  water  to  the 
boiler,  and  is  moved  by  the  rod  and  eccentric,  g, 
on  the  main  shaft. 

712.  The  cut  off. — The  supply  of  steam  both  to  the  high  and  low 
pressure  engine  is  further  regulated  by  a  contrivance  called  the  "  cut 

43 


478  PHYSICS    OF    IMPONDERABLE    AGENTS. 

off,"  which  may  be  set  to  cut  off  the  flow  of  steam  entirely,  or  at  any 
portion  of  the  stroke,  as  one-half,  or  one-third.  The  expansion  of  the 
steam  then  completes  the  work,  and  great  economy  of  fuel  is  found  to 
follow  its  use. 

713.  Steam  boilers. — The  form  of  steam  boilers  varies  very  much 
with  the  purpose  to  which  they  are  to  be  applied.  On  laud,  large 
boilers  may  be  safely  used,  which  would  be  wholly  valueless  at  sea,  or 
on  a  locomotive  engine. 

Plate-iron  strongly  riveted  and  braced,  is  the  material  combining  the  greatest 
economy  and  strength.  Copper  can  be  used  only  when  the  fuel  contains  no  sul- 
phur, and  is  the  best  material  to  resist  corrosive  agents.  Simple  cylindrical 
boilers,  laid  horizontally,  with  a  fire-flue  under  the  whole  lower  surface,  are 
commonly  used  for  high  pressures.  When  these  are  made  large  enough  to 
receive  the  furnaces  within  and  distribute  the  heat  in  interior  flues,  they  are 
called  Cornish  boilers.  When  their  505 

construction  is  still  further  modi- 
fied, with  reference  to  the  greatest 
possible  increase  of  fire  surface, 
they  are  called  locomotive  boilers, 
as  in  the  annexed  figure,  505; 
which  is  the  common  locomotive 
boiler  seen  in  section.  D,  is  the 
feed-door,  for  fuel  to  the  furnace 
or  fire-box,  A,  which  communi- 
cates by  numerous  small  hori- 
zontal tubes,  entirely  surrounded 
by  water,  with  the  base  of  the 
chimney,  B,  into  which  the  blast  of  exhaust  steam  from  the  engine  is  driven  at 
K.  E,  is  the  steam  chamber,  where  a  trumpet  tube  in  the  dome  conveys  the 
dry  steam  on  its  way  to  the  cylinder  through  P.  Steam  boilers  are  supplied 
with  hot  water  by  a  force  pump,  and  gauge  cocks  indicate  the  water  level. 

714.  Mechanical  power  of  steam.—^Horse-power. — As  steam- 
engines  were  originally  employed  to  take  the  place  of  horses  in  raising 
water,  it  was  natural  to  estimate  their  power  by  the  number  of  animals 
they  replaced.  The  value  of  any  force  is  correctly  stated  as  the  num- 
ber of  pounds  raised  one  foot  high  in  a  given  time  (foot-pounds).  As 
the  use  of  steam  became  general,  the  term  horse-power  was  retained, 
but  its  use  was  restricted  by  Watt  to  mean  33,000  Ibs.  raised  one  foot 
per  minute,  or  nearly  2,000,000  Ibs.  raised  one  foot  per  hour. 

As  one  cubic  foot  of  water  converted  into  steam  yields,  in  round  numbers, 
(.700  cubic  inches  of  vapor,  its  mechanical  effect  at  atmospheric  pressures,  is 
equivalent  to  raising  15  Ibs.  1700  inches  (or  142  feet)  in  a  tube  of  one  inch  area. 
But  15  Ibs.  raised  142  feet,  is  the  same  thing  as  142  times  15  Ibs.  raised  one  foot, 
or '1130  Ibs.,  or  nearly  a  gross  ton.  The  total  mechanical  force  developed  by 
cl  nging  one  cubic  inch  of  water  into  1700  cubic  inches  of  steam  is,  therefore, 
n»urly  one  ton.  Only  60  or  70  parts  of  this  power  are,  however,  regarded  us 
a.iually  available  in  use,  deducting  friction  and  loss  from  other  cau^s.  Then1- 


HEAT.  479 

fore,  the  evaporation  of  a  cubic  foot  of  water  in  an  hour,  subject  to  this  deduction, 
will  give  the  full  force  of  about  1000  cubic  inches  of  water  converted  into  steam, 
as  the  expression  of  one-horse  power  (viz.,  33,000  Ibs.  X  60  =  1,980,000  Ibs.), 
or  nearly  2,000,000  Ibs.  raised  one  foot.  This  is  a  somewhat  rough  approxima- 
tion, but  it  gives  constants  easily  remembered  and  sufficiently  near  the  truth. 

A  boiler  of  one-hundred  horse  power  means,  then,  a  boiler  capable  of  evapo- 
rating 100  cubic  feet  of  water  per  hour. 

In  practice,  it  is  common  to  allow,  in  large  land  engines,  for  every  horso 
power,  one  square  foot  of  fire  bars  in  the  grate,  three  cubic  feet  of  furnace 
room,  ten  cubic  feet  of  water  in  the  boiler,  and  ten  cubic  feet  of  steam  chamber. 
In  locomotives  and  steamships,  these  proportions  vai'y  very  much. 

715.  Evaporating  power  and  value  of  fuel. — let  England,  engi- 
neers estimate  ten  pounds  of  bituminous  coal  for  every  cubic  foot  of 
water  (i.  e.  every  horse  power)  to  be  evaporated.  In  carefully  con- 
structed boilers,  however,  this  effect  is  produced  by  seven  or  eight 
pounds  of  coal.  In  the  Cornish  boilers,  where  a  very  large  evaporating 
surface  is  allowed,  five  pounds  of  coal  only,  and  sometimes  less,  are  used 
per  horse  power.  In  the  United  States,  anthracite  coal  averages  ten 
pounds  of  water  evaporated,  for  every  pound  of  coal  burned.  This 
would  give  6*25  Ibs.  of  anthracite  for  each  cubic  foot  of  water  evapo- 
rated. A  well  regulated  current  of  vapor  conducted  over  the  flame  of 
bituminous  coal  by  Dr.  Fyfe,  raised  the  evaporative  effect  produced  37 
per  cent,  above  what  was  obtained  from  the  unassisted  coal.  This 
increase  is  due  to  the  decomposition  of  the  steam  by  the  hot  fuel,  and 
the  consequent  effect  of  the  pure  oxygen  on  the  carbon.  Well  seasoned 
wood  (beech  or  oak),  still  containing  about  20  per  cent,  of  water,  and 
well  dried  peat,  have  about  equal  evaporating  power,  and  are  only 
about  two-fifths  as  effective  as  an  equal  weight  of  ordinary  bituminous 
coal. 

Welter  has  observed  that  those  quantities  of  a  combustible  body  which  require 
an  equal  amount  of  oxygen  for  combustion,  evolve  also  equal  quantities  of  heat; 
although  later  researches  show  this  conclusion  not  to  be  strictly  true,  it  is  sup- 
ported by  many  facts.  In  all  cases  of  combustion,  the  action  is  reciprocal ;  the 
oxygen  is  burned  in  the  fuel  as  truly  as  the  fuel  by  the  oxygen,  and,  therefore, 
the  same  amount  of  heat  is  generated  by  a  given  amount  of  oxygen,  whether  in 
converting  carbon  into  carbonic  acid,  or  hydrogen  into  water.  To  burn  one 
part  of  carbon,  requires  2-66  parts  of  oxygen  (C02  =  16  -=-  6  —  2  66),  and  to 
burn  one  part  of  hydrogen,  requires  8  parts  of  oxygen.  It  has  been  proved 
experimentally  (by  Rumford)  that  78  parts  of  water  are  raised  from  32°  to  212° 
by  burning  one  part  of  carbon,  while  one  part  of  hydrogen  so  burned  will  raise 
236 '4  parts  of  water  through  the  same  degrees.  It  therefore  follows,  that  one 
part  of  oxygen,  burning  carbon,  will  heat  78  -^  2-66  =  29-25  parts  of  water 
from  32°  to  212°;  and  also  that  the  same  quantity  of  oxygen,  in  burning 
hydrogen,  will  heat  236-4  -j-^8  =  29-56  parts  of  water  through  the  same  degrees. 
The  heating  effect  of  oxygen  may,  therefore,  be  assumed  to  be  30,  or,  in  units 
of  heating  power,  5400. 

If  the  heating  effect  of  pure  carbon  is  tal'en  at  unity,  the  relative  heating 


480 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


effects  of  combustibles  will  range  Us  follows  for  equal  weights : — hydrogen,  3  ; 
vegetable  oil,  1-15— 1-22;  ether,  1-02;  carbon,  1;  wood  charcoal,  0-96;  alcohol, 
0-86;  good  coal,  077;  dry  wood,  0-46;  wood  (with  20  per  cent,  water),  0  35; 
peat,  0-33— 0-38.— (Knapp.)  Compare  $  753. 

The  best  expansive  steam-engines,  it  is  calculated,  give  back,  in  tha 
form  of  mechanical  work,  only  about  18  per  cent,  of  the  heat  generated 
by  the  fuel  burned  in  driving  them. 

Prof.  W.  R.  Johnson  ("experiments  on  coals")  and  others,  argue, 
as. the  result  of  experiment,  that  the  total  amount  of  carbon  in  a  fuel, 
is  the  measure  of  its  practical  evaporative  power.  His  results  very 
nearly  sustain  this  view.  He  found,  also,  that  about  86  per  cent,  of 
the  total  heating  power  were  expended  in  evaporating  water,  and  about 
14  per  cent,  were  lost  in  the  products  of  combustion.  Of  the  total 
heating  power,  by  calculation,  about  26  per  cent,  were  lost  in  practice, — 
as  deduced  from  the  experimental  effects  stated  in  his  tables. 

§11.  Ventilation  and  Warming. 

I.    VENTILATION. 

716.  Currents  in  air  and  gases  depend  upon  principles  which 
have  already  been  fully  explained, — but  the  subjects  of  ventilation  and 
artificial  heating  are  of  such  great  importance  in  daily  life,  that  they 
demand  a  brief  and  separate  consideration. 

Currents  arise  in  air  from  differences  of  temperature  and  variations 
of  pressure.  The  perfect  freedom  of  movement  in  air,  renders  its  fluc- 
tuations from  these  causes  incessant.  If  the  air  was  visible,  every 
candle,  gas-light,  stove,  furnace-flue,  and  human  body,  would  be  seen 
to  be  the  centre  of  an  ascending 
column  of  heated  air,  whose  place 
was  constantly  supplied  by  other  and 
colder  particles. 

On  the  law  of  the  equilibrium  of  flu- 
ids, the  ascending  currents  must  induce 
others,  descending  and  horizontal,  and 
thus  a  circulatory  motion  is  imparted, 
even  by  a  single  lighted  candle,  to  the 
whole  gaseous  contents  of  a  quiet  apart- 
ment. These  currents  are  made  visible 
whenever  the  candle  smokes.  If  the 
door  of  a  heated  apartment  stands  ajar, 
and  a  candle  is  held  near  the  top  crack,  c, 
fig.  506,  the  warm  air  of  the  room  is  seen 
to  draw  outwards,  carrying  the  flame  with 
it,  and  a  corresponding  cold  current,  a, 
Hows  in  at  the  bottom, — while  a  point, 
6,  will  be  found,  midway  its  height,  where  the  candle  flame  is  undisturbed.  So 


HEAT. 


481 


a  window,  partly  open,  will  occasion  a  draught  of  cool  air,  blowing  in  at  the 
bottom  of  the  opening,  and  a  compensating  warm  current  will  escape  outwards, 
above. 

This  constant  interchange  of  motion  in  unequally  heated  masses  of 
air,  while  it  soon  poisons  the  confined  atmosphere  of  a  close  apartment, 
where  many  persons,  with  or  without  lights,  are  assembled,  also  supplies 
the  easy  means  of  curing  one  of  the  greatest  evils  of  civilized  commu- 
nities. 

717.  Draught  in  chimneys. — Chimneys  draw  because  the  products 
)f  combustion  discharged  into  them,  are  specifically  lighter  than  the 
3uter  air.  The  column  of  heated  air,  C  D,  fig.  507,  rises  with  a  velocity 
proportionate  to  the  excess  of  weight  in  a  column  of  the  outer  air,  A  B, 
of  the  same  area  and  height.  The  laws  of  falling  bodies  (71)  apply 
to  this  case  in  every  particular. 

Suppose,  for  example,  a  chimney  is  18  feet  high,  and  the  gases  in  it  are 
heated  to  100°  F.,  the  outer  air  being  70°.  The  contained  column  would,  there- 


507 


fore  (607),  expand  ^j,  or  about  j'gth  of  its 
original  bulk  at  70°.  A  column  of  19  feet  of 
such  air  would,  therefore,  be  required  to  coun- 
terbalance one  of  18  feet  high  in  the  exter- 
nal air  at  70°,  and  of  the  same  area.  The 
heated  air  will,  therefore,  rise  (for  the  same 
reason  that  a  balloon  rises),  with  a  velocity 
equal  to  that  acquired  by  a  body  falling  through 
one  foot,  i.  e.,  a  space  equal  to  the  difference  in 
height  of  the  two  columns — of  equal  loeiylt. 
The  laws  of  gravity,  therefore,  supply  the 
means  of  calculating  the  theoretical  velocity 
of  the  ascending  column,  and  of  course  that, 
with  the  area  of  the  cross  section  of  the  flue, 
will  determine  the  quantity  of  air  passing 
through  the  chimney  in  a  given  time.  But  the 
friction  of  the  air  against  the  sides  of  the  flue, 
and  the  varying  density  of  the  products  of 
combustion  compared  with  air,  diminish  the 
theoretical  velocity,  and  it  is  usual  to  allow  a 
deduction  of  one-fourth  for  these  causes.  The  following  rule  will  be  found  to 
give  a  sufficiently  exact  practical  expression  of  the  velocity  of  air  in  chimneys 
and  ventilating  flues. 

Multiply  the  square  root  of  the  difference  in  height  of  the  two  columns 
of  air  (deduced  as  above]  expressed  in  feet  and  decimals  of  a  foot,  by 
eight;  deduct  one-fourth,  and  the  product  of  the  remainder,  multiplied 
by  sixty,  will  give  the  velocity  of  efflux  per  minute  ;  and  the  area  of  the 
flue  in  feet,  or  decimals  of  a  foot,  multiplied  by  the  velocity,  will  give  the 
number  of  cubic  feet  discharged  per  minute. — (Hood.) 

This  rule,  in  the  case  suj  posed,  would  be  £  (8j/T)  X  60  —  360  cubic 
43* 


482  PHYSICS    OF    IMPONDERABLE    AUENTS. 

feet  of  gases  discharged  per  minute,  by  a  flue  18  feet  high  and  one  foot 
area,  whose  temperature  is  30°  above  the  outer  air. 

Chimneys,  in  the  sense  we  mean,  were  not  known  to  the  ancients.  Holes  in 
the  roof,  and  windows  allowed  the  escape  of  smoke  from  the  kitchens  of  the 
luxurious  Romans.  But  the  mild  climate  of  the  Mediterranean  shores  did  not 
require  much  attention  to  means  of  artificial  warmth.  In  the  houses  of  ancient 
Herculancum  and  Pompeii,  exposed  in  modern  times,  there  are  no  chimneys. 
JJufc  even  in  England  and  France,  where  fires  in  winter  are  necessary,  chimneys 
wore  first  introduced  only  in  the  middle  of  the  14th  century.  The  Curfew  Bell 
(couvre-feu,  fire  cover)  was  needed  as  a  precaution  against  the  danger  of  fire;-, 
\yithout  chimneys. 

Reversed  draughts  and  smoky  chimneys  occur,  1st,  when  the 
Hue  or  fire-place  is  badly  constructed  ;  2d,  when  two  flues  open  into 
one  apartment,  or  two  connecting  apartments,  and  there  is  a  fire  in 
only  one  flue ;  3d,  when  a  powerful  fire  exists  in  one  part  of  the  house, 
as  the  kitchen,  for  instance,  without  an  adequate  supply  of  air  from 
without,  it  will  draw  the  needed  supply  through  the  smaller  flues  in  all 
parts  of  the  house,  reversing  the  draught  in  them ;  4th,  when  (as  in 
many  old  houses)  the  flue  is  so  large  that  cold  currents  may  descend  in 
the  angles,  while  a  heated  one  ascends  the  axis  ;  5th,  when  a  neighbor- 
ing higher  house  or  eminence  directs,  in  certain  states  of  the  wind,  a 
cold  current  down  the  flue. 

The  remedy  for  reversed  draughts  is  best  found  in  one  commanding 
central  stack,  into  which  all  the  minor  flues  discharge,  while  exhaust- 
ing cowls,  like  fig.  511,  are  the  best  cure  of  smoky  chimneys. 

718.  Products  of  respiration  and  combustion,  and  necessity 
for  ventilation. — By  contact  with  the  lungs,  and  with  burning  fuel, 
the  air  is  contaminated,  chiefly  with  carbonic  acid,  water,  effete  nitro- 
gen, oxyd  of  carbon,  and  animal  odors.  Every  full  grown  individual 
consumes,  in  every  minute  of  quiet  respiration,  about  500  cubic  inches 
of  air.  About  14  ounces  of  carbon  are  burned  by  the  air  out  of  the 
body  of  a  man  in  twenty-four  hours,  and  all  this  is  returned  in  the 
form  of  carbonic  acid  to  the  air. 

Such  air  cannot  be  breathed  again  without  danger.  Mixed  with  the  sur- 
rounding air,  it  contaminates  that  also.  Headache,  languor,  uneasy  respiration, 
nausea,  faintness,  and  syncope  are  results  which  always  follow  from  breathing 
air  contaminated  with  these  poisonous  exhalations,  even  in  very  moderate 
quantity.  Even  two  per  cent,  of  carbonic  acid,  derived  from  respiration  or 
combustion,  may  produce  all  the  symptoms  above  named.  The  full  chemical 
and  physiological  evidence  upon  this  important  subject  cannot  be  here  given, 
but  the  evils  arising  from  the  slow  and  insidious  effects  of  the  poison  of  bn.d 
ventilation,  can  hardly  be  over  estimated.  In  ordinary  combustion,  especially 
with  slow  fires  and  an  imperfect  supply  of  air,  carbonic  oxyd  is  also  produced,, 
and  this  is  one  of  the  gases  most  likely  to  leak  from  hot-air  furnaces  when  the 
joints  are  not  tight.  It  is  much  more  destructive  of  life  than  carbonic  acid,  or 
those  gases  of  sulphur,  whose  presence  is  at  once  declared  by  their  odor. 


HEAT.  483 

719.  The  quantity  of  vapor  given  off  by  the  body,  in  sensible 
and  insensible  perspiration,  and  by  the  lungs,  is  very  considerable, 
being  not  less  than  ten  or  twelve  grains  each  minute,  or  about  three 
pounds  per  day,  which,  with  the  quantity  of  carbonic  acid  expired, 
makes  about  three  and  a  third  pounds,  besides  other  excrementitious 
matter,  given  off  in  twenty-four  hours. 

If  the  air  of  a  crowded  apartment  is  conducted  through  water,  so  much  ani- 
nial  matter  is  collected  in  the  water  as  to  occasion  a  speedy  putrefactive  fermen- 
tation, with  a  disgusting  odor.  The  blast  of  air  escaping  at  the  upper  ventilator 
of  a  crowded  assembly  room,  is  so  oppressive  as  to  produce  immediately  the 
most  distressing  symptoms.  While  we  instinctively  shun  all  contact  with 
unclean  persons,  and  what  we  call  dirt,  even  refusing  a  cup  that  has  pressed 
the  lips  of  another,  and  esteem  all-water  not  transparent  as  foul,  it  is  marvellous 
with  what  thoughtlessness  we  resort  to  crowded  and  ill-ventilated  public  places, 
and  drink  in  the  subtle  poison  exhaled  from  the  lungs,  skin,  and  clothirTg  of 
every  individual  in  the  assembly.  Especially  when  we  remember  that  while 
the  digestive  apparatus  can  select  and  assimilate  nutriment  from  food  of  ques- 
tionable quality,  the  lungs  have  no  such  power  of  selection,  and  can  discharge 
their  duty  to  the  blood  only  by  a  full  supply  of  pure  air.  If  the  transparency 
of  air  was  troubled  by  the  exhalations  of  the  lungs  as  water  is  by  the  washings 
of  the  body,  no  argument  would  be  needed  to  secure  attention  to  the  importance 
of  ventilation ;  and  yet  it  is  quite  true  that  the  bodily  health  suffers  more  from 
inhaling  effete  air,  than  it  could  from  drinking  the  wash  alluded  to. 

720.  The  quantity  of  air  required  for  good  ventilation,  is  very 
variously  stated  by  different  authorities.     Enough  fresh  air  must  bo 
supplied,  obviously,  to  replace  all  that  is  contaminated  by  the  lungs, 
the  body,  and  sources  of  illumination.     But  to  determine  exactly  how 
much  these  several  sources  of  deterioration  demand,  is  not  so  easy. 
The  amount  of  air  needed  to  remove  the  products  of  respiration,  is 
very  much  less  than  is  required  to  absorb  the  vapor  of  water  given  off 
from  the  lungs  and  the  skin.     The  quantity  of  vapor  the  air  can  take 
up,  will  depend  on  its  dew-point  and  temperature.     Hood  estimates 
three  and  one-quarter  cubic  feet  of  air  per  minute,  for  each  individual, 
in  winter,  with  an  external  temperature  of  20°  or  25°,  and  a  quarter 
of  a  cubic  foot  per  minute  to  supply  the  waste  from  the  lungs,  making 
three  and  a  half  cubic  feet  per  mffiute,  or  two  hundred  and  ten  cubic 
feet  per  hour  in  winter,  and  five  hundred  in  summer.    Peclet  estimates 
it  at  two  hundred  and  twelve  cubic  feet  per  hour.     Dr.  Reid  estimates 
the  quantity,  as  high  even  as  thirty  cubic  feet  per  minute  per  individual. 
Brenan  puts  it  at  1O25  cubic  feet. 

721.  Products  of  gas  illumination. — Every  cubic  foot  of  gas,  of 
average  quality,  requires  the  oxygen  of  about  twenty  cubic  feet  of  air 
(viz.  4*25  cubic  feet  oxygen)  to  burn  it,  and  produces  rather  over  a 
cubic  foot  of  carbonic  acid,  still  more  water,  and,  if  the  gas  is  impure, 
sulphurous  acid  and  compounds  of  ammonia  will  be  added,  which. 


484 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


dissolving  in  the  watery  vapor,  condense  upon  and  corrode  furniture, 
books,  metallic  articles,  &c.  Every  pound  of  coal  gas  burned  produces 
2'7  Ibs.  of  water,  and  2'56  Ibs.  of  carbonic  acid;  and,  as  a  cubic  foot 
of  coal  gas  weighs  about  290  grains,  twenty  cubic  feet  will  weigh  a 
pound,  a  quantity  which  four  common  fish-tail  burners  consume  in  an 
hour.  The  capacity  of  air  for  moisture  at  68°,  is  7'31  grs.  per  cubic  foot. 
[t  would,  therefore,  require  2373  cubic  feet  of  air  at  68°  to  retain  the 
water  from  twenty  feet  of  gas,  and  nearly  five  times  as  much  at  20°  F., 
not  to  name  the  amount  required  to  dilute  the  carbonic  acid  and  free 
nitrogen  produced. 

It  is  needless  to  add,  that  the  ventilation  of  gas  burners  is  an  important 
matter.  Fortunately,  a  gas  chandelier  affords  one  of  the  best  means  of  pro- 
ducing an  upward  current  in  an  assembly  room.  Candles  and  oil  consume  more 
air,  a*nd,  of  course,  produce  more  effete  products  for  an  equal  amount  of  light 
than  gas. 

722.  The  actual  ventilation  of  buildings  is  a  practical  prob- 
lem, to  be  wrought  out  in  each  case,  with  careful  regard  to  the  prin- 
ciples and  facts  just  stated.    The  supply  of  air  required  may  be  obtained 
in  two  ways : — 1st,  by  the  ascending  column  of  heated  air  in  a  shaft, 
drawing  after  it  the  effete  air  to  be  removed,  and  supplying  its  place 
by  fresh  air,  warmed  in  its  progress  to  the  apartments.     This  is  called 
thermal  ventilation ;  or,  2d,  mechanical  force  may  be  508 
employed,  by  means  of  revolving  fan-wheels  driven  by 

a  steam-engine,  or  otherwise,  forcing  the  air  through 
the  apartments  to  be  warmed  and  ventilated.  This  is 
called  mechanical  ventilation. 

By  the  first  method,  Dr.  Reid  ventilated  the  House  of  Com- 
mons in  England.  By  the  second,  Mr.  Rice  ventilated  the 
House  of  Lords  with  a  fan-wheel,  over  thirty  feet  in  diameter. 

723.  Stone's  ventilating  shaft. — An  excellent  com- 
bination of  the  thermal  ventilation,  with  the  plan  of 
hot-air  furnaces,  so  generally  used  in  the  United  States, 
has  been  devised  by  S.  M.  Stone,  Architect,  which  has 
been  found  efficient  in  the  New  Haven  City  Prison,  the 
State    Reform    School,    and    other   similar    buildings. 
Fig.  508  shows  a  plan  and  section  of  this  system. 

A  ventilating  shaft  of  brick,  C,  rises  in  the  centre  of  the 
house,  through  the  axis  of  which  passes  a  cast-iron  smoke 
flue,  A,  carrying  off  the  waste  products  of  the  furnace.  The 
radiant  heat  of  this  iron  flue  heats  the  air  in  the  shaft  B. 
Openings,  D  and  D,  are  pierced  from  the  various  apartments 
into  this  shaft,  and  allow  the  air  of  the  rooms  free  opportunity 
of  escape,  solicited  by  the  powerful  ascending  draught  of  the  vertical  shaft. 
Distant  apartments  are  connected  with  the  shaft  by  horizontal  pipes  of  wood  or 


HEAT.  485 

tin.  The  openings,  D,  should  be  covered  with  wire  gauze,  and  fitted  with  Dr. 
Arnott's  self-acting  noiseless  valve,  which  allows  the  passage  of  an  upward  cur- 
rent only.  The  apartments  are  supposed  to  receive  their  supply  of  fresh  and 
warm  air  through  hot  air  flues,  ascending  in  the  walls.  In  summer  it  would  be 
found  needful  to  establish  a  current  in  the  shaft  by  an  occasional  fire  in  the 
furnace,  or  by  a  special  furnace  for  that  purpose  in  the  top  of  the  house.  In 
cities,  the  air  taken  into  buildings  may  be  strained  through  fine  wire  gauze  and 
spray  of  water,  as  was  accomplished  by  Dr.  Reid  in  the  House  of  Commons. 
By  the  rule  (717),  the  power  of  such  a  shaft  to  discharge  air  can  be  calculated. 

724  Cold  currents  produced  by  ice. — Refrigerators. — Air,  in 
contact  with  ice,  acquires,  of  course,  a  low  temperature,  and  parts  with 
a  large  part  of  its  moisture.  Thus,  snow-clad  mountains  and  glaciers 
naturally  send  down  to  the  valleys  below  a  current  of  cold  air,  flowing 
like  water  over  the  surface,  especially  at  night,  when  the  absence  of 
the  sun  prevents  the  accumulation  of  heat  on  the  earth's  surface. 

Adroit  use  has  been  made  of  this  cold  dry  current,  in  the  construction  of  re- 
frigerators for  preserving  food  in  warm  weather ;  and  the  same  principle  has 
been  applied,  on  a  large  scale,  to  the  cooling  of  large  apartments.  Figs.  509 
and  510  show  a  section  and  elevation  of  Winship's  Refrigerator.  The  ice,  A, 


510 


fig.  510,  is  sustained  upon  a  shelf  in  the  upper  part  of  the  box,  surrounded  with 
double  charcoal  linings.  The  air  enters  by  the  register  openings,  C,  and  coming 
in  contact  with  the  ice,  is  cooled,  and  falls  to  the  bottom,  as  indicated  by  the 
arrows,  where  it  finds  its  egress  at  E,  between  hollow  walls,  and  finally  escapes 
at  F,  as  in  an  inverted  syphon.  In  this  way  a  gentle  current  of  about  45°  F. 
is  steadily  maintained  as  long  as  the  ice  lasts,  and,  being  dry,  articles  of  food 
are  preserved  sweet  and  free  from  mould  for  a  long  time.  A  similar  device  baa 
been  used  for  large  apartments. 

725.  Cowls. — Emerson's  ventilators. — Advantage  is  taken  of  the 
currents  in  the  external  air,  to  aid  in  establishing  ventilation  in  houses, 
and  draught  in  chimneys,  by  the  use  of  ventilating  cowls. 

These  contrivances  are  often  conical,  and  hung  with  a  vane,  to  turn  against 
the  wind.  One  of  the  most  generally  approved,  however,  in  common  use,  appears 


486  PHYSICS    OF    IMPONDERABLE    AGENTS. 

to  be  the  ventilator  of  Emerson,  fig.  511,  which  is  simply  a  cone  of  metal,  sur- 
rounding the  flue,,  over  whose  vent,  and  a  short  distance  511 
above  it,  is  sustained  a  disc  of  metal.     If  the  wind  blows 
from  any  point,  its  effect,  on  striking  this  conical  surface,  is 
to  pass  upwards  and  across  the  open  flue,  with  an  increased 
velocity.     The  result  is  to  solicit  an  upward  current  in  the 
shaft,  as  shown  by  the  arrow,  in  the  figure. 

If  it  is  desired  to  direct  a  current  of  fresh  air  into  the 
shaft,  an  injecting  ventilator  is  used,  which  is  simply  the 
above  cone  inverted,  or  two  or  three  such  placed  one  over  the 
other.  These  are  found  very  efficient  in  projecting  fresh  air 
into  the  cabins  of  ships,  and  other  similar  situations. 

726.  The  supply  of  fresh  air  in  dwellings  is  de- 
rived, in  the  winter,  almost  exclusively  from  the  cracks 
and  joints  of  doors,  windows,  and  other  openings.     In 
all  good  systems  of  general  warming,  this  supply  is 
derived  from  the  open  air,  or  a  free  basement,  and  is 
warmed  in  its  progress  through  the  heating  apparatus. 
When  it  is  requisite  to  introduce  cold  air  into  a  house, 
it  is  important  to  do  so  in  such  a  manner  as  to  avoid 
local  and  sharp  currents ;  for  this  purpose,  perforated 

cornices,  or  openings  covered  by  wire  gauze,  are  provided.  A  too  rapid 
current  is  both  inconvenient  and  costly,  from  the  needless  waste  of  fuel. 
In  public  buildings,  the  supply  is  best  obtained  through  a  trench,  or  horizon- 
tal tube,  opening  into  a  clean  area,  and  protected  against  powerful  winds.  Tho 
injecting  cowl  may  be  advantageously  used  to  cover  the  opening  of  such  a  sup- 
ply. The  distribution  of  the  ascending  warm  current  is  best  made  through  a. 
hollow  or  double  floor,  perforated  with  numerous  openings,  while  the  spent  air 
is  taken  off  above,  as  already  described. 

II.     WARMING. 

727.  The  artificial  temperatures  demanded  in  cold  climates 
are  produced,  1st,  either  by  radiant  heat  solely,  as  in  the  common 
open  fire-place,  2d,  by  convection  only,  as  in  hot-air  furnaces  of  every 
description,  in  which  the  air  is  warmed  by  its  passage  through  a  heat- 
ing chamber,  and  then  introduced  into  the  apartments  to  be  warmed, — 
or  3d,  by  radiant  heat  and  convection  united,  as  in  stoves,  and  steam 
or  hot  water  pipes. 

728.  The  open  fire  contained  in  a  simple  brick  fire-place,  fig.  507, 
whether  coal  or  wood  is  burned,  warms  the  air  of  the  room  solely  by 
radiant  heat.     The  burning  fuel  solicits  the  air  of  the  apartment  to  be 
warmed  towards  the  chimney,  where,  coming  in  contact  with  the  fire,  it 
parts  with  a  portion  of  its  oxygen  to  sustain  combustion,  is  intensely 
heated,  and  rising,  escapes  at  the  flue,  with  the  heated  products  of  com- 
bustion. Hence  only  the  heat  radiated  from  the  burning  fuel  and  hot  walls, 
is  effectual  in  warming  the  apartment,  while  much  the  largest  part  of  the 
heat  (three-fourths  to  four  fifths  of  the  whole)  escapes  up  the  chimney. 


HEAT. 


487 


The  genial  effect  and  cheerful  aspect  of  an  open  fire,  combined  with  the  effi- 
cient means  of  ventilation  it  affords,  render  this  old  system  very  popular,  when 
combined  with  some  competent  general  plan  of  warming  the  whole  house. 

Dr.  Franklin  improved  the  common  fire-place  by  introducing  iron  stoves,  of 
the  same  general  form,  and  connecting  them  with  the  chimney  by  a  circuitous 
pipe,  by  which  means  a  much  better  economical  effect  was  attained.  Rumford 
improved  the  form  of  the  fire-place  very  much,  and  especially  with  reference  to  the 
throat  of  the  chimney  and  angle  of  the  jambs.  He  also  combined  it  with  a  circula- 
tion of  hot  air  behind  and  at  the  sides  of  the  fire,  so  as  to  obtain  the  effect  of  a  stove. 

Stoves  of  iron,  standing  in  the  apartment  to  be  warmed,  offer,  perhaps,  the 
most  economical  mode  for  burning  fuel — but  when,  as  is  too  often  the  case,  they 
are  closed  tight,  except  a  very  small  opening  for  draft,  they  are  among  the  vilest 
contrivances  in  use  for  the  ruin  of  the  public  health.  The  atmosphere  of  the 
room  unavoidably  becomes  over-heated  and  corrupted  by  the  products  of  respi- 
ration, in  the  almost  universal  absence  of  any  mode  of  ventilation. 

729.  Hot  air  furnaces. — Large  buildings  and  dwelling-houses  are 
frequently  warmed  by  air  heated  in  its  passage  through  a  structure  in 
the  lower  part  of  the  house.  One  of  512 

the  simplest  forms  of  apparatus  for 
this  purpose  is  seen  in  fig.  512,  being 
a  sectional  view  of  a  hot  air  furnace, 
in  which  the  cold  air  entering  at  A, 
passes,  as  indicated  by  the  arrows, 
through  an  extended  system  of  iron 
passages  set  in  brick  work  and  heated 
by  the  products  of  combustion,  and 
the  direct  action  of  the  fire,  F.  The 
heated  air  gains  the  apartment,  m, 
by  openings,  B,  in  the  floor  or  sides 
of  the  wall,  while  the  gases  of  com- 
bustion escape  by  the  flue,  0.  Such  an  apparatus  serves  only  to 
illustrate  the  general  principle,  and  would  prove  valueless  in  practice. 

Very  numerous  forms  of  hot-air  furnaces  are  in  use  in  the  United  States,  chiefly 
for  the  combustion  of  anthracite  coal.  They  are  essentially  alike  in  principle,  I  ut 
very  unlike  in  construction.  All  take  cool  air  from  with-  513 

out,  or  from  an  airy  basement,  and  after  heating  it  in  a 
brick  chamber,  by  contact  with  surfaces  of  hot  iron  sur- 
rounding the  fire,  and  conveying  away  the  products  of 
combustion,  distribute  it  by  flues  in  the  wall  to  the  several 
apartments.  Fig.  513  presents  a  sectional  view  of  one  of 
the  best  hot-air  furnaces  at  present  in  use  (Chilson's). 
The  fire  of  anthracite  is  contained  in  a  large  shallow  pot 
of  cast-iron,  with  soap-stone,  or  iron  staves,  and  the  heated 
products  of  combustion  are  expanded  in  an  extensive  sys- 
tem of  chambers  of  cast-iron,  all  communicating  with  an 
annular  cast-iron  pipe,  leading  to  the  chimney.  This 
arrangement  affords  a  very  extended  radiating  surface, 
with  few  joiuts,  to  allow  the  escape  of  noxious  gases  into  the  surrounding  hot- 
air  chamber.  The  arrows  indicate  the  direction  of  the  current. 


488  PHYSICS    OP    IMPONDERABLE    AGENTS. 

In  fig.  514  is  seen  the  furnace,  surrounded  in  the  brick  work,  which  is  hollow. 
The  cold  air  enters  at  the  bottom,  and  being  gently  heated  by  contact  with  the 
hot-air  surfaces  within  the  chamber,  as  well  as  by  the  514 

radiant  heat  from  the  same  source,  it  escapes  by  the 
openings,  o  n,  to  the  various  apartments.  The  extended 
iron  surface  in  this  apparatus  prevents  any  part  of  the 
furnace  from  becoming  very  hot,  usually  the  chief  causes 
of  complaint  against  this  mode  of  heating.  Air  is  inate- 
•ially  injured  for  purposes  of  respiration  by  contact  with 
Dver-heated  surfaces,  owing  to  the  charring  of  the  parti- 
pies  of  dust  and  dirt  always  floating  in  it.  The  chief 
objection  resting  against  this  and  similar  modes  of  heat- 
ing is  the  entire  absence  of  radiant  heat  in  the  apartments, 
whose  occupants  are,  so  to  speak,  immersed  in  a  warm 
air  bath,  and  require,  consequently,  several  degrees  more 
heat,  by  the  thermometer,  for  comfort,  than  when  radiant  heat  forms  a  part 
of  the  means  of  an  artificial  temperature. 

Hot-air  furnaces  are  commended  on  account  of  their  economy  of 
construction,  and  ease  of  management,  and  when  combined  with  a 
good  system  of  ventilation,  such  as  is  secured  by  an  open  fire  in  one 
or  more  apartments,  the  objections  to  them  are  in  great  measure 
removed. 

730.  Heating   by  hot  water,   distributed  in   pipes,   offers  many 
advantages  for  the  salutary  and  economical  distribution  of  heat.     The 
high  specific  heat  of  water  (653),  enables  it  to  heat  over  three  thousand 
times  its  own  bulk  of  air  in  cooling  through  a  single  degree  of  tempe- 
rature.    That  is,  one  cubic  foot  of  water,  by  cooling  one  degree,  will 
raise  the  temperature  of  3419  cubic  feet  of  air  a  like  amount;   for 
0-2379  :  1  =  813-435  :  3419.     In  this  proportion  the  specific  heat  of 
air  is  the  first  term,  and  the  third  term  is  the  bulk  of  air  equal  to  a 
unit  weight  of  water.     As  hot  water  is  usually  distributed  in  cast-iron 
pipes,  experiments  have  been  made  upon  the  rate  of  cooling  of  these 
pipes,  which  show  that  one  foot  in  length  of  pipe  four  inches  in  diameter, 
will  heat  222  cubic  feet  of  air  one  degree  per  minute,  when  the  differ- 
ence between  the  temperature  of  the  air  and  the  pipe  is  125°.     The 
advantage  of  hot  water  as  a  means  of  heating,  depends  much  on  its 
high  capacity  for  heat,  and  its  slow  rate  of  cooling,  by  which  the  tem- 
perature declines  very  slowly,  after  the  fire  is  extinguished. 

For  horticultural  and  manufacturing  structures,  and  other  buildings  where 
large  pipes  are  not  an  objection,  it  has  prominent  claims.  In  private  houses, 
where  the  hot  water  pipes  occupy  a  chamber  in  the  basement,  and  the  air  is 
heated  by  passing  among  them,  all  advantage  of  the  radiant  heat  is  lost,  and 
the  apparatus  becomes  comparatively  inefficient,  and  very  costly,  if  a  sufficient 
number  of  pipes  are  laid  in  to  do  the  work. 

731.  Perkins'  high  pressure  hot  water  apparatus. — The  system 
just  named  uses  \vater  at  a  very  low  pressure,  ne^er  over  six  Ibs.  to  the 


HEAT. 


489 


square  inch.  Mr.  Perkins  has,  however,  patented  a  system,  in  which 
the  hot  water  is  distributed  in  very  small  iron  pipes,  under  enormous 
pressure. 

The  plan  of  this  system  is  seen  in  fig.  515.  A  coil  of  pipe,  S  (1  inch  outside 
and  i  inch  inside),  is  heated  by  the  fire,/.  The  rising  515 

pipe,  ttt,  is  carried  to  the  top  of  the  circulation, 
and  in  each  story  or  apartment,  a  coil,  c'  c',  c  c,  dis- 
tributes the  heat,  the  water  returning  by  the  descend- 
ing pipe,  t'  t'  t',  as  indicated  by  the  arrows.  At  the 
highest  point  of  the  circulation  is  placed  a  ten  inch 
pipe,  called  the  "  expansion-pipe,"  fitted  with  a  cock 
for  the  escape  of  air,  and  the  admission  of  water.  A 
sufficient  void  is  left  to  accommodate  the  expansion 
of  the  water,  which  is  about  one-twelfth  the  whole 
bulk.  Thus  arranged,  the  temperature  of  the  pipes 
can  be  raised  to  any  required  degree — and  in  prac- 
tice it  varies  from  300°  to  550°— ?.  e.,  from  about  75 
Ibs.  to  about  675  Ibs.  to  the  square  inch.  No  safety 
valve  is  used  on  this  apparatus,  and  numerous  ex- 
plosions of  the  fire  coil  have  happened  with  its  use. 
The  high  temperature  of  the  pipes  endangers  build- 
ings, and  gives  to  the  air  heated  by  it  the  empyreu- 
matic,  burnt  odor,  which  is  so  objectionable  from 
cast-iron  stoves.  It  is  undoubtedly  more  efficient 
than  the  low  pressure  hot  water  system.  The  sys- 
tem of  high  pi*essure  steam  pipes  is  very  similar  to 
this,  and  equally  open  to  the  objection  of  over-heat- 
ing the  air,  and  endangering  buildings  from  fire. 

732.  Gold's  steam  heaters. — The  radiators. — In  this  system,  the 
heat  is  radiated  from  surfaces  of  japanned  sheetriron,  fastened  together 
by  rivets  at  the  bottom  of  concave  depressions  in  the  outer  sheet,  as 
seen  in  fig.  516.  This  arrangement  516 

divides  the  whole  steam  space  into 
numerous  communicating  cells,  as  seen 
in  the  cross  section,  D ;  the  steam  ar- 
rives from  the  boiler,  fig.  517,  under 
very  low  pressure  (one  pound  to  tin- 
inch),  by  the  inlet  cock,  A,  and  the  air 
escapes  at  an  outlet  cock  in  the  oppo- 
site corner  above.  The  water  of  con- 
densation returns  to  the  boiler  by  the  same  pipe  that  conveys  t!ie 
steam,  which  is  made  sufficiently  large  for  that  purpose. 

These  radiators  are  placed  in  the  apartments  to  be  heated,  either  singly  or  in 
groups  of  throe  or  four,  concealed  under  an  ornamental  screen  and  covered  with 
marble.  The  heat,  in  that  case,  is  both  radiant  heat  and  heat  of  convection. 
The  radiators  may  also  be  confined  in  a  space  below  the  apartments,  and  the 
air  to  be  wanned  passed  through  or  among  them,  in  which  ca,se  only  heat  of 
conve  'tion  reaches  the  apartments,  as  in  the  common  hot-air  furnaces.  This 

44 


490 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


517 


system  is  economical  of  fuel,  efficient  for  the  most  severe  weather,  and  when 
combined  with  a  proper  system  of  ventilation,  entirely  unexceptionable.  It  has 
the  great  merit  of  securing  exactly  the  desired  degree  of  heat  just  where  it  is 
wanted,  however  remote  from  the  boiler,  and  is,  by  means  of  the  air-cock, 
adjustable  to  any  temperature. 

733.  The  boiler  of  Gold's  steam  heater  is  pyfectly  automatic, 
and  is  a  beautiful  illustration  of  the  ease  with  which  so  powerful  an 
agent  as  steam  can  be  brought  under  entire  self-control  and  rendered 
quite  free  from  all  danger. 

Fig.  517  is  an  elevation  of  this  boiler,  set  for  use  in  its  masonry,  A.  The 
water  rises  in  the  tube,  J,  which  is  open  to  the  air,  to  counterpoise  the  pressure, 
which  is  adjusted  to  one  pound  on  the  inch.  J 
is  therefore  a  hydrostatic  balance.  The  lower 
ash  door,  C,  being  closed,  no  air  has  access  to 
the  fire  except  through  the  side  vent,  E.  This 
closes  by  a  conical  cover  at  the  end  of  a  chain, 
as  soon  as  the  limit  of  pressure  is  reached,  for 
then  the  lever,  F,  rises,  by  reason  of  the  water 
pressing  up  the  elastic  cover  of  F.  A  like  ar- 
rangement, G,  next  opens  the  upper  feed  door, 
C ;  if  the  fire  is  not  sufficiently  held  in  check  by 
F,  C  continues  to  open  until  sufficient  cold  air 
enters  the  flues  to  reduce  the  steam  to  its  limit 
and  hold  it  there.  The  safety  valve,  I,  is  like- 
wise under  the  control  of  a  similar  arrangement. 
II,  which  comes  into  action  after  F  and  G,  if 
needed.  K,  K,  are  the  steam-pipes  leading  to 
the  radiators,  and  the  smoke  reaches  the  chimney 
by  the  pipe,  R.  Such  nice  adjustments  secure  great  economy  of  fuel,  as  the 
combustion  cannot  proceed  faster  than  the  demands  of  the  radiators  require. 

§  12.  Sources  of  Heat. 

734.  Sources  of  heat. — Four  great  sources  of  heat  may  be  named : — 

1.  Mechanical  sources. — The  principal  of  these  are  friction,  compres- 
sion, and  percussion. 

2.  Physical  sources,  of  which  the  chief  are  solar  radiation,  stellar 
radiation,  terrestrial  radiation,  and  atmospheric  electricity. 

3.  Chemical  sources,  comprising  chemical  combinations,  the  chief  of 
these  being  combustion. 

4.  Physiological  sources,  comprising  the  production  of  heat  in  living 
beings.     This,  according  to  views  now  generally  received,  is  only  an 
extension  of  the  third  head. 

I.     MECHANICAL  SOURCES  OP  HEAT. 

735.  Friction. — When    two    bodies   are   rubbed   together,    heat   is 
generated  by  the  friction  of  their  surfaces.     The  supply  of  heat  from 
this  source   is   apparently  unlimited.     As   the    generation  of  heat  i* 


HEAT.  491 

unaccompanied  by  any  change  in  the  calorific  capacity  of  the  bodies, 
and  generally  by  no  chemical  action,  it  must  be  attributed  to  a  mole- 
cular movement  of  the  bodies  excited  by  friction. 

736.  Quantity  of  heat  produced  by  friction. — The  experiments 
of  Joule  show  that  the  amount  of  heat  developed  by  friction  depends 
3nly  on  the  amount  of  force  exerted,  and  not  upon  the  nature  of  the 
substances  rubbed  together. 

Count  E-umford  published  in  the  Royal  Philosophical  Transactions,  1798,  the 
results  of  some  of  his  experiments  upon  this  subject.  A  brass  cannon,  weighing 
113  Ibs.,  was  revolved  horizontally,  at  the  rate  of  32  revolutions  per  minute,  against 
a  blunt  steel  borer  with  a  pressure  of  10,000  Ibs.  In  half  an  hour  the  tempera- 
ture of  the  metal  had  risen  from  60°  to  130°  F.  This  heat  would  have  been 
sufficient  to  raise  the  temperature  of  5  Ibs.  of  water  from  32°  to  212°.  In  another 
experiment,  the  cannon  was  placed  in  a  vessel  of  water,  and  friction  applied  as 
before.  In  two  hours  and  a  half,  18|  Ibs.  of  water  actually  boiled.  The  heat 
generated  in  this  case  was  calculated  by  Rumford  to  be  at  least  equal  to  that 
given  out,  during  the  same  time,  by  the  burning  of  9  wax  candles,  f  inch  in 
diameter,  and  each  245  grains  in  weight.  A  remarkable  instance  of  the  excita- 
tion of  heat  by  friction  is  afforded  by  an  experiment  of  Sir  Humphrey  Davy,  in 
which  two  pieces  of  ice  rubbed  together  in  vacuo  at  a  temperature  below  32° 
were  melted  by  the  heat  developed  at  the  surfaces  of  contact. 

737.  Circumstances  which   vary   the    quantity   of  heat   de- 
veloped by  friction. — The  quantity  of  heat  developed   by  friction 
depends,  1st,  on  the  nature  and  state  of  the  surfaces  (138) ;  2d,  on  the 
pressure  ;  3d,  on  the  velocity. 

738.  Illustrations  and  application  of  the  heat  developed  by 
friction  are  of  frequent  occurrence  in  common  life. 

When  a  piece  of  steel  is  struck  by  a  flint,  particles  of  the  metal  are  torn  off, 
and  are  so  intensely  heated  as  to  ignite  in  the  air.  These  heated  particles  fall- 
ing upon  tinder  or  gunpowder  cause  it  to  burn.  Similar  sparks  often  fly  off 
from  the  iron  shoes  of  horses  as  they  strike  a  stone.  In  grinding  knives  and 
other  instruments  upon  a  dry  grindstone,  or  upon  an  emery  wheel,  a  brilliant 
train  of  sparks  is  produced.  Among  uncivilized  nations  fire  is  frequently  pro- 
duced by  the  friction  of  pieces  of  wood  against  each  other.  Seneca  relates  the 
same  fact,  and  adds  that  it  is  necessary  to  employ  particular  species  of  wood;  as, 
laurel  and  ivy. 

Sufficient  heat  is  caused  by  rubbing  a  match  on  a  rough  surface  to  ignite  the 
phosphorus  on  its  end.  The  axles  of  car  wheels,  and  other  parts  of  machinery, 
when  not  well  greased,  are  sometimes  heated  sufficiently  hot  to  cause  the  ignition 
of  the  surrounding  woodwork.  It  is  by  friction  that  the  brown  rings  sometimes 
seen  on  wooden  articles,  turned  in  a  lathe,  are  produced.  A  pointed  piece  of 
wood  is  held  against  the  rapidly  revolving  article,  the  heat  generated  by  the 
friction  is  sufficient  to  cause  the  wood  to  smoke  and  partially  char  it. 

In  a  few  instances  in  this  country  the  fall  of  water  has  been  used  to  produce 
friction,  and  thus  develop  heat.  In  the  state  of  Vermont,  plates  of  iron  were 
rapidly  revolved  against  each  other,  and,  by  the  beat  developed,  the  mill  was 
warmed.  The  thermogenic  apparatus  of  Messrs.  Beaumont  and  Mayer  (Am. 
Tour.  Sci.  [2]  XX.,  261)  is  a  most  successful  contrivance  for  converting  motion 


492  PHYSICS  OF  IMPONDERABLE  AGENTS. 

into  heat  by  means  of  friction,  and  where  there  is  abundant  and  cheap  water- 
power,  may  be  of  economical  importance  as  a  source  of  heat. 

739.  Compression. — When  any  substance  undergoes  a  diminution 
in  volume,  there  is  generally  a  development  of  heat.     The  evolution 
of  heat  by  compression  is  most  strikingly  seen  in  gases  which  undergo 
a  great  diminution  in  volume  by  pressure. 

The  condensing  syringe,  fig.  518,  is  an  admirable 
instrument  for  showing  the  phenomenon  referred  to. 
It  consists  of  a  metal  or  glass  tube  closed  at  one 
extremity.  Into  the  other  extremity  fits  tightly  a 
piston  which  has  a  bit  of  tinder  on  its  end.  When 
the  piston  is  forcibly  driven  into  the  cylinder,  the 
compression  of  the  air  develops  so  much  heat  that 
the  tinder  becomes  ignited. 

Owing  to  the  small  compressibility  of  liquid?, 
and  their  great  capacity  for  heat,  it  is  not  easy  to 
determine  the  heat  developed  in  them  by  compres- 
sion. Messrs.  Colladon  and  Sturm  have  obtained, 
with  certain  liquids,  at  a  pressure  of  30  atmospheres, 
an  elevation  of  temperature  of  as  much  as  from  7° 
to  10°  F.  The  heat  generated  by  the  compression 
of  solids  may  better  be  considered  as  by  percussion. 

740.  Percussion  is  a  combination  of  fric- 
tion and  compression,  and  is  an  active   me- 
chanical source  of  heat.    The  amount  of  heat 
developed  by  percussion  seems  to  depend  to  a 
great  extent  on  the  diminution  in  bulk  which 
the  body  struck  undergoes. 

This  is  strikingly  shown  by  an  experiment  of 
Berthollet,  in  which  a  piece  of  copper  was  sub- 
mitted to  the  action  of  a  stamping-press.  The  greatest  development  of  heat 
occurred  with  the  first  blow,  where  the  metal  underwent  the  greatest  diminution 
in  bulk,  and  diminished  with  the  succeeding  blows  as  did  the  amount  of  con- 
densation. The  quantities  of  heat  evolved  at  the  first  three  strokes  were  17°-3, 
7°-5,  and  l°-9  F. 

741.  Capillarity.— Pouillet  has  shown  that  the  simple  act  of  moist- 
ening any  dry  substance  is  attended  with  a  slight,  yet  constant,  disen- 
gagement of  heat. 

Pouillet  operated  on  the  powdered  metals,  the  insoluble  oxyds,  glass,  brick, 
clay,  &a.  The  liquids  used  were  water,  alcohol,  ether,  acetic  acid,  turpentine,  &c. 
The  rise  in  temperature  was  only  from  5°  to  2°  F.  It  appears  to  be  independent 
of  the  nature  of  the  body.  Organic  bodies  of  various  kinds  were  operated  upon  ; 
as,  flax,  wool,  silk,  starch,  wood,  sponge,  ivory,  horn,  &c.  :  with  these  there  is  a 
rise  in  temperature  of  from  3°  to  18°  F. 

These  results  cannot  be  attributed  to  chemical  action,  for  the  different  liquids 
produced  the  same  heat  when  they  were  absorbed  by  the  same  porous  body. 

The  development  of  heat  in  these  cases  is  attributed  to  the  condensa- 


HEAT.  493 

tion  of  the  liquid  on  the  surface  of  the  solid  which  it  moistens.  It  may 
also  be  due  in  part  to  the  effect  of  the  friction  of  the  liquid  molecules 
upon  those  of  the  solid,  as  they  move  into  their  position  of  equilibrium. 

II.     PHYSICAL  SOURCES  OF  HEAT. 

742.  The  suri  is  the  most  abundant  source  of  heat  to  our  globe.   Its 
distance  from  the  earth  is  95,000,000  of  miles.     The  diameter  of  the 
sun  is  about  888,000  miles,  or  about  111  times  that  of  the  earth,  con- 
sequently its  volume  is  1,400,000  times  the  earth's  volume.     The  sun 
turns  on  its  axis  once  in  about  25  days.     Philosophers  are  divided  as 
to  the  cause  of  the  immense  amount  of  heat  which  escapes  from  this 
body. 

It  is  conjectured  that  there  are  three  atmospheric  strata  about  the  sun.  That 
nearest  his  surface  is  called  the  cloudy  stratum.  It  is  incapable  of  reflecting 
light,  and  is  heavily  loaded  with  vapors.  The  next  in  elevation  is  thought  to 
consist  of  an  intensely  luminous  medium.  To  this  is  attributed  the  diffusion  of 
light  and  heat.  Beyond  this  there  probably  exists  a  third  envelope  of  a  trans- 
parent gaseous  nature. 

Dark  spots  are  often  seen  on  the  sun's  surface  (by  the  aid  of  a  telescope). 
These  are  of  immense  size,  and  often  rapidly  change  their  form.  One  noted  by 
Sir  John  Herschel  contained  an  area  of  400,000,000  square  miles.  These  spots 
are  supposed  to  be  formed  by  the  opening  and  dispersion  of  the  stratum  of  lumi- 
nous clouds,  revealing  the  dark  mass  within. 

743.  Quantity  of  heat  emitted  by  the  sun. — Pouillet,  by  means 
of  an  instrument  called  a  pyrheliometer,  has  made  observations  from 
which  he  estimated  that  the  amount  of  heat  annually  received  by  the 
earth  from  the  sun,  would  be  sufficient  to  melt  a  crust  of  ice  surround- 
ing the  earth  101  feet  thick.     The  atmosphere  absorbs  nearly  40  per 
cent,  of  the  heat  of  the  sun's  rays. 

From  the  size  of  the  earth,  and  its  distance  from  the  sun,  it  has  been  deter- 
mined that  the  entire  amount  of  heat  emitted  by  the  sun,  is  2,381,000,000  times 
as  great  as  the  heat  which  it  gives  to  the  earth  ;  and  it  is  calculated  that  the 
intensity  of  heat  at  the  surface  of  the  sun,  is  seven  times  as  great  as  the  heat 
of  an  ordinary  blast  furnace. 

The  fixed  stars,  the  suns  of  other  systems,  notwithstanding  their  great  dis- 
tance, exert  a  very  important  influence  upon  the  temperature  of  the  earth.  It- 
has  been  estimated  that  they  furnish  to  our  earth  four-fifths  as  much  heat  as 
the  sun  ;  and  that,  without  this  addition  to  the  sun's  heat,  neither  animal  nor 
vegetable  life  could  exist  upon  the  earth. 

744.  Extremes  of  natural  temperature. — Captain  Parry,  in  1819, 
found  at  Melville  Island,  a  temperature  of — 59°  F.,  and  Captain  Black, 
at  Fort  Reliance,  at  60°  46'  N.  latitude,  observed  a  temperature  of 
— 70°  F.    Dr.  Azariah  Smith  records  the  extreme  heat  at  Mosul,  West- 
ern Asia,  in  1844,  as  114°  F.    (Am.  Jour.  Sci.  [2]  ii.,  75.)    At  Bagdad, 
in  1819,  the  thermometer  rose  to  120°  F.  in  the  shade.     In  the  sun,  at 

44* 


494  PHYSICS    OF    IMPONDERABLE    AGENTS. 

Mosul,  near  the  site  of  the  ancient  Nineveh,  Dr.  Smith  records  the 
summer  temperature  at  146°  F.  This  is  probably  the  highest  natural 
temperature  authentically  recorded.  Thus,  the  extreme  range  of  natural 
temperature  observed  is  2060>46  -F.  In  this  latitude,  between  summer 
and  winter,  there  is  often  a  difference  of  110°  F.,  and  in  the  shade, 
comparing  the  temperature  in  the  sun  of  summer,  there  would  be  an 
increase  of  at  least  30°. 

745.  Terrestrial  radiation. — The  heat  which  the  earth  receives 
from  the  sun,  does  not  penetrate  more  than  from  50  to  100  feet.     At 
Paris,  this  stratum  (called  the  first  stratum  of  invariable  temperature) 
is  found  at  a  depth  of  86  feet.     Descending  into  the  earth,  below  the 
point  of  constant  temperature,  there  is  a  gradual  and  regular  increase 
of  temperature.     The  amount  of  this  increase  is  about  1°'8  for  every 
hundred  feet  of  descent. 

Observations  on  this  point  have  been  extensively  made  in  deep  mines  and 
Artesian  wells,  and  always  with  a  nearly  constant  result.  The  variations  un- 
doubtedly arising  from  the  nature  of  the  soil,  and  its  conductibility  for  heat. 
Water  from  Artesian  wells  has  always  a  higher  temperature  than  surface  water. 
Thus,  the  water  arising  in  the  Grenelle  Artesian  Well  near  Paris,  from  a  depth 
of  about  2100  feet,  has  a  temperature  of  86°  F.  At  Neusalzwerke,  in  Westpha- 
lia, is  a  well  2200  feet  deep.  The  water  rasing  from  it  has  a  temperature  of 
91°  F.  Compare  g  204. 

Assuming  the  ratio  given  above  for  the  increase  in  temperature  as  we  descend 
into  the  earth,  at  the  depth  of  two  miles  water  would  boil ;  at  about  23  miles, 
or  only  T£ff  of  the  earth's  radius,  there  would  be  a  temperature  of  2200°  F. 
At  this  temperature  cast-iron  melts  in  the  open  air,  and  trap,  basalt,  obsidian, 
and  some  other  rocks,  become  perfectly  fluid.  But,  as  Pouillet  observes,  the 
enormous  compression  produced  by  the  weight  of  the  upper  strata  resting  upon 
the  lower  portions  of  the  earth's  crust,  raises  the  point  of  fusion,  so  that  the 
point  of  perfect  or  partial  fluidity  is  carried  far  lower  than  a  direct  ratio  would 
give  ]  but,  with  due  allowance  for  the  effect  of  pressure  upon  the  temperature 
of  fusion,  the  thickness  of  the  earth's  crust  cannot  be  supposed  to  exceed  one 
hundred  miles. 

746.  Origin  of  terrestrial  heat. — Numerous  theories  have  been 
advanced  to  account  for  terrestrial  heat.     Some  attribute  the  heat  to 
local  chemical  action.     Thus,  Boyle  explained  it  by  the  decomposition 
of  pyrites — a  view  no  longer  esteemed  tenable.     The  belief  in  a  cen- 
tral fire  within  the  earth,  now  generally  entertained,  is  found  in  the 
mythology  of  many  nations,  originating,  most  likely,  in  observation 
of  volcanic  fires.     For  evidence  that  the  earth  was  once  a  fluid  mass, 
see  \\  91  and  102.     This  question  is  of  the  highest  geological  interest, 
and  its  discussion  must  be  referred  to  treatises  on  that  science. 

747.  Atmospheric  electricity. — Another  source  of  heat  is  atmo- 
spheric electricity,  the  origin  of  which  is,  at  present,  shrouded  in  mys- 
tery.    The  more  usual  form  in  which  its  calorific  powers  are  presented 


HEAT.  495 

to  us,  is  seen  in  the  effects  of  a  powerful  flash  of  lightnii  g,  which  not 
unfrequently  fuses  metals  arid  earthy  matter  with  which  it  comes  in 
contact. 

III.    CHEMICAL  SOURCES  OF  HEAT. 

748.  Chemical  combination. — When  two  substances  enter  into 
chemical  combination,  there  is  generally  an  elevation  of  temperature, 
but  sometimes  also  a  depression. 

Where  there  is  a  slow  and  gradual  chemical  combination,  the  development  of 
beat  cannot  always  be  appreciated.  The  same  amount  of  heat  is  developed  as 
if  the  combination  took  place  quickly,  but,  being  extended  over  a  greater  time, 
it  is  inappreciable  at  any  single  moment,  and  cannot  be  accurately  measured. 

Chemical  combination  sometimes  takes  place  at  the  ordinary  temperature ; 
but  it  is  often  necessary  to  heat  the  bodies  before  they  will  unite.  An  example 
of  the  first  class,  is  the  mixture  of  sulphuric  acid  with  water,  or  the  slaking  of 
burnt  lime, — in  both  cases  a  large  amount  of  heat  is  developed.  As  examples 
of  the  second  class,  are  wood,  sulphur,  and  phosphorus,  which  do  not  inflame 
at  the  ordinary  temperature. 

749.  Combustion. — When  the  heat  developed  by  the  chemical  com- 
bination of  two  bodies  produces  luminosity,  the  bodies  are  said  to  burn, 
and  the  phenomenon  is  called  combustion.    If  one  of  the  bodies  burning 
is  solid,  it  is  called  fire ;  if  gaseous,  flame.     As  bodies  are  usually 
burned  in  the  atmospheric  air,  the  term  combustion  has  come  to  be 
restricted,  in  a  popular  sense,  to  the  union  of  bodies  with  oxygen, 
developing  light  and  heat. 

In  a  chemical  sense,  however,  the  term  combustion  has  a  wider  range,  and 
refers,  generally,  to  chemical  union,  even  when  the  bodies  combining  together 
do  not  evolve  either  light  or  sensible  heat.  Thus,  iron  slowly  rusts  or  oxydizes 
in  the  air,  wood  gradually  decays ;  these,  to  the  chemist,  are  as  truly  cases  of 
combustion,  as  those  more  rapid  combinations  with  oxygen,  which  are  accom- 
panied by  the  splendid  evolution  of  light  and  heat. 

750.  On  the  cause  of  the  heat  generated  by  combustion,  there 
is  a  great  diversity  of  opinion.     According  to  the  dynamical  theory  of 
heat,  it  is  the  vibratory  motion  of  the  constituent  atoms  of  the  bodies, 
as  they  combine  together,  that  produces  the  rise  in  temperature. 

When  the  state  of  aggregation  of  one  or  both  of  the  bodies  combining 
is  changed,  the  heat  which  was  latent  becomes  sensible  ;  or  if  there  is 
a  depression  of  temperature,  as  is  sometimes  the  case,  a  portion  of  the 
sensible  heat  becomes  latent.  When  there  is  no  change  in  the  state 
of  aggregation  of  the  bodies  combining,  it  is  explained  by  the  specific 
heat  of  the  compound  being  less  or  greater,  according  as  there  is  a 
depression  or  elevation  of  temperature. 

751.  The  amount  of  heat  developed  by  chemical  action,  is  of 
freat  practical  importance,  and  has,  for  a  long  time,  engaged  the  atten- 
tion of  physicists.     The  first  experiments  upon  this  subject  were  made 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


in  1790,  by  Lavoisier  and  Laplace,  by  means  of  their  ice  calorimeter. 
Count  Rumford,  in  1814,  Welter,  in  1822,  and  Despretz,  in  1823,  are 
among  those  who  have  contributed  valuable  researches  upon  this  subject. 
Compare  §715.  The  most  elaborate  series  of  experiments  upon  this 
subject,  was  made  by  Favre  and  Silbermann,  in  1844 ;  a  portion  of 
their  results  is  found  below. 

The  thermal  unit  is  the  heat  necessary  to  raise  a  weight  of  water, 
equal  to  that  of  the  combustible,  one  degree  of  the  scale  of  Fahrenheit's 
thermometer. 

HEAT  DEVELOPED  BY  BURNING  DIFFERENT   SUBSTANCES  WITH  OXYGEN. 


Names  of  substances. 

Formulae. 

Quantity   of  heat  emitted 
by  one  of  the  combustibles. 

62031 

Oxyd  of  carbon   .... 
Marsh  gas  .          ... 

CO 
CoJL 

4325 
23513 

Wood  charcoal     .... 
Natural  graphite 

14544 
14006 
14184 

4032 

Olefiant  gas     ...          . 

C,IL 

21344 

Good  coal                   .     . 

10800 

Sulphuric  ether   .... 
Wood  spirit     

C4H50 
CoELO., 

16248 
9552 

Alcohol  .     . 

C    W     On 

12931 

Stearic  acid     
Acetic  ether 

c^o, 

CaHfiO., 

17676 
11326 

Beeswax 

18892 

Essence  of  turpentine  . 
Dry  wood  .     . 

C^HU 

19533 
6480 

Peat 

4860 

i 

The  quantity  of  heat  disengaged  during  the  combustion  of  an  elementary 
body,  is  the  same,  whether  it  attains  at  once  its  maximum  of  oxydation,  or  at  a 
number  of  times. 

Thus,  carbon  disengages  a  certain  amount  of  heat  during  its  conversion  into 
carbonic  acid.  The  same  amount  of  heat  is  evolved  when  it  is  first  converted 
into  carbonic  oxyd  and  afterwards  burned  to  convert  it  into  carbonic  acid. 

752.  The  pyrometrical  heating  effect  of  a  substance,  is  the 
intensity  of  the  heat  evolved  during  its  combustion.  This  varies  much 
with  different  substances,  and  depends  not  only  on  their  composition, 
but  also  on  their  state  of  aggregation.  The  conclusions  of  an  economic 
character  derived  from  this  subject,  are  as  follows : — 

1st.  The  pyrometrical  healing  power  of  carbon  is  greater,  and  that  of 
hydrogen  smaller,  than  those  of  any  other  combustible. 

2d.  The  pyrometrical  heating  power  of  the  ordinary  fuels,  composed 


HEAT. 


497 


of  carbon  and  hydrogen,  is  greater  in  proportion  to  the  amount  of  carbon 
they  contain. 

3d..  The  pyrometrical  heating  powers  of  different  fuels  are  much  greater 
in  oxygen  than  in  air.  Thus,  between  carbon  and  hydrogen  burned  in 
oxygen,  there  is  a  difference  of  12,000°  F.,  in  air  only  1500°  F. 

753.  Relative  value  of  fuel. — In  the  following  table  is  given  the 
absolute,  specific,  and  pyrometrical  heating  effects  of  different  combus- 
tibles :— 

TABLE  SHOWING  THE    HEATING   EFFECTS    OF    DIFFERENT  BODIES  BURNED  IN 

AIR. 


Heating  effect. 

Absolute. 

Specific. 

Pyrometrical. 

0-23 

0-0077 

2900° 

Gaseous  combustibles  .     . 
Vegetable  oils,  <fec.  .     .     . 
Sulphuric  ether  .... 
Wood          .          .     . 

0-80—025 
1-15—122 
1-02 
0-36  —  0-47 

0.00010—0-00027 
0-30 
0-21 
0-14  —  0-28 

1850—1150° 
1575  —  1750° 

Peat 

0-37     0-65 

1575     2000° 

Lignite  
Bituminous   coal  (5  p.  c. 
water,  5  p.  c.  ash.)    .     . 
Peat  charcoal      .... 
Wood  charcoal    .... 
Coke  (not  more  than  5  p. 
c.  ash.)    

0-43—0-85 

0-79—0-96 
0.33—0-85 
0-64—0-97 

0-84—0-97 

1-06—1.44 
0-10—0-20 
0-38—0-46 

1800—2200° 

2200—2350° 
2050—2350° 
2100—2450° 

2350—2450° 

The  lighter  woods  burn  more  quickly,  with  a  greater  flame,  and  more  intense 
bent  than  the  more  dense  woods.  The  amount  and  intensity  of  the  heat  from 
the  different  fuels  depends,  to  a  great  extent,  on  their  state  of  dryness. 

754.  Combinations  in  the  humid  way. — Messrs.  Hess,  AndreAvs, 
and  Graham  have  made  important  researches  upon  the  heat  evolved  in 
combinations  in  the   humid  way.      Their   principal   results   may  be 
summed  up  as  follows  : — 

1st.  Equivalents  of  the  different  acids  combining  with  the  same  base, 
produce  the  same  quantity  of  heat. 

2d.  Equivalents  of  the  different  bases  combining  with  the  same  acid, 
produce  different  quantities  of  heat :  generally  the  more  energetic  bases 
disengaging  the  most  heat. 

3d.  When  a  neutral  salt  is  converted  into  an  acid  salt,  there  is  no  dis- 
engagement of  heat. 

4th.  When  a  neutral  salt  is  converted  into  a  basic  salt,  there  is  a  dis- 
engagement of  heat. 

755.  Animal  heat ;  warm  and  cold-blooded  animals. — The  tem- 
perature of  organized  beings  is  seldom  that  of  the  medium  which  sur- 


498  PHYSICS    OF    IMPONDERABLE    AGENTS. 

rounds  them.     There  is  within  the  living  body  a  series  of  chemical 
actions  taking  place,  and  these  are  sources  of  heat. 

In  warm-blooded  animals,  as  the  mammifers  and  birds,  the  heat  produced  at 
each  instant  compensates  for  that  lost  from  the  exterior,  and  thus  the  body  is 
kept  at  a  uniform  temperature.  In  cold-blooded  animals,  as  reptiles,  fishes,  and 
mollusca,  heat  is  also  generated,  but  so  slowly,  that  their  temperature  is  but  a 
very  few  degrees  a.bovo  that  of  the  surrounding  medium,  and  often  is  only 
equal  to  it. 

756.  The  cause  of  animal  heat,  it  has  long  been  conjectured,  was 
the  chemical  action  taking  place  within  the  body. 

Crawford  appears  to  have  been  the  first  to  advance  the  doctrine  that  respira- 
tion was  the  cause  of  animal  heat.  Lavoisier  supposed  that  the  air  underwent 
in  the  lungs  a  real  combustion ;  its  oxygen  combining  with  the  carbon  and 
hydrogen  of  the  blood,  forming  carbonic  acid  and  the  vapor  of  water.  The 
lungs,  according  to  this  view,  were  the  furnaces,  the  arterial  blood  carrying 
the  heat  developed  by  the  combustion  into  all  parts  of  the  body.  This  view  of 
Lavoisier  has  been  essentially  modified.  A  new  theory,  founded  upon  the  re- 
searches of  Spallanzani  and  Magnus,  is  now  generally  received.  They  deter- 
mined that  the  arterial  blood  contained  a  large  quantity  of  oxygen,  and  the 
venous  blood  a  large  quantity  of  carbonic  acid.  It  has  been  concluded  that  the 
venous  blood  reaches  the  lungs  loaded  with  carbonic  acid,  which,  by  endosmose, 
traverses  the  humid  walls  of  the  pulmonary  cells,  and  passes  into  the  air.  Car- 
bonic acid  is  thus  exhaled,  and  oxygen  is  absorbed.  Becoming  then  arterial 
blood,  the  blood  is  forced  through  the  arteries  into  the  capillaries  of  the  differ- 
ent organs,  where  a  more  or  less  considerable  combustion  of  carbon  takes  place. 

It  has  not  as  yet  been  demonstrated,  that  the  hydrogen  of  the  blood  combines 
with  the  oxygen  of  the  air.  Indeed,  most  physiologists  think  that  the  vapor 
of  water  exhaled  in  respiration,  is  simply  an  evaporation  from  the  lungs. 

757.  Temperature  of  vegetables. — As  the  plant  is  the  seat  of 
numerous  chemical  actions,  so  also  it  is  a  source  of  heat.     The  tem- 
perature of  plants  is,  in  general,  from  00-9  to  1°*1  higher  than  that  of 
the  surrounding  air.     In  a  few  exceptional  cases,  it  is  much  higher. 
Thus,  the  Arum  cardifolium  of  the  Isle  of  France,  at  the  time  of  blos^ 
soming,  reaches  a  temperature  of  120°-2  F.,  while  that  of  the  air  is 
about  67°.     Plants  attain  their  highest  and  lowest  temperatures  some 
hours  later  than  the  maxima  and  minima  of  daily  temperature. 

g  13.  Correlation  of  Physical  Forces. 

I.     MECHANICAL  EQUIVALENT  OF  HEAT. 

758.  Relations  of  heat  and  force. — It  is  well  known  that  there  is 
an  intimate  relation  between  heat  and  mechanical  force,  and  that  one 
may  be  exchanged  for  the  other.     A  given  quantity  of  one  may  be 
converted  into  a  determinate  quantity  of  the  other,  as  is  shown  in  the 
case  of  the  steam-engine,  and  in  the  production  of  heat  by  mechanical 
means  (§§735- -741). 


HEAT.  499 

759.  Unit  of  measurement,  the  foot-pound. — In  the  experiments 
upon  the  mechanical  equivalent  of  heat,  the  unit  adopted  in  England 
and  in  this  country,  is  the  foot-pound,  or  the  mechanical  force  expended 
in  raising  a  pound  weight,  one  foot  high  (714).     In  France  and  other 
European  eountries,-the  unit  adopted  is  the  mechanical  force  expended 
in  raising  one  kilogramme  (2'2046  Ibs.)  one  metre  (39*37  in.)  high. 

760.  Determination  of  the  mechanical  equivalent  of  heat. — 
According  to  the  Dynamical  Theory  of  Heat,  the  mechanical  equivalent 
of  heat  is  independent  of  the  nature  of  the  body  by  whose  agency  the 
transformation  of  mechanical  force  into  heat  is  effected  ;  hence  the  same 
result  should  be  arrived  at,  whatever  course  of  experiment  is  adopted. 
Mr.  J.  P.  Joule,  of  Manchester,  England,  has  made  the  most  exact 
determination  of  the  mechanical  equivalent  of  heat  in  a  series  of  very 
careful  and  elaborate  experiments,  conducted  between  the  years  1840 
and  1843.*     He  determined  the  mechanical  equivalent  of  heat  in  a 
number  of  ways,  reversing  the  question,  and  determining  the  amount 
of  heat  produced  by  a  certain  expenditure  of  mechanical  force. 

One  method  was  by  the  compression  of  gases ;  compressing  air  with 
a  great  force  in  a  copper  receiver ;  in  one  series  of  experiments  filled 
with  air  only,  and  in  another  with  water.  The  whole  apparatus  was 
placed  in  the  water  of  a  calorimeter,  whose  temperature,  before  and 
after  the  experiment,  was  carefully  determined. 

The  heat  developed  by  the  friction  of  water  and  of  oil,  was  determined  in  an 
apparatus  consisting  of  a  brass  paddle-wheel,  fig.  519,  having  revolving  arms, 
b,  g,  working  between  stationary  vanes,  c,  f.  This  wheel  519 

was  made  to  revolve  by  the  descent  of  a  known  weight, 
and  thus  the  mechanical  force  exerted  was  determined.  A 
similar  apparatus,  of  smaller  size,  and  made  of  iron,  was 
used  for  experiments  on  mercury.  In  all  cases,  the  appa- 
ratus was  placed  in  a  metallic  vessel  filled  with  the  liquid, 
and  the  temperature  noted  before  and  after  the  experiment. 

In  his  experiments  on  the  friction  of  solids,  Mr.  Joule 
used  an  apparatus  consisting  of  a  vertical  axis,  which 
carried  a  beveled  cast-iron  wheel,  against  which  a  fixed 
cast-iron  wheel  was  pressed  by  a  lever.  The  whole  was 
plunged  jn  an  iron  vessel  filled  with  mercury,  the  axis 
passing  through  a  hole  in  the  lid.  In  all  of  these  experi- 
ments, the  temperatures  were  noted  by  thermometers,  which  indicated  a  varia- 
tion of  temperature  of  the  one  two-hundredth  of  a  degree  F. 

761.  Results  of  Joule's  experiments. — In  the  following  table  ate 
given  the  most  important  results  obtained  by  Mr.  Joule.     The  second 
column  gives  the  results  obtained  in  air,  the  thirri  column,  the  same 
results  corrected  for  a  vacuum. 


Phil.  Trans.  1850,  p.  61. 


500 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


FORCE  REQUIRED  TO  HEAT  ONE  POUND  OP  WATER  1°  F. 


Material  employed. 

Equivalent  (in  foot- 
pounds) in  air. 

Equivalent  in 
vacuo.                            Mean- 

Water,  .     .     . 

773:640 

772-692 

772-692 

Mercury,     .     . 

773-762 
776303 

772-814  1 
775-352  } 

774-083 

Cast-iron,   .     . 

776-997 
774-880 

776  045  I 
773930  J 

774-987 

Conclusions  deduced  from  Joule's  experiments. — 1.  Tkc  quan- 
tity of  heat  produced  by  the  friction  of  bodies  is  always  proportional  to 
the  force  employed. 

2.  The  quantity  of  heat  capable  of  increasing  the  temperature  of  one 
pound  of  water  (weighed  in  vacuo,  and  between  55°  and  60°)  by  1°  F., 
requires,  for  its  evolution,  the  expenditure  of  a  mechanical  force  repre- 
sented by  the  fall  of  772  Ibs.  through  the  space  of  one  foot. 

Consequently  a  force  of  one  horse  power  (714)  would  raise  42  7  Ibs.  of  water 
1°  F.  each  minute,  and  would  bring  it  to  boil  from  60°  in  two  and  a  half  hours. 
Prof.  Thomson  (Phil.  Mag.,  Feb.  1854)  says,  it  is  mathematically  demonstrated 
from  the  dynamical  theory  of  heat,  that  any  substance  may  be  heated  30°  F. 
above  the  atmospheric  temperature,  by  means  of  a  properly  contrived  machine 
driven  by  an  agent,  spending  not  more  than  one  thirty-fifth  of  the  energy  of  the 
heat  communicated,  and  that  a  corresponding  machine,  or  the  same  machine 
worked  backwards,  may  be  employed  to  produce  cooling  effects. 

When  a  body  is  heated  by  such  means,  ff  of  the  heat  is  drawn  from 
surrounding  objects,  and  -fa  is  produced  by  the  action  of  the  agent. 

II.     DYNAMICAL  THEORY  OF  HEAT. 

762.  The  dynamical  theory  of  heat,  which  rests  upon  the  suppo- 
sition that  heat  is  motion,  or  the  result  of  motion,  is  founded  upon  the 
constant  relation  which  exists  between  heat  and  mechanical  force. 

763.  Motions  of  the  molecules. — In  this  theory  it  is  assumed 
that  the  particles  of  all  bodies  are  in  constant  motion,  and  it  is  this 
motion  which  constitutes  heat ;  the  kind  and  quantity  of  the  motion 
varying  with  the  solid,  liquid,  or  gaseous  state  of  the  body. 

Thus  in  solids,  it  may  be  assumed  that  the  molecules  are  continualfy  oscilla- 
ting about  their  position  of  equilibrium.  This  motion  may  be  vibration  of  the 
constituent  atoms  of  a  molecule,  or  of  the  entire  molecule,  and  may  be  rectilinear 
or  rotary. 

In  liquids,  the  molecules  have  no  constant  position  of  equilibrium,  the  repul- 
sive and  attractive  forces  being  nearly  equalized.  The  movements  of  the  liquid 
molecules  may  therefore  be  either  vibratory,  rotary,  or  progressive. 

In  gases,  the  repulsive  force  predominating,  the  molecules  move  onward  in 
straight  lines. 

764.  Changes   in   the  state  or  volume  of  bodies. — This  view 


HEAT.  501 

explains  the  production  and  consumption  of  heat,  which  accompany 
changes  of  state  or  volume  in  bodies.  The  work  performed  is  partly 
internal  and  partly  external. 

Thus  when  a  solid  is  melted,  there  is  an  internal  work,  employed  in  changing 
the  relative  position  of  the  molecules,  and  in  consequence,  an  absorption  of  heat 
proportional  to  the  work  accomplished.  In  evaporation  there  is  an  internal 
work,  employed  in  separating  the  molecules,  and  an  external  work  in  overcoming 
the  forces  which  oppose  themselves  to  the  expansion  of  the  vapor. 

When,  on  the  contrary,  a  gas  or  vapor  is  liquefied  by  compression,  the  external 
work  is  supplied,  and  the  internal  work  due  to  the  cohesive  force  which  draws 
the  atmosphere  together,  is  transformed  into  heat.  Again,  when  a  liquid  solidi- 
fies, the  internal  work  which  unites  the  molecules  is  transformed  into  heat,  and 
appears  as  sensible  heat. 

It  is  evident  that  this  theory  would  modify  the  ideas  generally  received  of  the 
amount  of  heat  in  bodies.  Thus  the  heat  which  is  rendered  latent,  when  a  solid 
is  liquefied,  cannot  be  regarded  simply  as  being  insensible  j  it  must  be  consi- 
dered as  being  converted  into  motion. 

III.     ANALOGY  OF  LIGHT  AND  HEAT. 

765.  Vibrations  producing  heat  and  light. — A  careful  conside- 
ration of  the  phenomena  and  laws  of  heat  has  led  many  able  physicists 
to  conclude  that  heat  is  not,  as  was  formerly  supposed,  a  fine  imponder- 
able substance,  but  that,  like  light,  it  is  a  peculiar  vibratory  motion  of 
the  ultimate  particles  of  bodies.     The  exact  nature  of  the  vibratory 
motion  of  atoms  which  constitutes  heat  is  more  difficult  to  determine. 

The  polarization  of  heat  is  best  explained,  like  the  polarization  of 
light,  by  the  theory  of  transverse  vibrations.  On  this  theory : — Heat  and 
light  are  different  effects  produced  by  one  and  the  same  cause,  and  they 
differ  physically  only  in  the  rapidity  and  amplitude  of  their  vibrations. 
While  the  phenomena  of  light  are  due  to  vibrations  whose  utmost  range 
of  velocity  is  comprehended  within  the  limit  of  an  octave  in  music 
(531),  vibrations  of  less  rapidity  and  greater  amplitude  produce  heat, 
while  the  vibrations  which  produce  light,  also  in  their  turn  produce  the 
phenomena  of  heat. 

766.  Impressions  of  light  and  heat. — It  is  natural  to  admit  that 
the  more  rapid  vibrations  of  ether  are  generally  those  which  have  the 
least  amplitude.    In  fact  this  result  is  deduced  from  an  examination  of 
the  spectrum,  which  presents  a  more  feeble  illumination  in  the  blue  and 
violet.    It  is  the  same  with  sounds.    The  more  acute  sounds  have  gene- 
rally the  least  intensity,  while  the  bass  notes  are  more  prolonged.     As 
grave  sounds  have  little  intensity,  because  their  amplitude  is  great,  so 
with  vibrations  of  the  luminiferous  ether,  we  observe  that  the  extreme 
red  of  the  spectrum  has  but  little  brilliancy. 

Vibrations  impressed  upon  the  air  by  sonorous  bodies  may  produce  upon  us 
two  sorts  of  sensations ;  the  one  perceived  by  a  special  organ,  the  ear,  when  the 
45 


502          PHYSICS  OP  IMPONDERABLE  AGENTS. 

vibrations  are  sufficiently  rapid,  the  other  affecting  the  entire  surface  of  our 
bodies,  producing  that  general  trembling  which  results  from  energetic  vibra- 
tions, as  in  the  case  of  thunder  or  the  roar  of  cannon.  Only  grave  sounds  cor- 
respond to  vibrations  of  sufficient  amplitude  to  produce  this  general  effect.  On 
the  other  hand,  vibrations  of  too  great  rapidity,  and  consequently  too  littla 
amplitude,  may  fail  to  affect  even  the  ear,  as  is  the  case  with  vibrations  exceed- 
ing 36,500  per  second,  g  378.  We  may  consider  the  same  vibrations  communicated 
to  the  ether  by  the  molecules  of  luminous  bodies  as  giving  rise  to  two  sorts  of 
impressions  j  the  one  peculiar  to  the  organ  of  vision,  the  other  affecting  the  whole 
surface  of  the  body ;  the  former  constituting  the  impression  of  light,  the  other 
giving  the  impression  of  heat  when  the  amplitude  of  the  vibrations  is  sufficiently 
great. 

But  the  colored  rays  which  pertain  to  the  extreme  violet  of  the  spectrum  are 
produced  by  vibrations  which  are  very  rapid,  and  which  consequently  have  very 
little  amplitude.  Such  vibrations  are  not  suited  to  produce  the  general  effect 
which  is  denominated  heat.  But  when  the  vibratory  energy  is  feeble,  as  in  the 
spectrum  obtained  from  the  electric  light,  there  are  more  evident  signs  of  heat 
in  the  violet  portion  of  the  spectrum.  In  general,  the  less  rapid  vibrations  found 
in  the  yellow,  orange,  and  red,  produce  heat,  and  even  beyond  the  extreme  red, 
where  the  vibrations  are  too  slow  to  produce  light,  the  greater  amplitude  of  the 
vibrations  gives  them  great  power  to  produce  the  phenomena  of  heat.  Compare 
§463. 

Aerial  vibrations  of  great  amplitude,  and  a  moderate  degree  of  rapidity,  affect 
the  entire  system  (386),  and  when  less  than  32  per  second,  they  seldom  produce 
the  sensation  of  sound.  So  also  if  the  vibrations  exceed  36,500  per  second,  their 
amplitude  is  so  small  that  no  audible  sound  is  produced. 

The  gradual  weakening  of  the  violet  tint  of  the  spectrum,  and  the  existence 
of  invisible  rays  beyond  the  extreme  violet,  as  attested  by  chemical  action  and 
fluorescence,  $$  463,  533,  prove  the  same  thing  in  regard  to  light.  Heat  and 
light  may  therefore  be  regarded  as  different  effects  of  the  same  cause. 

767.  Bodies  become  luminous  by  incandescence. — When  a 
body  is  heated,  the  source  of  heat  first  communicates  vibrations  to  the 
ether,  and  then  to  the  molecules  of  the  body.  The  vibrating  molecules 
in  turn  react  upon  the  ether,  and  excite  undulations  of  different  lengths  ; 
the  longer  vibrations  corresponding  to  the  calorific  rays  of  least  refran- 
gibility,  will  have  a  greater  amplitude,  and  will  be  the  first  to  become 
sensible  as  light. 

Melloni  discovered  that  the  heat  rays,  emitted  by  bodies  of  low  temperature, 
are  but  little  refracted  by  a  prism  of  rock-salt,  but  as  the  heat  of  the  body 
becomes  more  intense,  and  the  amplitude  of  all  the  vibrations  may  be  consi- 
dered greater,  the  rays  of  heat  are  more  refracted,  the  more  refrangible  rays 
appear  as  light,  and  the  body  becomes  luminous.  This  result  takes  place  at  the 
temperature  of  about  947°  Fahrenheit,  whatever  be  the  nature  of  the  luminous 
substance.  Draper  formed  a  spectrum  by  means  of  light  from  a  narrow  opening, 
and  examined  with  a  lens  and  micrometer  the  positions  of  the  dark  lines  of 
Fraunhofer  (461).  He  afterwards  employed,  instead  of  the  narrow  opening,  a 
platinum  wire,  the  temperature  of  which  he  caused  to  vary  by  means  of  an  electric 
current,  more  or  less  intense,  and  he  found  that  the  red  part  of  the  spectrum 
appeared  first,  and  as  the  heat  and  brilliancy  of  the  wire  increased,  the  other 
colors  of  the  spectrum  successively  appeared  up  to  the  violet.  This  result  is  in 


HEAT.  503 

beautiful  harmony  with  the  theory  stated  above.  Common  observation  also 
shows  that  a  heated  body  becomes  first  red,  then  yellow,  purple,  and  at  length 
a  full  white  heat.  Compare  g  178. 

768.  Heat  and  light  produced  by  chemical  and  mechanical 
action. — It  is  easy  to  understand  that,  in  the  molecular  conflict  which 
constitutes  chemical  action,  the  ether  around  the  molecules  will  be 
violently  agitated,  and  become  the  seat  of  undulations  of  different 
rapidity.  If  the  chemical  action  is  weak,  the  vibrations  will  be  slow, 
and  they  will  have  only  sufficient  amplitude  to  be  sensible,  and  it  has 
been  observed  that  the  heat  thus  produced  furnishes  rays  more  and 
more  refrangible  as  the  chemical  action  becomes  more  active.  When 
this  action  becomes  sufficiently  energetic  to  give  to  the  more  rapid 
vibrations  a  sufficient  amplitude,  light  accompanies  the  heat. 

Experiments  show  that  the  color  of  the  luminous  rays  depends  upon  the  nature 
of  the  substance  from  which  they  proceed,  and  it  is  also  probable  that  the  tem- 
perature at  which  light  begins  to  appear,  depends  also  on  the  nature  of  the 
substance  or  the  color  which  it  gives  forth.  We  can  easily  understand  that  the 
nature  of  the  molecules  will  affect  the  rapidity  of  the  vibrations,  and  we  may 
presume  that,  if  it  were  possible  to  augment  gradually  the  energy  of  the  chemi- 
cal action,  we  should  find  the  temperature  at  which  light  begins  to  appear  is 
more  elevated  in  proportion  as  the  color  of  the  light  which  the  substance  affords 
approaches  to  white  or  violet.  This  conjecture  is  confirmed  by  the  fact  that  the 
incandescence  due  to  chemical  action,  when  it  is  feeble,  gives  forth  red  light. 

In  mechanical  action,  the  vibrating  molecules  impress  upon  the  ether  vibra- 
tions of  different  rapidity,  and  when  the  action  is  sufficiently  violent,  as  in  the 
shock  of  two  flints,  or  in  the  sudden  compression  of  a  gas,  light  is  emitted  in 
connection  with  the  heat.  Here,  again,  if  we  could  graduate  the  intensity  of  the 
action,  we  ought  to  obtain  a  color  approaching  more  nearly  to  white  as  the  me- 
chanical action  is  more  energetic. 

We  thus  see  how  the  effects  which  heat  and  light  exercise  upon  bodies  can  be 
explained  by  the  theory  of  undulations. 

The  phenomena  of  heat  in  the  interior  of  bodies  are  more  difficult  to  compre- 
hend, and  it  is  impossible  to  explain  them  by  the  system  of  emission ;  but  by 
comparing  them  with  other  effects  in  elastic  bodies,  they  are  readily  explained 
by  the  theory  of  undulations. 

769.  Dilatation  and  change  of  state. — The  heat  received  by  a 
body  agitates  the  ether ;  this  agitation  is  communicated  to  the  mole- 
cules, and  the  volume  of  the  body  is  increased  in  proportion  as  the 
amplitude  of  the  oscillation  of  the  molecules  becomes  greater.  It  is 
thus  that  bodies  which  vibrate  longitudinally  appear  larger,  and  a 
vibrating  cord  appears  swollen.  In  the  same  manner,  obstacles  opposed 
to  vibrating  parts  become  repelled,  if  they  are  so  light  as  not  to  arrest 
the  vibrations. 

This  explanation,  leads  us  to  a  very  simple  and  clear  definition  of 
temperature : —  Temperature  consists  in  the  vibratory  state  of  the  ether 


504  PHYSICS    OF   IMPONDERABLE    AGENTS. 

within  the  body,  and  its  intensity  depends  upon  the  amplitude  of  the 
vibrations. 

The  theory  of  changes  of  temperature  is  naturally  explained  by  the  tendency 
to  establish  an  equilibrium  between  the  amplitude  of  the  vibrations  of  bodies 
near  each  other,  through  the  medium  of  the  ether  which  fills  the  space  that 
separates  them.  The  molecules  of  bodies  should,  therefore,  be  considered  as  in 
a  perpetual  state  of  agitation.  There  can,  then,  be  no  absolute  zero  only  where 
there  is  a  state  of  perfect  repose. 

The  only  difficulty  in  admitting  the  existence  of  such  a  state,  is  the  fact  that 
celestial  space  is  certainly  filled  with  agitation  by  the  transmission,  in  every 
possible  direction,  of  the  different  radiations  which  emanate  from  the  multitude 
of  stars  which  people  space. 

Change  of  state  produced  by  heat. — If  the  motion  of  the  mole- 
cules is  sufficiently  energetic,  they  leap  out,  as  it  were,  from  each  other, 
and  become  independent,  as  a  glass  rod  vibrating  rapidly  in  the  direc- 
tion of  its  length,  is  divided  into  many  pieces.  We  thus  explain  the 
phenomena  of  fusion. 

If  we  revert  to  the  theory  of  the  mechanical  equivalent  of  heat,  we  can  under- 
stand how  the  conversion  of  heat  into  mechanical  work,  and  vice  versa,  is  a 
direct  consequence  of  the  preceding ;  for,  according  to  this  theory,  heat  is  a 
species  of  motion,  and  the  work  which  produces  this  motion  of  the  ether,  ought 
to  be  changed  into  vibrations  of  this  latter  sort  j  that  is,  it  should  be  transformed 
into  heat. 

It  is  the  same  with  the  mechanical  work  developed  by  a  vibrating  body.  The 
work  represented  is  that  which  has  been  expended  in  putting  it  into  vibration. 
The  heat  developed  in  moving  bodies,  by  electro-dynamic  induction,  and  the 
work  which  it  represents,  are  all  related  to  the  same  theory. 

770.  Quality  of  heat  changed  by  absorption  and  radiation. — 
In  all  experiments  upon  radiant  heat,  it  has  been  observed,  that  heat, 
once  absorbed,  retains  none  of  the  peculiarities  of  the  source  from 
which  it  was  derived ;  but  its  refrangibility  and  other  properties,  when 
again  radiated,  depend  only  on  its  temperature,  and  the  nature  of  the 
body  from  which  it  is  again  emitted. 

Heat,  transmitted  through  diathermanous  bodies,  appears  to  be  sifted,  or  to 
leave  behind  some  of  those  rays  which  are  transmitted  with  difficulty  through 
that  substance ;  so  that  a  larger  percentage  of  the  remaining  heat  will  be  trans- 
mitted through  another  similar  screen. 

Even  rock-salt,  generally  considered  colorless  for  heat  (646),  has  been  found, 
by  the  later  researches  of  Prof.  Forbes,  to  transmit  a  somewhat  greater  propor- 
tion of  heat  of  high  temperature  than  of  heat  of  low  temperature. 

It  is  well  known  that  heat  of  great  refrangibility,  or  small  wave-length,  passes 
more  readily  through  glass  and  mica  than  heat  having  the  opposite  qualities. 
The  difficulty  with  which  heat  radiated  by  rock-salt  penetrates  these  substances, 
as  compared  with  ordinary  heat,  would  lead  us  to  infer  that  heat  from  rock-salt 
has  a  greater  wave-length  than  ordinary  heat  radiated  from  lampblack.* 

*  See  an  able  article  on  radiant  heat,  by  B.  Stewart,  Esq.,  in  the  Trans,  of 
Royal  Soc.  of  Edinburgh,  Vol.  XXII.,  part  I. 


HEAT.  505 

771.  Difference  between  quantity  and  intensity  of  heat. — 

Another  curious  fact  connected  with  this  subject  is,  that  no  amount  of 
heat  of  low  temperature  can  be  so  applied  to  an  object  as  to  raise  it  to 
a  higher  temperature  than  that  of  the  source  from  which  the  heat  ema- 
nated. Thus,  the  heat  of  the  sun,  when  absorbed  by  a  blackened  wall, 
and  radiated,  cannot  be  again  raised  to  the  intensity  requisite  to  ignite 
ordinary  combustible  substances,  which  are  readily  ignited  by  the  direct 
rays  of  the  sun  concentrated  by  a  burning-glass. 

The  same  degradation  of  heat,  or  loss  of  intensity,  is  observed  in  condensing 
steam  in  distillation.  The  whole  heat  of  the  steam,  both  latent  and  sensible,  is 
transferred  without  loss  to  perhaps  fifteen  times  as  much  condensing  water ;  but 
the  intensity  of  the  heat  is  reduced  from  212°  to  perhaps  100°  F.  The  heat  is 
not  lost;  for  the  fifteen  parts  of  water  at  100°  are  capable  of  melting  as  much 
ice  as  the  original  steam.  But  by  no  quantity  of  this  heat  at  100°  can  tem- 
perature be  raised  above  that  degree ;  no  means  are  known  of  giving  it  inten- 
sity. 

If  heat  of  low,  is  ever  changed  into  heat  of  high  intensity,  it  is  by  mechani- 
cal means,  as  by  the  compression  of  gases  or  vapors  to  a  smaller  volume,  when 
the  temperature  is  elevated;  but  this  is  rather  the  conversion  of  mechanical 
force  into  heat,  than  the  elevation  of  the  intensity  of  heat  previously  existing 
as  such.  Graham's  Chemistry,  Vol.  I.,  p.  100. 

It  is  stated  that  Dr.  Wollaston  received  the  beam  of  the  full  moon,  concen- 
trated by  a  powerful  lens,  in  his  eye,  without  feeling  the  least  heat.  Melloni 
obtained  only  an  extremely  feeble  indication  of  heat,  by  concentrating  the  rays 
of  the  moon  by  a  lens  over  three  feet  in  diameter,  and  directing  the  brilliant 
focus  of  light  upon  the  face  of  a  very  sensitive  thermo-multiplier.  This  may 
merely  show  that  the  heat  reflected  or  radiated  by  the  moon,  has  become  heat  of 
too  low  intensity  to  pass  through  a  glass  lens,  or  to  warm  bodies  at  the  ordinary 
terrestrial  temperature. 

All  these  phenomena  are  more  readily  explained  on  the  undulatory  theory, 
than  by  the  theory  of  emission. 

772.  Conclusion. — We  conclude,  from  what  has  been  stated,  that 
the  theory  of  undulations,  which  so  completely  explains  the  phenomena 
of  heat  and  light,  as  well  as  the  different  sensations  produced  upon  our 
organs  by  the  two  sorts  of  radiations,  may  also  enable  us  to  compute, 
with  a  little  uncertainty  in  some  cases,  the  different  effects  which  heat 
and  light  exercise  upon  bodies.     We  see  that  heat  and  light  are  due  to 
the  same  cause,  to  ethereal  vibrations  ;  and  that  the  same  vibrations  also 
produce  the  two  sorts  of  effects  when  their  amplitude  is  sufficient,  and 
their  rapidity  comprised  between  certain  limits. 

It  remains  only  to  explain,  by  these  movements  of  the  ether,  the  numerous 
and  complex  phenomena  which  are  presented  to  us  by  electricity. 

It  is  possible  that  these  effects  are  produced  by  either  longitudinal  or  rotary 
vibrations,  which  accompany  the  transverse  vibrations  corresponding  to  light 
and  heat. 

But,  while  it  is  very  easy  to  understand  the  facts  relative  to  the  propagation 
of  electricity,  it  is  somewhat  difficult  to  conceive  how  vibratory  movements 
45* 


506          PHYSICS  OF  IMPONDERABLE  AGENTS. 

produce  attraction  and  repulsion.  We  ought  not  to  regard  this  difficulty  as 
insurmountable,  especially  when  we  remember  that  polarization  was,  for  a  long 
time,  considered  inconsistent  with  ethereal  vibrations,  until  the  idea  of  trans- 
verse vibrations  dissipated  the  objection,  and  gave  new  clearness  to  the  whole 
series  of  phenomena. 

If  this  difficulty  were  once  conquered,  there  would  appear  a  possibility  of 
uniting  to  the  system  of  ethereal  vibrations,  the  grand  phenomena  of  universal 
gravitation,  which  has  been  attempted  hitherto  without  success. 

But,  when  all  the  phenomena  of  nature,  in  their  infinite  variety,  are  reduced 
to  one  and  the  same  cause,  wonderful  simplicity  will  be  joined  to  the  idea  which 
we  form  of  the  power  and  majesty  of  the  GREAT  AUTHOR  of  all  things. 

To  bring  the  detailed  study  and  interpretation  of  facts  to  prove  this  grand 
unity  of  cause,  is  the  mission  which  science  should  propose  to  herself  at  the 
present  day. 

This  close  correlation  of  physical  forces,  is  in  harmony  with  recent 
philosophical  views  entertained  by  many  of  the  first  Physicists  of  our 
time,  but  by  no  one  more  felicitously  expounded  than  by  Prof.  Grove.* 

A  full  and  satisfactory  discussion  of  this  subject  will  be  found  in  the 
excellent  Traite  de  Physique  of  Daguin  (Vol.  III.,  1859),  from  which 
the  foregoing  is  condensed. 


Problems  on  Heat. 
Thermometers. 

209.  What  number  of  Centigrade  and  Reaumur  degrees  correspond  to  the  foJ 
lowing  temperatures  in  Fahrenheit's  degrees  ? 

Melting-point  of  mercury,      ......     — 40°  F. 

"  bromine,      .          .          .          .         .         .    —  4 

"  white  wax, -f  158 

"  sodium,        .         .         .  .          .       194 

tin, 442-4 

"  antimony     ......       771-8 

Incipient  red  heat,         .          .          .          .         .          .          .977 

Clear  cherry-red  heat 1,832 

Dazzling  white  heat, 9,732 

210.  How  many  Fahrenheit  and  Reaumur  degrees  correspond  to  the  following 
temperatures  in  Centigrade  degrees  ? 

Temperature  of  maximum  density  of  water,  .          .      -|-30'87  C. 

Boiling-point  of  liquid  ammonia,  ....  — 40 
"  "  sulphurous  acid,  ....  — 10 

"  "  alcohol,  -f-75 

"  "  phosphorus,  .....  290 

"  "  mercury,  .....  360 

211.  How  many  times  must  the  capacity  of  the  bulb  of  a  thermometer  exceed 
the  capacity  of  the  tube,  in  order  that  the  thermometer  may  measure  tempera- 
tures from  40°  below  zero  to  500°  F.  ? 

*  The  Correlation  of  Physical  Forces  :  pp.  229.     London,  1855. 


HEAT.  507 

Expansion. 

212.  If  rods  of  the  following  substances,  iron,  brass,  copper,  glass,  platinum, 
eilver,  measure  each  3  feet  2  inches  in  length  at  the  temperature  of  50°  F.,  what 
will  be  their  respective  lengths  at  temperatures  of  10°,  25°,  75°,  and  100°  F.  ? 

213.  If  a  glass  globe  holds  exactly  one  gallon  at  60°  F.,  what  will  be  its  ca- 
pacity if  measured  at  the  temperature  of  boiling  water  ? 

214.  If  a  railroad  is  constructed  in  winter,  when  the  average  temperature  is 
25°  F.,  how  far  apart  must  the  ends  of  the  iron  rails,  18  feet  long,  be  laid  to 
allow  sufficient  room  for  expansion  at  the  temperature  of  120°  F.  ? 

215.  What  change  of  temperature  is  required  to  produce  an  elongation  of  3 
inches  in  a  portion  of  the  Britannia  tubular  bridge  ($  172),  917  feet  in  length? 

216.  Gas-pipes,  laid  3  feet  below  the  surface  of  the  earth,  are  exposed  to  a 
change  of  temperature  of  60°  F.,  from  summer  to  winter;  what  is  the  extent  to 
which  the  joints  (10  feet  apart)  will  be  opened  in  winter,  if  the  strain  is  equally 
divided  among  the  several  joints  ? 

217.  Calculate  the  lengths  of  the  steel  and  brass  rods  required  to  adapt  Harri- 
son's gridiron  pendulum  to  vibrate  seconds  at  the  following  places :  London, 
Paris,  New  York,  and  St.  Petersburgh. 

218.  Reduce  the  following  heights  of  the  barometer,  observed  at  the  annexed 
temperatures,  to  the  equivalent  heights  at  the  freezing-point : — 

1.  30-1  in.  t  =  40°  F.     I      5.  23  2  in.  t  =  50°  F. 

2.  29-4  «  t  =  25°  6.  24-7  «  t  =  80° 


3.  27-9  «  t  =  65C 

4.  28-3  "  *  =  75C 


7.  17-4  «  ( =  19° 

8.  15-8  "  «  =  10° 


219.  Reduce  the  following  barometric  observations  made  at  8°  C.,  to  the  tem- 
peratures indicated  by  the  values  of  t,  given  below  : — 

1.  24     in.     reduce  to  t  =  30°  C.       I      3.     28-5  in.     reduce  to  t  =  55°  C. 

2.  27-5  "  "      "  t  =  25°  4.     19-5  "  "      "  t  =  19° 

220.  A  sphere  of  brass,  3  inches  in  diameter,  immersed  in  water,  is  suspended 
from  the  pan  of  a  hydrostatic  balance,  and  counterpoised  at  the  temperature  of 
60°  F.     What  weight  will  be  required  to  restore  the  equilibrium  when  the  tem- 
perature of  the  water  and  globe  is  raised  to  200°  F.  ? 

221.  To  what  temperatures  must  an  open  vessel  be  heated,  the  pressure  re- 
maining constant,  that  J,  i,  and  J  of  the  air  it  originally  contained,  may  be 
successively  driven  out  of  it  ? 

222.  A  balloon  containing  1000  cubic  feet  of  gas  at  80°  F.,  and  29  inches 
barometric  pressure,  rises  to  a  position  where  the  thermometer  stands  at  40°, 
and  the  barometer  at  22  inches.     Calculate  the  volume  of  the  gas,  supposing 
the  capacity  of  the  balloon  to  allow  it  to  expand  freely. 

Specific  Heat. 

223.  How  much  heat  is  required  to  raise  the  temperature  of 

50  Ibs.  of  water       from  40°  F.  to  150°  ? 

24  "     "   sulphur,     "      63°       "  212°? 
45   "     "   charcoal,    "      45°       "  930°? 

25  "     "  alcohol,       "      35°       "     65°? 
11    "     «   ether,          «        5°        «  132°? 

224.  The  following  quantities  of  water  were  mixed  together, — 2  Ibs.  of  water 
at  40°  F. ;  5  Ibs.  at  65°  ;  7  Ibs.  at  70° ;  and  3  Ibs.  at  90°.   What  was  the  tempera- 
ture of  the  mixture  ? 

225.  How  much  water  at  200°  F.,  and  how  much,  water  at  50°,  must  be  mixed 
together,  in  order  to  obtain  20  Ibs.  of  water  at  85°? 


508  PHYSICS    OF    IMPONDERABLE   AGENTS. 

226.  Equal  volumes  of  mercury  at  212°  F.,  and  water  at  32°,  are  mixed  toge« 
tber.     What  is  the  temperature  of  the  mixture  " 

227.  What  temperature  will  be  produced  by  mixing  equal  volumes  of  mercury 
at  32°  F.,  and  water  at  212°  ? 

228.  Five  pounds  of  ice  at  32°,  are  mixed  with  7  Ibs.  of  water  at  200°  F. 
What  will  be  the  temperature  of  the  mixture  after  the  ice  is  melted  ? 

229.  How  much  ice  at  32°,  must  be  mixed  with  100  Ibs.  of  water  at  50°  F.,  in 
order  to  reduce  the  temperature  of  the  mixture  to  35°  F.  ? 

230.  How  much  ice  at  32°,  is  required  to  cool  10  Ibs.  of  mercury  at  300°,  to 
the  freezing-point  of  water  ? 

231.  In  order  to  determine  the  heat  of  fusion  of  lead,  200  ounces  of  melted 
lead  at  the  melting-point  were  poured  into  1850  ounces  of  water  at  50°  F.    After 
the  lead  had  cooled,  the  water  was  found  at  20°-76  Centigrade.     Required  the 
heat  of  fusion  of  lead  in  degrees  Fahrenheit. 

232.  How  much  heat  is  required  to  raise  the  temperature  of  a  cubic  foot  each 
of  air,  oxygen,  carbonic  acid,  and  hydrogen  from  32°  F.  to  75°,  if  the  gas  is 
allowed  to  expand  freely,  and  the  barometer  remains  stationary  at  30  inches  ? 

233.  In  a  room  20  by  30  feet,  and  10  feet  high,  the  barometer  standing  at  30 
inches,  how  many  units  of  heat  are  required  to  raise  the  temperature  of  the  air 
from  40°  F.  to  75°  ? 

234.  In  the  last  example,  how  many  units  of  heat  are  expended  in  expanding 
the  air  of  the  room  ? 

Tension  of  Vapors. 

235.  Before  filling  a  barometer  with  mercury,  a  small  quantity  of  water  was 
poured  into  the  tube.     How  high  will  the  mercury  stand  in  the  barometer  when 
the  temperature  is  75°  F.,  and  the  pressure  of  the  air  is  29  inches  in  an  accu- 
rate barometer  ? 

236.  Solve  the  last  problem,  assuming,  first,  that  alcohol,  secondly,  that  sul- 
phuric acid,  and  thirdly,  that  oil  of  turpentine  were  used  instead  of  water. 

237.  Calculate  the  tension  of  the  vapor  of  water  at  the  following  -temperatures  : 
50°,  75°,  110°,  175°,  220°,  265°,  and  300°  F. 

238.  Determine  the  boiling-point  of  water,  ether,  and  alcohol  at  the  following 
pressures :  31  in.,  29-75  in.,  29-21  in.,  28  in.,  27'4  in.,  23-7  in. 

239.  A  cylinder  is  filled  with  steam  at  a  temperature  of  250°  F.,  and  a  pres- 
sure of  two  atmospheres.     What  will  be  the  tension  of  the  vapor  if  its  volume 
is  diminished  one-half  by  pushing  down  the  piston  ?     What  will  be  the  tension 
of  the  vapor  if  it  is  allowed  to  expand  to  twice  its  former  volume  ? 

240.  If  a  cubic  inch  of  water  is  hermetically  sealed  in  a  bomb-shell,  capable 
of  holding  200  cubic  inches,  and  strong  enough  to  sustain  a  pressure  of  450  Ibs. 
to  the  square  inch;  what  temperature  is  required  to  burst  the  bomb-shell? 

Ventilation  and  "Warming. 

241.  How  many  flues,  each  six  by  twelve  inches,  and  fifty  feet  high,  are  re- 
quired to  ventilate  a  lecture-room  seating  1200  persons,  when  the  temperature 
of  the  room  is  70°  F.,  and  the  external  air  at  30°,  allowing  each  person  three 
and  a  half  cubic  feet  of  fresh  air  per  minute  ? 

242.  Repeat  the  calculations  of  the  last  problem,  on  the  supposition  that  1500 
persons  are  in  the  room,  and  make  additional  allowance  for  illumination  by  50 
gas  burners,  consuming  each  3J  cubic  feet  of  gas  per  hour,  at  an  expenditure 
of  20  feet  of  air  for  every  cubic  foot  of  gas  consumed. 


ELECTRICITY.  509 


CHAPTER  III. 

ELECTRICITY. 

773.  General  statement. — Electricity  is  conveniently  subdivided 
into,  1.  Magnetic  electricity  or  magnetism ;   2.  Statical  or  frictional 
electricity ;  and,  3.  Dynamical  or  Voltaic  electricity.   We  will  consider 
the  subject  in  this  order. 

g  1.  Magnetic  Electricity. 

I.     PROPERTIES  OF  MAGNETS. 

774.  Lodestone — natural  magnets. — There  is  found  in  nature  an 
ore  of  iron,  called  by  mineralogists  magnetite,  or  magnetic  iron,  some 
specimens  of  which  possess  the  power  of  attracting  to  themselves  small 
fragments  of  a  like  kind,  or  of  metallic  iron.     This  power  has  been 
called  magnetism,  from  the  name  of  the  ancient  city  of  Magnesia,  in 
Lydia  (Asia  Minor),  near  which  the  ore  spoken  of  was  first  found.     It 
crystallizes  in  forms  of  the  monometric  system,  often  modified  octo- 
hedra,  like  fig.  520,  and  is  a  compound  of  one  equivalent         520 

of  peroxyd  of  iron  with  one  of  protoxyd.  (FeO  +  Fea03 
=  Fe304.)  It  is  one  of  the  best  ores  of  this  valuable 
metal. 

Formerly  all  magnets  were  lodestones,  or  natural  mag- 
nets.    A  fragment  of  this  ore  rolled  in  iron  filings  or  mag- 
netic sand,  becomes  tufted,  as  in  fig.  521,  not  alike  in  all  parts,  but 
chiefly  at  the  ends.     Fig.  522  shows  a  similar  mass  mounted  in  a 
frame,  II,  with  poles,  pp',  of  soft  iron.  521  522 

Thus  mounted,  the  lodestone  gains  in 
strength,  by  sustaining  a  weight  from 
the  hook  below,  on  a  soft  iron  cross-bar. 

775.  Artificial  magnets  are  made 
by  touch  or  influence  from  a  lodestone, 
or  from  another  magnet,  or  by  an  elec- 
trical current.     Hardened  steel  is  found  to  retain  this  influence  perma- 
nently, while  masses  of  soft  iron  become  magnets  only  when  in  contact 
with,  or  within  a  certain  distance  of  a  permanent  magnet.     Artificial 
magnets  are  more  powerful  than  the  lodestone,  and  possess  properties 


510 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


entirely  identical  with  it.  Magnets  attract  at  all  distances,  but  their 
power  increases,  like  all  forces  acting  from  a  centre,  inversely  as  the 
square  of  the  distance.  Heat  diminishes  the  power  of  magnets,  but  if 
not  heated  beyond  a  certain  degree  (full  redness),  this  power  returns 
cooling,  and  is  increased  at  lower  temperatures.  Above  that  point, 
the  coercitive  force  is  destroyed,  and  they  lose  all  magnetic  power. 

Various  forms  are  given  to  magnets.  The  bar  magnet  is  a  simple  straight  bar 
of  hardened  steel.  If  curved  so  as  to  bring  the  ends  near  together,  it  is  called 
a  horse  shoe  magnet,  and  if  several  bars,  straight  or  curved,  are  bound  together 
into  one,  fig.  523,  it  is  called  a  compound  magnet,  or  magnetic  battery.  The 

523 


most  powerful  artificial  magnets  can  sustain  only  about  twenty-eight  or  thirty 
times  their  own  weight.     Usually  they  sustain  very  much  less  than  this. 

Magnetic  needles  are  light  bars,  fig.  524,  suspended  on  a  central  point 
so  as  to  move  in  obedience  to  terrestrial   or  artificial  at-  524 

tractions.     The  mode  of  making  magnets,  and  the  circum- 
stances influencing  their  power,  are  noticed  hereafter. 

776.  Distribution  of  the  maguetic  force — 
polarity. — The  magnetic  force  is  not  equally  dis- 
tributed in  all  parts  of  a  magnet,  but  is  found  con- 
centrated chiefly  about  the  ends,  and  diminishing 
toward  the  centre,  which  is  neutral.  The  points  of  greatest  attraction 
are  called  poles.  When  a  magnet  is  rolled  in  iron  filings  or  magnetic 
sand,  the  position  of  the  poles  is  seen  as  in  the  bar  magnet,  fig.  525, 

525 


whose  centre  is  found  to  be  quite  devoid  of  the  attracted  particles  which 
cluster  about  the  ends.  The  point  of  no  attraction  is  called  the  neutral 
point — line  of  magnetic  indifference,  or  equator  of  magnetism.  Every 
magnet  has  at  least  two  poles,  and  one  neutral  point.  The  magnetic 
poles  are  distinguished  as  N  or  S,  Austral  or  Boreal  (A  and  B),  or  by 
the  signs,  plus  (+)  and  minus  ( — ),  all  these  signs  having  reference  to 
the  earth's  attraction,  and  to  the  antagonism  between  the  poles  of  unlike 
name.  The  law  regulating  the  distribution  of  magnetic  force  in  a  bar, 


ELECTRICITY 


511 


was  determined  by  Coulomb,  by  means  of  the  torsion  balance,  \  820, 
to  be  very  nearly  as  the  squares  of  the  distance  of  any  given  point, 
from  the  magnetic  equator  or  neutral  point. 

777.  Magnetic  phantom — magnetic  curves. — The  distribution 
of  the  magnetic  force  about  the  poles  of  a  magnet  is  beautifully  shown 
by  placing  a  sheet  of  stiff  paper  over  the  poles  of  a  horse-shoe  magnet, 
and  scattering  fine  iron  filings  or  magnetic  sand  from  a  sieve  or  gauze 
bag  over  the  paper.  As  they  touch  the  surface  of  the  paper,  each 
filing  assumes  a  certain  position,  marking  the  exact  place  of  the  mag- 
netic poles  and  of  the  neutral  line,  as  seen  in  fig.  526.  The  magnet 
may  be  laid  horizontally,  or  a  series  of  magnetic  bars  may  be  placed 
as  in  fig.  532,  producing  very  pleasing  and  instructive  results.  Tapping 

526 


the  edge  of  the  paper  gently  with  the  nail,  or  a  pen-stick,  facilitates 
the  adjustment  of  the  filings.  The  curves  exhibited  by  the  magnetic 
phantom  have  been  mathematically  investigated  by  De  Haldat,  who  for 
that  purpose  transferred  them  to  a  glued  paper. 

To  fix  the  curves,  Nickles  uses  a  waxed  paper,  and  when  the  figures  are  pro- 
duced, they  may  be  fixed  in  position  by  holding  a  heated  plate  of  iron  near  the 
surface  of  the  paper.  As  soon  as  the  wax  is  fused,  which  is  easily  perceived  by 
its  shining  appearance,  the  source  of  heat  is  withdrawn,  and  as  the  wax  cools 
the  filings  become  fixed  in  position  and  in  full  relief.  (Am.  Jour.  Sci.  [2]  XXX. 
62.)  The  curves  may  then  be  more  conveniently  studied. 

778.  Magnetic  figures  may  be  produced  on  the  surface  of  a  thin 
steel  plate,  by  marking  on  it  with  one  pole  of  a  bar  magnet.  Magnetism 
is  thus  produced  in  the  steel  along  the  line  of  contact,  which  is  after- 
wards made  evident  by  magnetic  sand,  or  iron  filings  sprinkled  on  the 
plate.  These  lines  may  be  varied  or  multiplied  at  pleasure,  with 
pleasing  effects ;  their  polarity  is  always  the  reverse  of  that  carried  by 
the  bar.  They  may  be  made  even  through  paper  or  card-board,  and 
will  remain  for  a  long  time.  Blows,  or  heat,  will  remove  them.  Hard 


512 


PHYSICS    OP   IMPONDERABLE    AGENTS. 


plate  steel  is  best  for  this  purpose,  about  one-twentieth  to  one-eighth  of 
an  inch  thick,  and  six  inches  to  twelve  inches  square. 

779.  Anomalous  magnets  are  such  as  have  more  than  two  poles. 
Thus  the  bar  seen  in  fig.  527  has  a  pair  of  similar  poles   ( — ),  at  the 
centre,  and   its   ends   are    con-  527 

sequently  similar  (+),  while  it 

has  two  neutral  points  at  a  and 

c.     Fig.  528  shows  a  bar  with 

three    sets    of   poles,    arranged  528 

alternately  —  and  -f,  with  three  neutral  points  at  m,  o,  and  n.   Broken 

at  these  neutral  points,  every  magnet  becomes  two  or  more  separate 

magnets,  with  corresponding  polarity. 

780.  Attraction  and  repulsion. — The  law  of  magnetic  attraction 
and  repulsion  is,  that  like  poles  repel,  and  unlike  poles  attract  each  other. 

If  a  piece  of  soft  iron  is  presented  to  either  pole  of  a  magnetic  needle,  fig. 
524,  there  is  attraction,  which  is  reciprocal  between  the  needle  and  the  iron ;  for 
if  the  iron  is  suspended,  and  the  needle  approached  to  it,  the  iron  is  attracted 
by  either  end  of  the  needle.  If,  however,  a  magnet  is  approached  to  the  needle, 
-j-  to  — ,  there  is  attraction ;  if  —  to  —  or  -|-  to  -f->  there  is  repulsion. 

If  the  unlike  poles  of  two  equal  magnetic  bars,  tufted  with  iron  filings,  are 
approached,  the  tufts  join  in  a  festoon ;  but  if  the  poles  are  of  the  same  name, 
most  of  the  filings  fall.  For  the  same  reason,  if  a  magnetic  bar,  B,  fig.  529,  is 

529 


slid  upon  another  bar,  A,  of  equal  power  to  B,  as  the  two  opposite  ends  approach 
each  other,  the  key,  previously  suspended,  falls,  because  the  two  bars  mutually 
neutralize  each  other  by  the  opposing  action  of  the  austral  and  boreal  magnetism. 

781.  Magnetism  by  contact. — When  a  mass  of  iron,  or  of  any 
magnetizable  body,  is  placed  in  contact  with  a  magnet,  it  receives  mag- 
netism throughout  its  mass,  and  of  the  same  name  as  the  pole  with 
which  it  is  in  contact.  Thus,  in  fig.  530,  the  soft  iron  key  is  sustained 
by  the  north  pole  of  a  magnetic  bar ;  a  second  key,  a  nail,  a  tack,  and 
some  iron  filings,  are,  in  succession,  also  sustained  by  the  magnetism 
imparted  by  contact  from  the  bar  magnet  through  the  soft  iron.  The 
series  of  soft  iron  rings,  in  fig.  531,  is  sustained  from  the  bar  magnet 
under  the  same  conditions  of  polarity.  Tested  by  a  delicate  needle, 


ELECTRICITY.  513 

every  part  of  the  sustained  masses  will  manifest  only  north  polarity,  and 
we  may  regard  them  as  only  prolongations  of  the  original  pole.  This  is 
analogous  to  electrical  conduction.  530 

Pure  soft  iron  receives  magnetism  sooner  and  more  power- 
fully than  steel  or  cast  iron,  and  also  parts  with  it  sooner. 
Hardened  steel  and  hard  cast  iron  retain  more  or  less  of  the 
magnetic  force  permanently.  No  other  metals  beside  iron, 
nickel,  cobalt,  and  possibly  manganese,  can  receive  and  retain 
magnetism  by  contact.  531 

These  are,  therefore, 
called  the  magnetic 
metals. 

782.  Magnetism  in 
bodies  not  ferrugin- 
ous.— Beside  the  mag- 
netic metals,  so  called, 
Cavallo  has  shown  that 
the  alloy,  brass,  becomes 
magnetic  (slightly)  by 
hammering,    but    loses 

that  property  again  by  heat.  Some  minerals  are  magnetic,  particu- 
larly when  they  have  been  heated.  The  pure  earths,  and  even  silica, 
are  found  to  have  the  same  property.  In  the  case  of  silica,  and  some 
other  minerals  containing  oxyd  of  iron  in  combination,  this  is  not  so 
surprising.  M.  Biot  determined  in  the  case  of  two  specimens  of  mica, 
one  from  Siberia  (muscovite),  and  the  other  from  Zinnwald  (lithia  mica), 
that  their  magnetic  powers  were  (by  the  method  of  oscillations)  as  6'8 
to  20,  and  he  remarked,  if  the  oxyd  of  iron  be  the  cause  of  their  magnetic 
virtue,  it  should  exist  in  the  minerals  in  the  above  proportion  ;  and  curi- 
ously enough,  the  result  of  Vauquelin's  analyses  (then  unknown  to  M. 
Biot)  corresponded,  almost  exactly,  to  these  numbers. 

Some  states  of  chemical  combination,  however,  appear  to  destroy,  or  cloak, 
the  magnetic  virtues  of  iron ;  e.  g.  an  alloy  of  iron,  one  part,  with  antimony 
four  parts,  was  found  by  Seebeck  to  be  utterly  devoid  of  magnetic  action  ;  and  the 
magnetic  power  of  nickel  is  entirely  concealed  in  the  alloy  called  German  silver. 

The  researches  of  Faraday  have  shown  matter  of  all  kinds  to  be  subject  to  a 
certain  modified  degree  of  influence  by  magnetism  (§  799.  Diamagnetism). 

II.     MAGNETIC  INDUCTION1  OR  INFLUENCE. 

783.  Induction. — Esrery  magnet  is  surrounded  by  a  sphere  of  mag- 
netic influence,  which  has  been  called  its  magnetic  atmosphere.    Every 
magnetizable  substance  within  this  influence  becomes  magnetic  also 
(without  contact),  the  parts  contiguous  to  the  magnet  pole,  having  an 

46 


514  PHYSICS   OP   IMPONDERABLE   AGENTS. 

opposite,  and  those  remote  from  it,  a  similar  name.     This  influence  ia 
called  induction. 

Thus,  in  fig.  532,  the  north  end  of  a  bar  magnet  induces  south  polarity  in  the 
contiguous  ends  of  the  five  bars  surrounding  it,  and  north  polarity  in  their 
remote  ends.  If  these  bars  are  of  hardened  steel,  they  532 

will  retain  a  small  portion  of  the  magnetic  force  induced 
from  a  powerful  bar,  but  if  they  are  of  soft  iron,  they 
will  part  with  their  magnetism  as  soon  as  the  source 
of  excitation  is  withdrawn.  In  this  case,  the  magnetized 
bars  have  a  tendency  to  move  up  to  the  magnet,  and  are 
prevented  from  doing  so  only  by  friction  and  gravity. 
The  attraction  is  reciprocal,  and  we  hence  infer  that 
there  is  induction  in  every  case  of  magnetic  attraction. 

In  the  iron  filings,  arranged  in  magnetic  curves,  fig. 
526,  on  a  glass  plate,  or  card-board,  the  same  tendency 
is  observed. 

Small  pieces  of  soft  iron  wire  suspended  from  the  ends  of  a  thread  near,  and 
parallel  to  each  other,  when  approached  by  a  bar  magnet,  receive  induced  mag- 
netism, the  farther  ends  diverging  by  mutual  repulsion.  Two  sewing-needles 
thus  suspended  and  influenced,  become  permanent  magnets. 

The  ingenuity  of  the  teacher  will  furnish  many  pleasing  and  instructive  illus- 
trations of  magnetic  induction. 

784.  Theoretical  considerations. — The  real  nature  of  the  magnetic 
force  is  unknown  to  us ;  but  the  analogies  offered  by  electro-magnetism 
and  magneto-electricity,  lead  to  the  conviction  that  it  is  one  mode 
of  electrical  excitement.     Unlike  light,  heat,  and  statical  electricity, 
magnetism  affords  no  phenomena  immediately  addressed  to  the  senses. 
It  is  distinguished  from  statical  electricity  chiefly  by  its  permanent 
character  when  once  excited,  and  by  the  very  limited  number  of  sub- 
stances capable  of  receiving  and  manifesting  it. 

785.  Theory  of  two  fluids. — It  may  be  assumed  that  there  are  two 
magnetic  or  electrical  fluids  (the  Boreal  or  positive,  and  the  Austral  or 
negative),  which  are  in  a  state  of  equilibrium  or  combination  in  all 
bodies  ;  that  in  iron,  nickel,  &c.,  these  two  forces  are  capable  of  sepa- 
ration, by  virtue  of  the  inductive  influence  of  the  earth,  or  of  another 
magnet,  while,  in  other  bodies,  this  permanent  separation  cannot  be 
effected.     The  two  magnetic  forces  are  never  seen  isolated  from  each 
other,  but  are  always  united  in  one  bar.     Hence,  we  cannot  have  a 
boreal  magnet,  or  an  austral  magnet,  as  we  may  in  statical  electricity 
produce,  at  pleasure,  vitreous  or  resinous  excitement  over  the  whole 
surface  of  a  body.     Both  poles  must  coexist  in  every  magnet.     If  we 
break  a  magnetic  bar  at  its  neutral  point,  we  have  two  magnets  of 
diminished  force,  but  each  half  has  its  two  poles  like  the  original  bar, 
and  its  neutral  point  also.     The  anomalous  magnets,  figs.  527,  528,  will 
render  this  statement  intelligible.     Every  magnet  must,  in  this  view, 


ELECTRICITY.  515 

be  regarded  as  an  assemblage  of  numberless  small  magnets,  every 
molecule  of  steel  having  its  own  poles  antagonistic  to  those  of  the  next 
contiguous  particle.  This  conception  is  rendered  clearer  to  the  senses 
by  fig.  533.  Here  the  N  and  S  poles  533 

of  the  several  particles  are  each  re- 


presented as  pointing  one  way  re-  r=S^=Sf=SN=SFS!=S^=SI=^' 
spectively,  and  towards  the  N  and  S  n  s  n  s  n  s  n  s  n  s  n  s  n  s  n  s 
ends  of  the  bar.  These  opposing  forces,  therefore,  constantly  increase 
from  the  centre  or  neutral  point,  where  they  are  in  equilibrium,  to  the 
ends,  where  they  find  their  maximum.  This  arbitrary  illustration 
enables  us  to  conceive  how  such  a  body  may  excite  similar  manifesta- 
tions of  power  in  another,  without  itself  being  weakened,  and  how 
each  part  becomes  a  perfect  magnet,  if  the  bar  is  broken.  The  experi- 
ment shown  in  fig.  529,  illustrates  well  the  reunion  of  the  two  fluids, 
to  form  the  neutral  state  of  the  undecomposed  influence. 

De  Haldat  has  shown  that  a  brass  tube,  filled  with  iron  filings,  confined  by 
screwed  caps  of  brass,  can  be  magnetized  by  any  of  the  modes  used  for  bars, 
and  have  its  poles  and  neutral  point  like  a  bar  magnet;  but  if,  by  concussion, 
the  particles  of  iron  are  disarranged,  the  magnetic  force  diminishes,  and  finally 
disappears. 

The  magnetic  pastes  of  Dr.  Knight  and  of  Ingenhausz,  also  illustrate  the  fact, 
that  little  particles  of  magnetic  iron,  or  of  pulverized  lodestone,  may  determine 
the  existence  of  the  magnetic  poles,  and  a  neutral  line,  when  they  are  compacted 
into  a  mass,  by  drying  oils,  or  by  the  use  of  some  gummy  substance. 

Even  so  small  a  quantity  as  one-sixth  of  ferruginous  particles,  in  five-sixths 
of  sand  or  earthy  matter,  can  be  magnetized  as  a  bar,  showing  clearly  the  de- 
composition of  the  neutral  fluid  in  each  particle. 

786.  Coercitive  force. — The  resistance  which  most  substances  show 
to  the  induction  of  magnetism,  has  been  distinguished  by  the  term  co- 
ercitive  force.    In  soft  iron,  this  force  may  be  regarded  as  at  a  minimum, 
since  this  substance  will  receive  magnetic  influence  even  from  being 
placed  in  the  line  of  magnetic  dip,  while  in  steel  which  has  been  hard- 
ened, a  peculiar  manipulation  is  required  to  induce   any  permanent 
magnetism.     Soft  iron  parts  with  its  induced  magnetism  as  readily  as 
it  receives  it ;  but,  if  it  is  hardened  by  blows,  or  violent  twisting,  or  by 
small  portions  of  phosphorus,  arsenic,  or  carbon  combined  with  it,  a 
portion  of  magnetism  is  permanently  retained  by  it  from  induction. 

As  blows,  by  hardening,  may  induce  permanent  magnetism  in  soft  iron,  so,-  in 
steel,  the  coercitive  force  may,  by  simple  vibration,  as  by  blows  on  a  magnetic 
bar,  or  by  an  accidental  fall,  destroy  a  large  part  of  the  force  developed,  by 
giving  opportunity  to  the  coercitive  force  to  resume  its  supremacy.  In  general, 
whatever  cause  induces  hardness,  increases  the  coercitive  force  ;  and,  conversely, 
it  is  diminished  by  annealing,  or  any  cause  which  results  ir  softening  the  mass. 

III.     TERRESTRIAL  MAGNETISM. 

787.  Magnetic  needle. — Directive  tendency. — A  magnetic  nee- 


516 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


die,  suspended  over  the  poles  of  a  horse-shoe  magnet,  comes  to  rest  in 
the  plane  of  the  poles ;  and,  in  obedience  to  the  fundamental  law  of 
magnetic  attractions,  its  A  and  B  poles 
will  be  opposite  to  the  B  and  A  poles 
of  the  attracting  magnet.  The  sus- 
pended needle,  in  fig.  534,  assumes  its 
position  by  reason  of  the  same  law,  and 
comes  to  rest  with  its  A  pole  toward  the 
N  pole  of  the  earth,  and  its  B  pole  to- 
wards the  south.  All  bar  magnets,  S,- 
having  a  free  motion  in  a  horizontal 
plane,  arrange  themselves  in  this  man- 
ner in  every  part  of  the  earth. 

This  directive  tendency  of  the  magnet  has 
been  known  to  European  nations  since  the 
twelfth  century;  but  was  known,  it  is  said,  to  the  Chinese,  2000  B.  c.  Th« 
earliest  mariner's  compass,  used  by  Syrian  navigators  in  1242,  was  a  common 
sewing-needle,  rendered  magnetic,  thrust  through  a  reed  or  cork,  and  allowed 
to  float  on  water.  (Klaproth.)  This  directive  power  renders  the  compass  in- 
valuable to  the  explorer  of  a  pathless  wilderness,  to  the  surveyor  and  the  miner; 
the  mineralogist  and  the  physicist  also  find  it  indispensable  in  many  researches. 

The  terms  Austral  and  Boreal  have  been  applied  to  the  polarity  of  the  mag- 
netic needle,  in  allusion  to  the  free  Austral  and  Boreal  magnetism  assumed  to 
exist  respectively  in  the  southern  and  northern  regions  of  the  earth.  In  accord- 
ance with  magnetic  law,  the  end  of  the  needle  pointing  north  is  called  Austral, 
and  that  pointing  south,  Boreal.  For  greater  simplicity,  the  mariner's  compass 
is  marked  N  on  that  point  which  turns  to  the  north,  and  conversely ;  but  the 
terms  austral  and  boreal  may  be  used  interchangeably  with  positive  and  nega- 
tive, or  north  and  south  polarity. 

The  mariner's  compass  is  arranged  in  a  box  (K,  fig.  535)  called  a 
535  536 


binnacle,  illuminated  at  night  through  the  glass,  M.     The  magnetic 


ELECTRICITY.  517 

needle,  a  b,  fig.  536,  delicately  poised  on  a  socket  of  agate,  is  attached 
to  the  lower  side  of  a  card  or  plate  of  mica,  t,  on  which  is  printed  the 
star  of  thirty-two  points, — seven  between  each  two  of  the  cardinal 
points,  N.,  E.,  S.,  and  W.  The  compass-box,  00,  is  hung  on  points 
called  gimbals,  c  d  c  z  (pronounced  gimbles),  which  allow  it  to  remain 
always  horizontal,  however  the  ship  may  roll.  The  transom  or  cross- 
sights,  A,  may  be  placed  at  pleasure  on  the  face,  m,  of  the  compass, 
wheii  the  object  is  to  measure  points  on  the  coast.  Both  parts  of  the 
figure  are  similarly  lettered. 

The  astatic  needle  is  an  instrument  in  which  the  directive  tendency  of 
the  earth's  magnetism  is  neutralized,  by  placing  two  equal  needles,  a  b,  b'  a', 
fig.  537,  parallel,  one  above  the  other,  with  their  unlike  poles  537 

opposed  to  each  other.  This  system  is  suspended  by  a  fibre 
of  raw  silk,  and  is  a  most  sensitive  test  for  feeble  magnetic 
curreiits.  Such  is  the  construction  adopted  in  the  galvani- 
scope,  to  be  hereafter  described.  The  two  needles  must  be 
of  exactly  equal  force,  or  a  b  and  a'  b'  will  not  neutralize 
each  other,  and  the  system  will  have  a  directive  tendency, 
equal  to  any  difference  of  force  in  the  two  needles. 

The  most  simple  astatic  needle  is  made  by  touching  a  steel 
sewing-needle,  at  its  centre  of  weight,  by  the  N.  pole  of  a 
powerful  magnet ;  the  point  touched  develops  two  S.  poles, 
and  the  two  ends  are  N.  Such  a  needle  is  very  nearly  astatic. 

788.  Magnetic  meridian — declination  or  variation. — There  are 
but  few  places  in  the  world  where  the  magnetic  needle  points  to  the 
true,  or  astronomical  North ;  and  in  all  other  places,  a  plane  passing 
through  the  axis  of  the  magnetic  needle  (the  magnetic  meridian),  fails 
to  coincide  with  the  geographical  meridian.  Moreover,  the  magnetic 
meridian  in  any  given  place  is  not  constant,  but  changes  slowly  from 
year  to  year  (called  secular  variation],  being  now  on  the  E.,  and  again 
on  the  W.  side  of  the  true  North.  This  is  called  the  declination  or 
variation  of  the  magnetic  needle.  The  declination  is  called  Eastern, 
or  Western,  according  as  it  may  be  to  the  East  or  to  the  West  of  the 
astronomical  meridian.  The  angle  formed  by  the  meeting  of  the  true 
and  the  magnetic  meridians  is  called  the  angle  of  declination.  Thus, 
at  Washington  City,*  the  angle  of  declination  in  1855-6,  was  2°  36'  W., 
and  at  New  Haven  it  was  6°  37X'9  W.,  August  12,  1848.  Js.  Ruth, 
observer. 

Columbus,  in  his  first  voyage  to  America,  found  the  needle  to  have,  as  he 
sailed  westwards,  an  increasing  variation  from  the  true  North,  a  circumstance 
not  before  observed,  and  which  caused  the  greatest  consternation  in  his  super- 
stitious crew,  "  who  thought  the  laws  of  nature  were  changing,  and  that  the 
compass  was  about  to  lose  its  mysterious  power."  (Irving's  Columbus.)  Not- 

*  U.  S.  Coast  Survey  Report,  1858,  196.     C.  A.  SOHOTT,  Observer. 
46* 


518  PHYSICS    OF    IMPONDERABLE    AGENTS. 

withstanding  these  and  other  similar  observations,  it  was  not  until  the  middle 
of  the  seventeenth  century,  that  the  variation  of  the  compass  was  an  established 
fact  in  magnetic  science.  The  observations  on  the  declination  cf  the  compass 
in  England,  date  from  1580.  The  following  table,  from  Harris,  contains  the 
declination  with  the  mean  rate  of  motion,  as  referred  to  certain  periods  of  obser- 
vation in  London,  between  1580  and  1850,  or  about  two  hundred  and  seventy 
years.  Eastern  declination  being  distinguished  by  the  negative  sign,  and  west- 
ern by  the  positive  sign. 

Eastern  Declination.         Zero.  Western  Declination. 

Years,  1580.       1622     1660,     1692.  1730.        1765          1818          1850 

Declination,  —11°  15'  —6°  0  -f  6°  +13°  +20°  -f  24°  41'  -f  22°  30' 
Rate  per  year,  7'  8'  10'  11'  ll'-5  9'  0'  5' 

Thus,  in  a  period  of  eighty  years  from  the  first  observation,  the  needle  gradu- 
ally reached  the  true  meridian,  and  then,  for  a  period  of  one  hundred  and  fifty- 
eight  years,  it  moved  Westward,  reaching  its  maximum  Westerly  declination  in 
1818,  and  it  is  now  again  slowly  moving  Eastwards.  The  rate  of  this  move- 
ment is  not  uniform,  but  is  greater  near  the  minimum,  and  least  near  the  maxi- 
mum, point  of  declination. 

Observations  since  1700  establish  the  same  facts  in  the  United  States,  at  a 
great  number  of  places.  Thus,  at  Burlington,  Vt.,  in  1790,  the  declination  was 
-f7°-8;  in  1830,  +8°-30  j  in  1840,  -f9°-07  ;  and,  in  1860,  -flO°-30.  In  Cam- 
bridge, Mass.,  in  1700,  it  was  -|-90-9,  and  steadily  diminished  to  1790,  when  it 
was  -j-6°'9,  and  has  since  regularly  increased  to  the  present  time,  being,  in 
1855,  -f-10°-90.  At  Hatborough,  Pa.,  in  A.  D.  1680,  the  declination  was  -f  8°-5 ; 
in  1800  it  had,  by  a  regular  rate,  decreased  to  -f  1°'8,  and,  in  1860,  was  -f-5°-32. 
At  Washington,  D.  C.,  it  was  -f-0'6  in  A.  D.  1800,  and  in  1860  had  increased  to 
-|-20-9. 

South  of  Washington,  the  declination  is  uniformly  Easterly,  ranging,  at 
Charleston,  S.  C.,  from  —3° -7  in  A.  D.  1770,  to  — 1°-7  in  1860.  On  the  Western 
Coast  of  North  America,  it  is  also  Easterly ;  being,  for  example,  at  San  Fran- 
cisco, in  1790,  — 13°-6,  and  in  1860,  — 15-°8.  The  annual  change  (increasing  E. 
declination)  being,  in  1840,  — 1'-6  ;  in  1850,  — 1'-2  j  and  in  1860,  — 0'-8. 

For  a  full  discussion  of  Magnetic  Declination  in  the  United  States,  the  stu- 
dent will  refer  to  the  Reports  of  the  United  States  Coast  Survey  ;  and  for  an 
able  extract  of  all  the  results  of  secular  change  on  the  Atlantic,  Gulf,  and  Pa- 
cific Coasts  of  the  United  States,  refer  to  a  "  Report  by  Assistant  Charles  A. 
Schott,"  in  Am.  Jour.  Sci.  [2]  XXIX.,  p.  335. 

The  first  attempt  to  systematize  the  variations  of  the  magnetic  needle, 
and  to  connect  by  lines,  called  isogonic  lines,  all  those  places  on  the 
earth  where  the  declination  was  similar,  was  made  by  Halley,  about 
1700.  He  thus  discovered  two  distinct  lines  of  no  inclination,  called 
agonic  lines,  one  of  which  ran  obliquely  over  North  America  and  across 
the  Atlantic  Ocean,  and  another  descended  through  the  middle  of  China 
and  across  New  Holland ;  and  he  inferred  that  these  lines  communi 
cated  near  both  poles  of  the  earth. 

789.  Variation  chart.— Isogonal  lines.— In  fig.  538,  is  seen  a 
projection  of  the  lines  of  equal  and  no  decimation,  on  a  Mercator's 
chart  of  the  earth,  embracing  observations  down  to  1835.  The  Ameri- 


ELECTRICITY. 


519 


can  line  of  no  variation,  or  agone,  crosses  the  eastern  point  of  South 
America,  in  latitude  20°  S.,  skirts  the  Windward  Antilles,  enters  North 

538 


140  120  100  80  60   40  20   0   20  40  60   80  100  120  140  160 


140  120  100  80  60   40  20   0  20  40 


100  120  140  160 


Carolina  near  Cape  Lookout,  and  passing  through  Staunton,  in  Vir- 
ginia, crosses  Lake  Erie  midway  on  its  course  to  Hudson's  Bay.  The 
chief  Asiatic  agone  (for,  in  fact,  there  are  two  lines  of  no  variation), 
after  traversing  the  Indian  Ocean  in  a  southerly  direction,  crosses  the 
western  part  of  New  Holland  near  120°  E.  All  the  entire  lines  on  this 
chart  indicate  western  declination,  while  the  dotted  lines  mark  eastern 
declination.  According  to  the  theory  of  Gauss,  the  eminent  German 
astronomer,  no  lines  of  equal  variation  can  form  diverging  branches,  or 
be  tangents  to  each  other ;  but  when  there  is  a  space  within  which 
the  declination  is  less  than  outside  any  portion  of  its  limiting  line, 
that  line  must  form  a  loop,  the  two 
branches  intersecting  at  right  angles. 
The  observed  line  of  8°  40'  in  the 
Pacific,  beautifully  illustrates  and 
confirms  this  theoretical  position,  as 
shown  on  the  chart,  fig.  538. 

Figure  539  illustrates  the  circum- 
polar  relations  of  the  corresponding 
lines  of  equal  variation  in  the  north- 
ern hemisphere.  It  will  be  seen 
that  much  the  larger  number  of  the 
isogonal  lines,  converge  on  the  Mer- 
cator's  projection  at  a  point  near 


Baffin's  Bay,  in  lat.  73°'0  N.,  long.  70°'0  W.,  its  opposite  pole  is  to  the 
southward  of  New  flolland. 


520          PHYSICS  OF  IMPONDERABLE  AGENTS. 

Halley's  original  chart  assumes  the  existence  of  two  magnetic  poles  in  each 
hemisphere,  one  fixed,  and  the  other  revolving  about  it  in  a  certain  period. 
Hansteen,  in  1828,  in  his  well-known  chart,  accepts  the  same  view.  By  Gauss's 
theory  of  terrestrial  magnetism,  only  one  magnetic  pole  in  each  hemisphere  is 
required,  and  thus  far  observation  has  shown  a  wonderful  conformity  between 
the  theory  of  Gauss  and  the  facts. 

790.  Daily  variations  of  the   magnetic    needle. — Besides   the 
great  secular  movements  of  the  magnetic  needle  already  noticed  (788), 
it  is  found  to  vary  sensibly  from  day  to  day,  and  even  with  the  different 
periods  of  the  same  day.     The  most  refined  means  have  been  in  our 
time  applied  to  the  exact  investigation  of  this  phenomenon,  first  noticed 
by  Graham,  a  London  optician,  in  1722.     It  has  been  shown  that  the 
north  pole  of  the  needle  begins  between  seven  and  eight  A.  M.  to  move 
westward,  and  this  movement  continues  until  one  p.  M.,  when  it  becomes 
stationary.     Soon  after  one  o'clock  it  slowly  returns  eastward,  and  at 
about  ten  p.  M.,  the  needle  again  becomes  stationary  at  the  point  from 
which  it  started.   During  the  night,  a  small  oscillation  occurs,  the  north 
pole  moving  west  until  three  A.  M.,  and  returning  again  as  before.    The 
mean  daily  change,  as  observed  by  Capt.  Beaufoy,  is  not  quite  one 
degree.     This  daily  disturbance  of  the  magnetic  needle  is  undoubtedly 
due  to  the  action  of  the  sun,  and  it  will  therefore  vary  in  different  lati- 
tudes.    In  the  Southern  hemisphere,  the  daily  oscillations  are  of  course 
reversed  in  direction  to  those  of  the  Northern  hemisphere. 

The  annual  variation  of  the  needle  was  discovered  by  Cassini,  in  1786. 
We  have,  therefore,  1st,  the  great  secular  variations,  continued  through  long 
periods  of  time;  2d,  annual  variations,  conforming  to  the  movement  of  the  sun 
in  the  solstices ;  3d,  daily  variations,  conforming  nearly  to  the  perfods  of  maxi- 
mum and  minimum  temperature  in  each  day,  and  lastly,  irregular  variations, 
connected  with  the  aurora  borealis,  or  other  cosmical  phenomena,  which  Hum- 
boldt  has  called  magnetic  storms. 

791.  Dip  or  inclination. — A  needle,  hung  as  in  fig.  540,  within  a 
stirrup  upon  the  points  a  6,  the  whole  system  being  suspended  by  a 
thread,  will,  before  magnetizing,  if  carefully  adjusted,  stand  in  any 
position  in  which  it  may  be  placed.     If  now  the  needle  be  magnetized, 
it  forthwith  assumes  the  position  seen  in  the  figure,  its  pole  dipping 
toward  the  North  pole  of  the  earth.     In  this  latitude  (41°  W),  the  dip 
was,  in  1848,  73°  31X'9.     Such  a  needle  is  called  a  dipping  needle,  and 
if  constructed  as  in  the  figure,  it  shows  both  the  declination  and  dip,  or 
inclination,  of  terrestrial  magnetism  for  any  given  locality.     As  the 
whole  system  is  free  to  move,  it  will  obviously  arrange  itself  in  the 
magnetic  meridian,  and  its  position  of  equilibrium  will  be  the  resultant 
of  the  two  forces  of  declination  and  dip.     Approaching  the  equator, 
the  dipping  needle  becomes  constantly  less  and  less  inclined,  until  at 


ELECTRICITY. 


521 


last  a  point  is  found  where  it  is  quite  horizontal,  and  this  point  will  be 
in  the  magnetic  equator;  an  imaginary  plane  near,  but  not  coincident 
with,  the  equator  of  the  earth.  540 

The  discovery  of  the  magnetic  dip  or  inclination, 
was  made  in  1576,  by  Robert  Norman,  a  practical 
optician  of  London,  who  constructed  the  first  dipping 
needle,  by  which  he  determined  the  dip  at  London  at 
that  time  to  be  nearly  72°.  The  magnetic  dip,  like 
the  declination,  is  subject  to  continual  and  progres- 
sive changes,  both  secular  and  periodical,  and  it  is 
at  this  moment  rapidly  decreasing.  Thus  at  London 
in  1576  it  was  71°  50',  in  1676  it  had  become  73°  30', 
and  in  1723  it  was  74°  42',  having  then  reached  its 
maximum.  In  1790  it  had  decreased  to  71°  3',  and 
in  1800  to  70°  35'.  Sabine,  in  1821,  fixed  it  at  70°  3', 
and  Kater,  in  1830,  at  69°  88'.  It  is  now,  in  England, 
about  68°  30',  having  decreased  in  128  years  about 
6°  12',  or  at  the  rate  of  nearly  3'  yearly,  the  mean 
annual  movement  from  1830  to  1850  being  at  the 
rate  of  more  than  4'  yearly,  while  between  1723  and 
1790  it  was  about  2-5'  yearly,  showing  an  accelerated 
and  retarded  movement  in  the  secular  changes  of  the 
dipping  needle,  or  magnetic  inclination. 

792.  The  action  of  the  earth's  magnet- 
ism on  the  dipping  needle  is  neatly  illustrated 

by  the  simple  arrangement  seen  in  fig.  541,  where  the  magnetic  bar  sn, 
is  placed  horizontally  on  the  diameter  of  a  semicircle,  representing  an 
arc  of  the  meridian,  on  which  a  small  dipping  needle  is  made  to 
occupy  successively  the  position  541 

seen  at  a,  a/,  a//,  a"'. 

At  a',  the  needle  is  horizontal, 
being  at  the  magnetic  equator,  and 
equally  acted  on  by  both  poles.  In 
every  other  position,  the  influence 
of  one  pole  must  predominate,  to  a 
greater  or  less  extent,  over  the  other. 
Several  sewing-needles,  suspended 
over  a  magnetic  bar  at  equal  dis- 
tances, one  over  each  end,  one  over 
the  centre,  and  one  intermediate,  will 
illustrate  the  same  point  satisfac- 
torily. 

793.  Dipping  needle. — The  dipping  needle  of  Biot,  shown  in  fig. 
542,  is  wholly  of  brass,  and  embraces  two  graduated  circles,  m  and  M, 
one  horizontal  and  one  vertical.     The  circle,  M,  with  its  supporting 
frame,  A,  moves  in  azimuth  over  m,  by  which  it  is  placed  in  the 
magnetic  meridian.     It  is  leveled  by  the  level,  n,  adjusted  by  three 


522 


PHYSICS    OP   IMPONDERABLE    AGENTS. 


542 


milled  heads  in  the  feet.  The  needle,  a  b,  is  suspended  on  the  bars, 
r.  To  fix  the  magnetic  meridian  by  this  instrument,  the  circle,  m,  is 
revolved  until  the  needle, 
a  6,  stands  vertical  and 
points  to  90°,  it  is  then 
in  the  magnetic  equator, 
a  position  of  course  ex- 
actly 90°  from  the  mag- 
netic meridian,  which  is 
then  obtained  by  revolv- 
ing the  frame,  A,  90° 
backwards.  The  angle, 
a  c  dy  is  the  angle  of  in- 
clination (or  dip),  and  is 
read  on  the  arc  M. 

Two  small  errors  of  ob- 
servation exist  in  this  in- 
strument ;  1st,  from  the  fact 
that  the  magnetic  axis  of 
the  needle  does  not  coincide 
with  the  axis  of  its  form, 
and  2d,  from  the  circum- 
stance that  the  centre  of 
gravity  of  the  needle  does 
not  lie  in  the  points  of  sus- 
pension, and  that  therefore  the  angle,  d  c  a,  is  greater  or  less  than  the  true 
angle  of  inclination,  by  a  very  small  quantity.  The  first  is  corrected  by 
reversing  the  plane  of  the  instrument,  by  a  revolution  of  180°,  and  taking  the 
mean  of  the  two  readings ;  the  second,  by  reversing  the  polarity  of  the  needle 
by  touch  on  the  opposite  poles  of  two  bar  magnets,  provided  for  the  purpose. 
By  this  means,  the  centre  of  gravity  is  brought,  first  above,  and  then  below 
the  point  of  suspension,  and  the  mean  of  the  two  readings  is  the  true  angle 
sought. 

794.  Inclination  map,  or  isoclinal  lines. — In  fig.  543,  is  pre- 
sented a  Mercator's  projection  of  the  line  of  no  dip,  or  magnetic 
equator,  and  the  position  of  the  isoclinal  lines  of  30°,  50°,  70°,  80°,  and 
85°  north,  and  30°,  50°,  and  70°  south.  It  will  be  noticed  that  the 
magnetic  is  below  the  terrestrial  equator,  in  all  the  western  hemis- 
phere, and  is  above  it  in  the  eastern,  crossing  it  near  the  island  of  St. 
Thomas,  in  longitude  3°  E.,  and  again  in  the  Pacific  ocean.  These 
points  of  intersection  of  course  vary  with  the  progressive  changes  of 
the  magnetic  dip.  The  greatest  declination  of  the  magnetic  equator 
from  the  equinoctial  line,  amounts  to  about  20°  N.,  near  53°  E.  longi- 
tude, and  its  greatest  southern  declination  is  13°,  in  about  40°  W. 
longitude,  near  the  bay  of  Bahia,  on  the  East  coast  of  South  America. 


ELECTRICITY. 


523 


The  inclination  of  the  needle  at  any  place  is,  approximately,  twice 
its  magnetic  latitude.     (Kraft.) 

543 

160    140   120~80 60      40      20~  6 


Figure  544  shows  the  relation  of  the  isoclinal  lines  of  80°  and  85°  in 
the  northern  hemisphere,  to  the  lines  of  latitude,  and  to  the  N.  magnetic 
pole,  near  Baffin's  Bay.  Sir  James  544 

Ross,  in  1832,  found  the  needle  to 
dip  near  Prince  Regent's  Inlet,  lat. 
70°  N.,  longitude  96°  N.,  within  one 
minute  of  90°. 

It  is  to  be  observed,  that  the  lines 
of  equal  magnetic  inclination  (isocli- 
nal lines),  are  found  to  approach  in 
position,  with  very  considerable  con- 
formity, to  the  isothermal  lines,  or 
lines  of  equal  temperature,  thus  indi- 
cating a  close  relation  between  the 
earth's  magnetism  and  the  distribu- 
tion of  the  terrestrial  heat. 

795.  Magnetic  intensity. — It  is  plain,  from  the  phenomena  of  the 
magnetic  declination  and  dip  already  considered,  that  the  distribution 
of  magnetic  force  over  the  earth  is  unequal,  although  in  general  it  is 
most  active  about  the  poles,  and  least  so  about  the  equator.  The  ques- 
tion arises,  how  may  the  magnetic  intensity  at  any  given  point  of  the 
earth  be  determined  ?  This  question  is  answered  by  the  use  of  the 
needle  of  oscillation.  A  large  number  of  facts  serve  to  show,  that  a 
freely  suspended  needle  in  a  state  of  oscillation,  is  influenced  by  the 


524  PHYSICS    OF   IMPONDERABLE    AGENTS. 

magnetic  force  of  the  earth,  in  a  way  analogous  to  that  of  a  common 
pendulum,  oscillating  by  the  influence  of  gravity ;  and  that  hence  by 
means  of  such  a  needle,  we  may  determine  the  ratio  of  the  intensity 
of  terrestrial  magnetic  force  throughout  the  whole  extent  of  the  earth's 
surface. 

This  mode  of  determining  the  magnetic  intensity  in  different  regions  of  the 
earth,  was  first  suggested  by  Graham,  in  1775,  and  was  afterwards  more  fully 
perfected  and  employed  by  Coulomb,  Humboldt,  Hansteen,  and  Gauss.  Hum- 
boldt  carefully  determined  the  time  of  a  given  number  of  oscillations  of  a  small 
magnetic  needle,  first  at  Paris,  and  afterward  in  Peru.  At  Paris,  the  needle 
made  two  hundred  and  forty -five  oscillations  in  ten  minutes  :  in  Peru,  it  made 
only  two  hundred  and  eleven  in  the  same  time.  The  relative  intensities  were 
therefore  as  the  square  of  these  two  numbers,  or  as  1  :  1-3482,  which,  assuming 
the  point  on  the  magnetic  equator  in  Peru  as  unity,  will  give  the  magnetic 
intensity  at  Paris  as  1-3482.  This  kind  of  observation  has  since  been  extended 
to  nearly  every  known  part  of  the  globe,  and  full  tables  have  been  published, 
giving  the  results.  Thus  the  intensity  at  Rio  de  Janeiro  is  0-887  j  Cape  of  Good 
Hope,  0-945;  Peru,  1-;  Naples,  1-274;  Paris,  1-348;  Berlin,  1-364;  London, 
1-369;  St.  Petersburg,  1-403;  Baffin's  Bay,  1-707. 

The  most  complete  statement  of  the  results  of  American  observations  on  the 
magnetic  elements  has  lately  been  published  by  Dr.  A.  D.  Bache,  in  Am.  Jour. 
Sci.  [2]  XXIV.,  p.  1,  where  all  the  earlier  observations  are  collated,  with  the 
more  extended  results  of  the  Coast  Survey,  with  maps. 

796.  Isodynamic  lines,  or  lines  of  equal  power,  are  such  as  con- 
nect places  in  which  observations  show  the  magnetic  intensity  to  be 
equal.  These  lines  are  not  always  parallel  to  the  isoclinal  lines? 
although  nearly  so,  and  the  points  of  greatest  and  least  intensity  are 
not  exactly  identical  with  the  points  of  greatest  and  least  inclination. 
Hence  the  intensity  of  the  magnetic  equator  may  not  be  everywhere  the 
same.  These  lines  are  probably  curves  of  double  curvature  returning 
into  themselves,  implying  the  existence  of  two  intensity  poles,  the 
western,  near  Hudson's  Bay,  in  lat.  50°  N.,  Ion.  90°  W ;  and  the  eastern 
or  Siberian  pole,  about  70°  N.,  and  Ion.  120°  E.  The  two  southern 
poles  have  been  placed,  one  to  the  south  of  New  Holland,  in  lat.  60° 
S.,  Ion.  140°  E. ;  the  other,  in  the  South  Pacific,  also  in  lat.  60°  S.,  but 
Ion.  120°  W.  These  four  poles  are  not  therefore  diametrically  opposite 
to  each  other. 

The  terrestrial  magnetic  force  increases  toward  the  south  pole,  nearly  in  the 
ratio  of  1  :  3,  and  as  both  the -maximum  and  minimum  magnetic  intensity  on 
the  globe  are  found  in  the  southern  hemisphere,  it  would  appear  that  the  ratio 
of  1  :  3  expresses  very  nearly  the  maximum  and  minimum  magnetic  force  of  the 
whole  earth.  From  the  profound  inquiries  of  Gauss,  it  appears  that  the  absolute 
terrestrial  magnetic  force,  considering  the  earth  as  a  magnet,  is  equal  to  six 
magnetic  steel  bars  of  a  pound  weight  each,  magnetized  to  saturation,  for  every 
cubic  yard  of  surface.  Compared  with  one  such  bar,  the  total  magnetism  of  the 
earth  is  as  8,864,000,000,000,000,000,000:  ),  a  most  inconceivable  proportion. 
(Harris  ) 


ELECTRICITY. 


525 


797.  The  inductive  power  of  the  earth's  magnetism  is  mani- 
fested by  the  polarity  developed  in  any  bar  of  soft  iron,  or  of  steel, 
placed  in  an  erect  position,  as  in  fig.  545,  or  better,  in  the  angle  of  the 
dip  of  the  place.     The  end  of  the  bar  toward  the  earth  is  always 
Austral,  Boreal  magnetism  existing  at  the  upper  end,  B,  and  a  neutral 
point  at  the  centre,  M.     These  facts  are  demonstrated  by  the  action  of 
a  small  needle,  held  in  the  hand  at  the  three  545 
positions,  shown  in  the  figure.     If  the  experi- 
ment were  made  in  the  southern  hemisphere, 

the  polarity  would  be  reversed. 

For  this  reason,  all  masses  of  iron  standing  in  a 
vertical  position  become  magnetic.  In  soft  iron  this 
magnetism  is  transient,  but  in  steel  tools,  especially 
such  as  are  subject  to  vibration,  as  drills,  the  mag- 
netism developed  is  permanent. 

Barlow  found  that  globes  of  iron,  like  bomb  shells, 
a  foot  or  more  in  diameter,  become  miniature  copies 
of  the  earth  by  virtue  of  the  inductive  force  exerted 
upon  them  by  the  earth's  magnetism ;  having  a  mag- 
netic axis  in  the  line  of  dip  at  the  place  of  experiment, 
and  an  equator  at  right  angles  to  their  axis.  Delicate 
needles,  poised  on  the  equatorial  line  of  such  globes, 
suffered  no  disturbance,  while  in  any  other  position 
on  the  sphere,  both  declination  and  dip  were  mani- 
fest. 

Barlow   further   discovered,    that  such   a   sphere 
of  iron,  placed  in   a  certain  relation  to  a  compass 
needle  on  board  a  ship,  united,  and  harmonized   the  local  attractions  of  the 
ship's  iron,  so  as  to  free  the  compass  from  the  effects  of  such  disturbing  causes. 

798.  System  of  simultaneous   magnetic   observations. — The 

distinguished  Prussian  philosopher,  Alex.  v.  Humboldt,  in  1836,  pro- 
posed to  the  scientific  world  to  set  on  foot  a  series  of  connected  and 
simultaneous  observations,  to  be  made  over  as  large  a  portion  of  the 
earth's  surface  as  possible,  for  the  purpose  of  establishing  the  laws 
relating  to  the  magnetic  forces. 

In  accordance  with  this  suggestion,  the  leading  governments  of  Europe 
(France  excepted),  a.ud  many  of  the  scientific  societies  both  in  the  old  and  nej? 
world,  commenced  such  observations,  with  instruments  specially  contrived  for 
the  purpose,  and  in  buildings  made  without  iron,  both  on  and  beneath  the  earth's 
surface.  Expeditions  were  sent  to  the  Arctic  and  Antarctic  circles,  to  Africa,  to 
South  and  North  America,  and  to  the  Pacific  Ocean,  while  at  numerous  stations 
in  India,  Russia,  Europe,  and  North  and  South  America,  hourly  and  simulta- 
neous observations  have  been  carried  on  for  a  long  period,  and  in  many  places 
are  still  continued.  In  this  way  a  great  mass  of  facts  has  been  accumulated, 
from  a  careful  comparison  of  which  the  laws  of  terrestrial  magnetism  already 
announced  have  beon  educed  or  confirmed. 

Perhaps  the  most  remarkable  result  of  these  observations  is  the  fact,  firat 
47 


526 


PHYSICS    OF    IMPONDERABLE   AGENTS. 


established  by  them,  that  not  only  the  greater  variations  in  the  earth's  magnet- 
ism, but  the  most  minute  and  irregular  disturbances  occur  at  the  same  instant 
in  places  the  most  distant  from  each  other,  showing  a  wonderful  connection  and 
coincidence  in  the  causes  of  these  phenomena  throughout  the  world. 

799.  Lines  of  magnetic  force. — The  illustrious  English  philoso- 
pher, Faraday,  has  demonstrated  that  all  matter  is  subject  to  magnetic 
influence. 

As  the  evidence  on  which  this  important  induction  rests  is  chiefly  derived 
from  the  use  of  electro-magnetism,  its  particular  consideration  is  more  conve- 
niently referred  to  that  subject.  His  general  views,  connected  with  terrestrial 
magnetism,  may  be  thus  stated.  All  space  both  above  and  within  the  limits  of 
our  atmosphere  may  be  regarded  as  traversed  by  lines  of  force,  among  which 
are  the  lines  of  magnetic  force.  The  condition  of  the  space  surrounding  a 
magnet,  or  between  its  poles  (777),  may  be  taken  as  an  illustration  of  this 
assumption.  It  is  not  more  difficult  to  conceive  of  force  existing  without 
matter,  than  the  converse,  and  it  is  certain  that  we  know  matter  chiefly  by  the 
effects  it  produces  on  certain  forces  in  nature.  The  lines  of  magnetic  force  are 
assumed  to  traverse  void  space  without  change,  but  when  they  come  in  contact 
with  matter  of  any  kind,  they  are  either  concentrated  upon  it,  or  dispersed, 
according  to  the  nature  of  the  matter.  Thus  we  know  that  a  suspended  needle 
is  attracted  axially  by  a  magnet,  while  a  bar  of  bismuth,  and  many  other  solid, 
liquid,  or  gaseous  bodies,  similarly  placed  between  the  poles  of  a  magnet,  are 
held  in  a  place  at  right  angles  to  the  axis,  or  equatorially.  Hence  all  substances 
may  be  classified  either  as  those  which,  like  iron,  point  axially,  and  are  called 
PARAMAGNETIC  substances,  and  those  which  point  equatorially,  and  termed 
DIAMAGNETIC.  The  force  which  urges  bodies  to  the  axial  or  equatorial  lines  is 
not  a  central  force,  but  a  force  differing  in  character  in  the  axial  or  radial  direc- 
tions. If  a  liquid  paramagnetic  body  were  introduced  into  the  field  of  force,  it 
would  dilate  axially,  and  form  a  prolate  spheroid ;  while  a  liquid  diamagnetic 
body  would  dilate  equatorially,  and  form  an  oblate  546 

spheroid. 

The  diagram,  fig.  546,  will  serve  to  render  more 
clear  the  action  of  diamagnetic  and  paramagnetic 
substances,  upon  the  lines  of  magnetic  force.  Thus 
a  diamagnetic  substance,  D,  expands  the  lines  of  • 
force,  and  causes  them  to  open  outwards,  while  a  paramagnetic  body,  P,  con- 
centrates these  lines  upon  itself.  Bodies  of  the  first  class  swing  into  the  equator 
of  force,  or  lie  at  right  angles  to  the  lines  of  force,  while  those  of  the  paramag- 
netic class  become  axially  arranged,  parallel  to  the  lines  of  force. 

800.  Atmospheric  magnetism. — The  discovery,  by  Faraday,  of  the 
highly  paramagnetic  character  of  oxygen  gas,  and  of  the  neutral  cha- 
racter of  nitrogen,  the  two  chief  constituents  of  the  atmosphere,  is 
justly  esteemed  a  fact  of  great  impcirtanoe  in  studying  the  phenomena 
of  terrestrial  magnetism.     We  thus  see  two-ninths  of  the  atmosphere, 
by  weight,  consisting  of  a  substance  of  eminent  magnetic  capacity, 
after  the  manner  of  iron,  and  liable  to  great  physical  changes  of  den- 
sity, temperature,  &c.,  and  entirely  independent  of  the  solid  earth.     In 
this  medium  hang  suspended  the  magnetic  bars,  which  are  used  as 


ELECTRICITY.  527 

tests,  and  this  magnetic  medium  is  daily  heated  and  cooled  by  the  sun'a 
rays,  and  its  power  of  transmitting  the  lines  of  magnetic  force  is  thus 
affected,  influencing,  undoubtedly,  those  diurnal  changes  already  con- 
sidered. 

801.  Notions  of  the  origin  of  the  earth's  magnetism. — Two 
hypotheses  have  hitherto  divided  the  opinions  of  philosophers  in  ex- 
plaining the  phenomena  of  terrestrial  magnetism. 

The  older  of  these  views  (Hansteen's)  assumes  the  existence  of  an  indepen- 
dent magnetism  in  the  earth,  with  its  focus,  or  seat,  near  the  earth's  centre. 
This  internal  power  manifests  itself  chiefly  at  four  points  near  the  surface,  two 
of  which,  at  the  opposite  ends  of  the  supposed  magnetic  axis,  are  the  most  ener- 
getic, and  are  known  as  the  magnetic  poles.  The  minor  poles  have  their  own 
independent  axis,  and  move  around  the  principal  axis  from  west  to  east  in  the 
western  hemisphere,  and  the  reverse  in  the  southern,  giving  origin  to  the  well- 
known  phenomena  of  the  secular  variation  of  the  needle.  However  well  this 
hypothesis  met  the  facts  of  terrestrial  magnetism  some  years  since,  the  rapid 
progress  of  our  knowledge  of  magnetic  phenomena,  both  terrestrial  and  general, 
within  a  short  period,  has  material!  changed  scientific  opinion.  The  diurnal 
and  irregular  variations  in  the  magnetic  forces,  cannot  be  explained  upon  Han- 
steen's hypothesis,  and  especially  the  simultaneous  occurrence  of  these  disturb- 
ances at  different  points  of  observation.  Nearly  all  bodies  are  now  known  to  be 
susceptible  to  magnetic  influence,  while  the  maximum  and  minimum  magnetic 
intensity  are  found  in  those  regions  of  the  globe  where  the  minimum  and  maxi- 
mum of  superficial  heat  exist. 

It  is  hence  now  argued,  that  the  crust,  or  surface,  and  not  the  interior  of  the 
earth,  is  the  seat  of  the  magnetic  force.  That  this  force  is  manifested  with  least 
energy  at  the  equator  of  magnetism,  and  with  increasing  power  toward  the 
poles,  where,  as  in  an  artificial  magnet,  it  attains  its  maximum  development, 
because  there  we  find  the  most  perfect  separation  of  the  magnetic  fluids  :  that 
the  coercitive  force  (786)  of  the  materials  of  the  earth's  surface  is  resolved  by 
the  solar  heat,  and  that  the  depth  to  which  this  separation  occurs  is  closely  con- 
nected with  the  mean  heat  of  the  earth's  crust,  if  not  absolutely  dependent  upon 
it.  Axes  and  poles  have,  therefore,  in  view  of  this  hypothesis,  no  existence  in 
fact,  but  are  merely  convenient  mathematical  terms  for  expressing  our  ideas  of 
magnetic  phenomena  more  closely,  just  as  in  crystallography  we  employ  the 
same  terms  for  the  same  reasons. 

In  conformity  to  this  view,  the  manifestation  of  the  magnetic  forces  will  vary 
with  all  the  diurnal  changes  of  temperature,  giving  the  relation  of  cause  and 
effect  between  these  changes,  and  the  magnetic  perturbations.  The  annual  fluc- 
tuations in  the  mean  temperature  of  the  earth's  surface  will,  therefore,  be  repro- 
duced in  corresponding  movements  in  magnetic  declination  and  dip.  Hence, 
the  magnetic  meridian,  and  the  system  of  isoclinal  and  isogonic  curves  ought  to 
correspond  closely,  as  they  do  with  isothermal  lines,  and  the  peculiar  distribu- 
tion of  temperature  in  both  hemispheres.  Indeed,  we  may  assume,  should  this 
hypothesis  prevail,  that  the  differences  now  noticed  between  the  isothermes  and 
isogones  (due,  probably,  to  imperfect  observations),  will  vanish  under  new  and 
more  extended  researches. 

IV.    PRODUCTION  OF  MAGNETS. 

802.  Artificial  magnets  are  produced  (1.)  by  touch,  or  friction  from 


528 


PHYSICS    OP    IMPONDERABLE    AGENTS. 


another  magnet ;  (2.)  by  induction ;  (3.)  by  electrical  currents  ;  and 
(4.)  by  the  solar  rays. 

The  method  by  touch  is  accomplished  by  very  various  modes  of  ma- 
nipulation, of  which  we  shall  describe  only  one  or  two,  referring  the 
reader  to  larger  treatises  on  magnetism  for  fuller  details.  Since  the 
introduction  of  the  method  by  electro-magnetism,  the  old  methods  of 
producing  magnets  by  touch  are  far  less  important  than  formerly. 

The  circumstances  affecting  the  value  of  magnets,  are  chiefly 
the  nature  and  hardness  of  the  steel,  the  form  and  proportion  of  its 
parts,  and  the  mode  of  keeping.  The  most  uniform  and  fine-grained 
cast-steel,  wrought  with  as  little  dis-  547 

turbance  of  its  particles  as  possible, 
forms  the  best  magnets. 

This  is  tempered  as  high  as  possible, 
and  the  temper  is  then  drawn  by  heat  to 
a  violet  straw  color,  at  which  hardness 
it  has  been  found  to  receive  and  retain 
a  maximum  of  magnetism.  The  pro- 
portions of  a  bar  magnet  should  be,  for 
width,  about  one-twentieth  the  length  ; 
and  the  thickness,  one-third  to  one-fourth 
the  width.  In  a  horse-shoe,  the  dis- 
tance between  the  poles  ought  not  to  be 
greater  than  the  width  of  one  of  the 
poles.  The  faces  should  be  smooth  and 
level,  and  the  whole  surface  be  highly 
polished.  It  is  quite  essential  for  pre- 
serving the  power  of  a  magnet,  that  its 
poles  should  be  joined  by  a  keeper  or 
armature  of  soft  iron,  made  to  fit  its 
level  ends,  and  be  suspended,  as  seen  in 
fig.  547.  Thus  armed,  a  magnet  gains 
power ;  but  if  left  unarmed,  it  suffers 
material  loss.  Bar  magnets  are  arranged  as  in  fig.  548,  either  four  magnets 
with  their  opposite  poles  in  contact,  or  two  magnetic  bars,  side  by  side,  with 
two  pieces  of  soft  iron  joining  their  opposite  poles. 

548 


803.  Magnets  by  touch. — Touch  one  pole  of  a  powerful  magnet 
with  one  end  of  a  sewing-needle,  or  the  point  of  a  pen-knife,  and  it 
becomes  instantly  a  magnet,  attracting  iron  filings,  and  repelling  or 
attracting  the  magnetic  needle.  The  coercitive  force  has,  in  this  case. 


ELECTRICITY. 


529 


been  decomposed  by  simple  touch.  If  the  magnet  is  very  powerful,  a 
near  approach  of  the  needle  to  it  without  contact  will  develop  a  feeble 
magnetism  by  induction. 

More  powerful  magnetism  is,  however,  developed  by  drawing  the  bar  to  be 
magnetized,  from  its  centre  to  the  end,  several  times  over  one  pole  of  a  magnet, 
returning  it  each  time  through  the  air,  and  repeating  the  stroke  in  the  same 
direction.  Then  place  the  other  pole  in  the  middle  of  the  bar,  and  stroke  the 
opposite  end  as  before. 

Two  magnets  may  be  placed  together,  with  their  dissimilar  poles  in  the  middle 
of  the  bar,  as  in  fig.  549,  and  then  be  moved  in  opposite  directions,  at  a  low 

549 


550 


angle,  to  the  extremities  of  the  bar.  The  impregnation  of  the  bar  will  be 
more  powerful  and  speedy  if  it  rests  by  its  ends  on  the  two  opposite  ends  of  two 
other  magnets,  as  practiced  by  Coulomb.  By  inspecting  the  letters  in  fig.  549, 
this  arrangement  will  be  quite  clear.  Care  is  taken  to  prevent  the  ends  of  the 
two  inclined  bars  from  touching,  by  placing  a  bit  of  dry  wood  between  them. 
This  is  called  single  touch,  and  is  to  be  explained  in  accordance  with  $  785. 

To  magnetize  a  bar  by  means  of  the  double  touch,  two  bars,  or  horse-shoe 
magnets  are  fastened  together,  with  a  wedge  of  dry  wood  between  them,  so  that 
their  dissimilar  poles  may  be  about  a  quarter  of  an  inch  asunder ;  or  a  horse- 
shoe magnet  may  be  Uvsed  if  its  poles  are  quite  near  together.  The  magnet,  in 
this  mode,  is  placed  upright,  on  the  middle  of  the  bar,  and  is  then  rapidly  drawn 
towards  its  end,  taking  care  that  neither  of  its  poles  glides  over  the  end  of  the 
bar.  The  magnet  is  then  passed  over  the  opposite  end 
of  the  bar  as  before.  The  poles  will  be  dissimilar  to 
those  of  the  touching  magnet. 

804.  Horse-shoe  magnets  are  easily  mag- 
netized by  connecting  the  open  ends  by  a  soft  iron 
keeper,  while  another  horse-shoe  magnet  of  the 
same  size  is  passed  from  the  poles  to  the  bend,  in 
the  direction  of  the  arrow  in  fig.  550 ;  the  poles 
being  arranged  as  indicated  by  the  figure. 

The  easiest  mode  of  obtaining  a  maximum  magnetic  effect  in  a  bar,  by  touch, 
is  that  of  Jacobi,  viz. :  to  rest  its  ends  55^ 

against  the   poles   of  another  magnet, 

and  then  to  draw  a  piece  of  soft  iron, ^ 

called  a  feeder,  from  it  several  times  j  ^estammiwassa: 
along  the  bar.  This  mode  is  applied  to  VBiaii^iihiniimiMamTOi 
horse-shoe  magnets,  as  seen  in  fig.  551. 

The  dissimilar  poles  are  placed   together,  and  the  feeder  is  drawn  over  the 
horse-shoe,  in  the  direction  of  the  arrow ;  when  it  reaches  the  curve,  it  is  to  be 
47* 


530 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


replaced,  and  the  process  repeated ;  turn  the  whole  over  without  separating  the 
poles,  and  treat  the  other  side  in  like  manner. 

A  horse-shoe  of  one  pound  weight  may  be  thus  charged,  so  that  it  will  sustain 
26-5  pounds.  By  the  best  method  of  touch  before  known,  fig.  550,  21  Ibs.  9  oz. 
was  the  highest  attainable  result.  (Peschel.) 

805.  Magnets  by  electro-magnetism. — The  mode  of  producing 
electro-magnetic  currents  will  be  hereafter  described.    By  their  means, 
powerful  magnets  of  soft  iron  are  easily  produced,  and,  from  these,  by 
the  methods  of  touch  just  described,  very  powerful  artificial  magnets 
may  be  made. 

Logemann,  of  Haarlem,  in  Holland,  has  in  this  way  produced  the  most  pow- 
erful magnets  ever  made.  One  in  possession  of  the  authoi-,  sustained  28£  Ibs. ; 
its  own  weight  being  1  Ib.  The  mode  of  producing  these  powerful  magnets 
will  be  understood  from  fig.  552. 
A  spiral  of  insulated  copper  wire, 
t,  is  wound  on  a  paste-board  tube, 
A  B,  in  the  manner  of  the  electro- 
magnetic helix.  The  bar  to  be 
magnetized  is  armed  with  two 
heavy  cores,  or  cylinders  of  soft 
iron,  S  N,  just  fitting  the  inside 
of  the  spiral;  when  in  its  place, 
the  ends  of  the  spiral,  c  z,  are  connected  with  a  few  cells  of  Grove's  or  Bunsen's 
battery,  and  the  powerful  temporary  magnetism  induced  in  the  masses  of  soft 
iron,  reacts,  to  induce  an  uncommonly  strong  permanent  magnetism  in  the  bar 
of  steel.  A  horse-shoe  magnet  is  charged  in  a  similar  way,  by  encircling  it 
with  a  helix  of  proper  form,  with  similar  armatures  of  soft  iron.  The  close 
analogy  of  this  mode  to  that  of  Jacobi,  in  the  last  section,  will  be  noticed. 

806.  Compound  magnets  are  made  of  several  plates  of  steel,  sepa- 
rately magnetized,  as  in  fig.  523  and  549.   As  the  coercitive  power  of  steel 
appears  to  be  overcome,  chiefly,  on  its  surfaces,  553 

there  is  an  advantage  in  multiplying  the  number 
of  plates,  but  as  each  plate  serves  to  neutralize  a 
portion  of  the  polarity  of  its  neighbor  (similar 
poles,  of  necessity,  being  brought  into  contact), 
there  is  soon  found  a  limit  beyond  which  there  is 
no  advantage  in  extending  these  batteries. 

Large  magnets  are  not  as  powerful,  in  proportion  to 
their  weight,  as  small  ones.  Sir  Isaac  Newton  is  said 
to  have  worn  in  his  finger-ring  a  magnet  (lodestone) 
weighing  three  grains,  and  capable  of  sustaining  over 
250  times  its  own  weight  (760  grains).  A  lodestone 
of  three  or  four  pounds  weight,  mounted  as  in  fig.  534, 
can  rarely  sustain  over  two  or  three  times  its  own 
weight. 

The  most  powerful  artificial  magnet  on  record,  was 
that  made  by  Dr.  G.  Knight,  of  London,  and  now  in 
possession  of  the  Royal  Society.  It  consisted  of  two  prismatic  bundles,  each 


ELECTRICITY.  531 

of  240  powerful  bar  magnets  five  feet  in  length,  mounted  on  w  heels ;  between 
the  end  plates  of  this  combination,  the  poles  of  the  most  energetic  single  magnet 
were  reversed  or  powerfully  reinforced. 

807.  Magnetism  of  steel  by  the  sun's  rays. — Although  the  fact 
is  doubted  by  some  experimenters,  the  weight  of  testimony  appears  to 
support  the  conclusion,  that  the  sun's  violet  rays  possess  the  power  of 
inducing  permanent  magnetism,  when  concentrated  by  a  lens,  on  steel 
needles. 

808.  To  deprive  a  magnet  of  its  power,  it  is  only  necessary  to 
reverse  the  order  adopted  to  impart  magnetism  to  it,  stroking  it  from 
the  ends  to  the  centre  with  poles  of  the  same  name  opposed.     In  this 
way  the  magnetic  virtue  may  be  wholly  or  very  nearly  destroyed. 

The  approach  of  a  feeble  magnet  to  a  strong  one  may  reverse  its  polarity. 
Leaving  a  magnet  without  its  keeper  greatly  impairs  its  power.  Suddenly  jerking 
it  off  the  keeper,  or  striking  it  with  a  hammer,  in  a  way  to  make  it  vibrate,  does 
the  same.  Heat  accomplishes  the  total  destruction  of  magnetism,  and  in  short, 
anything  which  weakens  its  coercitive  power.  Conversely,  hanging  an  armed 
magnet  in  the  position  it  would  assume  if  free  to  obey  the  solicitation  of  the 
forces  of  terrestrial  magnetism,  is  the  best  position  to  favor  its  greatest  develop- 
ment. Every  magnet  which  has  been  charged  while  its  poles  are  connected  by 
a  keeper,  possesses  more  power  before  the  keeper  is  removed  than  after.  It  is 
indeed  overcharged,  and  the  excess  may  be  likened  to  that  residual  force  which 
retains  the  keeper  of  an  electro-magnet  in  its  place  after  the  circuit  which  excited 
it  is  broken,  or  to  the  residual  charge  of  a  Ley  den  jar.  Every  time  the  keeper 
of  a  magnet  is  moved  suddenly,  a  loss  of  power  is  sustained,  and  hence  the 
keeper  should  be  removed  by  sliding  it  gradually  off  endways,  and  only  when 
it  is  required  for  the  performance  of  an  experiment. 

I  2.  Statical  or  Frictional  Electricity. 

I.     ELECTRICAL  PHENOMENA. 

809.  Definitions. — Electricity  is  the  ethereal  or  imponderable  power 
which  in  one  or  another  of  its  forms  affects  all  our  senses.     In  this 
respect  it  is  unlike  all  other  ethereal  influences.     It  appears,  as  far  as 
our  knowledge  goes,  to  extend  throughout  nature,  and  is  probably  con- 
nected inseparably  with  matter  in  every  form.    Bodies  in  their  natural 
state  give  no  evidence  of  its  presenc%  but  by  different  means  it  may 
be  evoked  from  all.     Hence  statical  electricity  implies  that  condition  of 
this  subtle  ether  existing  in  all  bodies  in  a  state  of  electrical  quiescence. 
Statical  electricity  is  the  opposite  of  that  state  of  excitement  following 
friction,  chemical  action,  &c.,  which  is  called  dynamic  electricity,  or 
electricity  in  motion. 

An  arbitrary  meaning  has,  however,  attached  itself  to  the  terms 
statical  and  dynamical  electricity,  materially  different  from  the  exact 
meaning  of  those  terms  as  used  in  mechanics.  Statical  or  frictional 
electricity  means  only  that  form  of  electrical  excitement  produced  by 


532  PHYSICS    OF    IMPONDERABLE    AGENTS. 

friction,  while  dynamical  electricity  is  a  term  confined  to  the  electrical 
excitement  produced  by  chemical  action,  or  voltaic  electricity.  Strictly 
speaking,  all  quiescent  electricity  is  static,  and  all  electricity  in  motion, 
from  whatever  source,  is  dynamic.  Such,  however,  is  not  the  established 
use  of  these  terms. 

Electricity  is  a  term  derived  from  the  Greek  word  for  amber  (yjtexrpov}. 

The  ancients  knew  this  resin  to  be  capable  of  what  we  now  call  electrical 
excitement,  when  it  was  rubbed. 

810.  The   chief  sources  of  electrical  excitement  are : — 1st, 
Friction  of  dry  substances,  as  of  glass,  by  cat's  fur  or  silk,  and  of 
sulphur  or  resin  by  flannel :  this  is  ordinary  or  statical  electricity  ;  that 
of  the  atmosphere  and  of  common  electrical  machines ;  2d,   Chemical 
action,  or  the  contact  of  dissimilar  substances,  under  circumstances 
favorable   to   chemical  change ;    3d,  Magnetism,  producing  magneto- 
electricity;  4th,  Heat,  or  thermo-electricity;  5th,  Animal-electricity. 

The  electricity  from  all  these  several  modes  of  excitement  differs  in  degree 
and  intensity,  according  to  its  source,  but  not  in  kind,  and  each  may,  in  turn, 
be  cause  or  effect.  Each  will  be  the  subject  of  separate  consideration. 

811.  Electrical  effects. — A  dry  and  warm  glass  rod,  rubbed  with 
a  cat's  fur  or  silk  handkerchief,  is  excited  in  such  a  manner  as  to 
attract  to  itself  bits  of  paper,  shreds  of  silk  or  cotton,  metallic  leaf, 
pith,  feathers,  and  a  variety  of  light  substances,  holding  them  for  an 
instant,  and  then  repelling  them  again,  to  the  table  or  support,  as  in 
fig.  554.  554 

In  the  dark,  a  feeble  bluish  light  is  seen  in  the  path 
of  the  rubber.  If  the  excited  glass  is  presented  to  the 
knuckle,  or  to  a  metallic  body,  a  bright  purple  spark 
will  dart  off  from  the  glass,  with  crackling  sound,  to 
the  object  presented.  Brought  near  to  the  face,  a  creeping  sensation 
is  felt,  as  if  a  delicate  cobweb  was  in  contact  with  the  skin.  These 
effects  are  produced  by  the  rubber,  as  well  as  by  the  body  rubbed,  and 
may  be  evolved  from  a  number  of  substances  as  well  as  from  glass.  A 
peculiar  odor  always  accompanies  electrical  excitement,  thus  completing 
the  list  of  the  effects  of  this  subtle  agent  on  our  senses,  if  we  add  the 
taste  from  voltaic  electricity. 

Bodies  thus  excited  are  said  to  be  electrified;  a  condition  which  is  only 
transient. 

These  very  simple  experiments,  which  can  be  repeated  anywhere  and  with  the 
simplest  means,  contain  the  germ  of  electrical  science. 

812.  Attraction  and  repulsion. — In  the  electrical  pendulum,  fig. 
555,  the  pith-ball  is  first  attracted  to  the  excited  glass  or  resin,  and  at 
the  next  instant  is  repelled,  until,  by  touching  some  body  in  connection 


ELECTRICITY.  533 

with  the  earth,  or  in  some  other  way,  it  has  parted  with  its  excitement. 
The  two  balls  in  fig.  556,  when  thus  555 

excited,  mutually  repel  each  other, 
because   they  are  similarly  excited. 
The  light  bodies  in  fig.  554,  oscillate 
between  the  table  and  the  rod,  first 
by   attraction,    and   then   by    repul- 
sion ;  when,  losing  their  excitement 
by  contact  with  the  table,  they  are 
again  attracted,  and  so          555 
on.    So  with  the  balls  in 
fig.  556.     We  recognise 
in  these  simple  experi- 
ments the  similarity  be- 
tween these  actions  and 
the    law    of    magnetic 
attractions  and  repulsions.   Bodies  similarly  excited  repel,  and  those  which 
are  of  unlike  excitement  attract  each  other. 

The  phenomena  of  attraction  and  repulsion  are  not  however  so  simple  as 
might  at  first  appear,  since  for  their  correct  explanation  a  knowledge  of  the 
phenomena  of  induction  is  required,  and  these  remain  to  be  explained  further  on. 

813.  Vitreous  and  resinous,  or  positive  and  negative  electri- 
cities.— The  species  of  electrical  excitement  depends  upon  the  kind 
of  material  which  is  subjected  to  friction.  If  the  pith-balls,  fig.  556, 
are  repelled  by  the  excitement  from  glass  rubbed  by  silk,  they  will  be 
attracted  by  a  stick  of  wax,  gum  lac,  or  sulphur  rubbed  by  flannel ;  or 
vice  versa. ' 

This  difference  of  action  is  due  to  an  inherent  difference  in  the  two 
substances,  and  the  kind  of  electrical  excitement  which  the  two  respec- 
tively produce,  is  entirely  opposite  and  antagonistic  each  to  the  other. 
The  one  is  vitreous  or  positive,  the  other  resinous  or  negative.  This 
fundamental  distinction  in  the  kind  of  excitement  produced  by  friction 
in  various  substances,  was  first  recognised  by  the  French  philosopher, 
Du  Fay,  in  1733,  and  was  re-discovered  by  Franklin  in  1747.  Glass 
and  resin  are  but  types  of  two  large  classes  of  substances,  which  pos- 
sess more  or  less  perfectly  this  characteristic  difference  in  respect  to  the 
sort  of  electricity  which  they  are  capable  of  developing. 

Electroscopes  serve  to  distinguish  the  two  sorts  of  electrical  excite- 
ment from  each  other.  The  pith-balls,  fig.  556,  form  a  convenient 
electroscope — two  silk  ribbons,  or  the  electrical  pendulum,  fig.  555, 
answer  the  same  purpose.  Much  more  delicate  instruments  of  this 
kind  will  be  described  shortly. 


534  PHYSICS    OF   IMPONDERABLE    AGENTS. 

It  is  only  requisite  to  excite  the  balls,  fig.  556,  with  known  vitreous  or  resinous 
electricity,  when  the  approach  of  any  excited  body  whose  electrical  state  is  un- 
known, will,  if  of  the  same  kind,  cause  a  farther  repulsion,  and  if  of  a  different 
sort,  will  occasion  an  attraction  of  the  balls. 

814.  Conductors  of  electricity. — Bodies  electrically  excited  part 
with  their  excitement  variously, — some  instantly,  others  very  slowly, — 
depending  both  on  the  nature  of  the  substance  excited,  and  of  those 
with  which  it  is  brought  in  contact.  The  pith-balls  of  the  electroscope 
lose  their  excitement  very  slowly,  the  electricity  being  removed  only 
by  the  surrounding  air.  Touched  by  the  finger,  or  a  metallic  body  in 
connection  with  the  earth,  they  are  instantly  discharged,  and  return  to 
their  natural  unexcited  condition.  The  electricity  is  removed  by  con- 
duction over  the  touching  body.  And  as  bodies  vary  very  much  in 
their  power  to  conduct  electricity,  they  are  called  good  and  bad  conduc- 
tors, or  conductors  and  non-conductors. 

Good  conductors  propagate  the  excitement  to  all  parts  of  their 
surface,  and  when  in  connection  with  the  earth,  part  with  it  as  quickly 
as  they  receive  it. 

The  following  are  among  the  good  conducting  bodies,  placed  in  the 
order  of  their  conducting  power.  The  metals,  as  a  class  (silver  and 
copper  standing  first,  and  lead  and  quicksilver  last),  well-burnt  char- 
coal, plumbago,  coke,  hard  anthracite,  acids,  saline  solutions,  numerous 
fluids,  metallic  ores,  sea,  spring,  and  rain  water,  ice  above  13°  F., 
snow,  living  things,  flame,  smoke,  vacuum,  vapor  of  alcohol  and  ether, 
earths  and  moist  rocks,  powdered  glass,  and  flowers  of  sulphur. 

Bad  conductors  receive  and  part  with  electricity  very  slowly.  If 
touched  by  an  electrified  body,  they  receive  excitement  only  at  the 
point  touched ;  or  if,  when  excited  over  their  whole  surface,  they  are 
touched  by  a  good  conductor,  the  excitement  is  removed  only  from  the 
part  touched.  They  retain  free  electricity  for  a  long  time,  and  obstruct 
its  motion. 

Insulation. — Good  conductors  are  capable  of  manifesting  electrical 
excitement  only  when  their  communication  with  the  earth  is  cut  off  by 
some  bad  conductor.    So  situated,  they  are  said  to  be  insulated,  and  the 
poor  conductors  used  for  this  pur- 
pose (glass,  resin,  or  dry  wood),  are 
called  insulators.     Fig.  557  shows 
a  brass  tube  thus  insulated  by  a 
handle  of  glass.     Among  the  chief  insulating  bodies  are  the  following, 
placed  in  the  reverse  order  of  their  insulating  power,  viz. :  dry  metallic 
oxyds,  oils,  ashes  ice  below  13°  F.,  many  crystalline  bodies,  lime  and 
chalk,  lycopodium,  native  caoutchouc,  camphor,  porcelain,  dry  vegeta- 
bles, baked  wood,  dry  air,  and  gases,  steam  above  212°,  leather,  par^h- 


ELECTRICITY.  535 

ment,  paper,  hair,  dyed  silk,  white  silk,  diamond  and  precious  stones, 
mica,  glass,  jet,  wax,  sulphur,  the  resins,  amber,  gum  lac.  Gutta  per- 
cha,  and  whalebone  rubber,  are  among  the  best  insulators  known  ; 
probably  better  than  gum  lac. 

Some  bodies  which,  when  solid,  are  non-conductors,  become  conductors  when 
liquefied  by  fusion,  viz.:  metallic  chlorids,  glass,  wax,  sulphur,  resin,  &c.  Heat 
diminishes  the  electric  conducting  power  of  metals.  Length  of  conductor 
retards  electrical  motion,  while  an  increase  in  other  dimensions  favors  the 
rapid  transmission  of  electricity.  Every  body  has  a  certain  electrical  retarding 
power  (818),  which  is  inverse  to  its  conducting  power.  Tables  of  electrical 
conducting  powers  will  be  found  in  larger  works ;  but,  in  general,  this  power  is 
very  nearly  the  same  as  any  given  body  has  for  conducting  heat. 

815.  The  earth  is  the  great  common  reservoir  or  receptacle  into 
which  all  electrical  excitements  are  returned,  and,  regarded  as  a  whole, 
is  a  good  conductor.     The  air,  even  in  its  ordinary  condition,  is  a  very 
poor  conductor,  and,  in  view  of  its  immense  extent,  is  by  far  the  most 
important  of  non-conductors.     It  serves  to  insulate  the  earth  in  a  non- 
conducting envelope,  more  or  less  perfect,  in  proportion  to  its  density, 
and  the  absence  of  aqueous  vapor.     Except  for  this  property  of  the  air, 
all  electrical  phenomena  would  have  remained  invisible  and  unknown 
to  us.     The  earth  is  always  negatively  excited. 

In  a  vacuum,  all  electrified  bodies  speedily  lose  their  excitement, 
while  in  dry,  dense  air,  they  retain  it  longest.  Nevertheless,  slight 
electrical  excitement  can  be  produced  in  a  vacuum  by  friction. 

816.  Theories  of  electricity,  or  electrical  hypotheses. — Philo- 
phers  generally  agree  in  attributing  the  phenomena  of  electricity  to 
the  existence  of  an  assumed  electrical  fluid.     This  supposed  fluid  is  so 
subtle  and  ethereal  as  to  escape  detection  by  all  the  means  used  to  re- 
cognise matter,  being  imponderable,  and  manifesting  itself  only  by  its 
effects.     It  is  assumed  to  pervade  all  nature,  and  to  exist  in  a  state  of 
combination  or  electrical  quiescence  in  all  bodies  in  their  natural  state. 
This  quiescence  is  disturbed  by  friction,  and  various  physical  and 
chemical  causes.     All  electrical  phenomena  are  supposed  to  be  due  to 
the  efforts  of  the  electrical  fluid  to  regain  its  previous  condition  of 
static  equilibrium.     Two  principal   hypotheses  have  been  devised  to 
explain  the  phenomena  of  electricity,  namely :  1st,  that  of  Franklin 
and  ^Epinus  ;  2d,  that  of  Symmer,  sometimes  attributed  to  Du  Fay. 

Franklin's  single-fluid  hypothesis  is  recommended  by  its  sim- 
plicity, and  was,  for  a  long  time,  the  view  generally  adopted,  both  in 
England  and  America.  It  assumes  a  single  electrical  fluid,  whose  par- 
ticles are  self-repellent,  but  attracted  by  matter  of  all  kinds,  combining 
therewith,  and  when  so  combined,  losing  this  self-repellent  tendency. 
This  fluid  is  present  in  all  bodies,  but  in  varying  proportion,  each  sub- 


536  PHYSICS    OF    IMPONDERABLE    AGENTS. 

stance  possessing  a  certain  capacity  of  saturation  peculiar  to  itself. 
In  its  natural  state,  every  substance  has  exactly  its  own  quantity  of  the 
electric  fluid,  and  is  consequently  in  a  state  of  electrical  indifference. 
If  any  cause  of  electrical  excitement  exists,  this  state  of  quiescence  is 
disturbed,  and  the  body  becomes  negatively  electrical,  if  its  natural 
charge  is  diminished,  and  positively,  if  it  is  in  excess.  By  this  hypoth- 
esis, bodies  become  electrical  either  by  addition  to,  subtraction  from, 
or  disturbance  in  the  equal  distribution  of,  the  normal  quantity  of  the 
electric  fluid  proper  to  them.  In  those  bodies  which  manifest  positive 
electricity,  the  equilibrium  is  restored  by  parting  with  the  excess,  and 
in  those  whose  excitement  is  negative,  by  receiving  from  surrounding 
bodies  enough  to  satisfy  their  deficiency. 

This  hypothesis  will  be  recognised  as  strikingly  like  that  commonly  received 
in  explanation  of  the  equilibrium  of  heat. 

JEpinus  found,  that,  in  order  to  account  mathematically  for  the  mutual  repul- 
sion of  two  negatively  electrified  bodies  on  the  single-fluid  hypothesis,  it  was 
necessary  to  assume  that  the  particles  of  matter  were  mutually  repulsive  instead 
of  attractive,  according  to  the  Newtonian  law  of  universal  attraction.  This 
reductio  ad  absurdem  has  led  to  the  almost  universal  rejection  of  the  Franklin- 
ian  hypothesis. 

The  hypothesis  of  Symmer,  or  Du  Fay,  assumes  the  existence 
of  two  fluids,  extremely  tenuous,  imponderable,  in  the  highest  degree 
expansive,  mutually  repellent  (as  a  consequence  of  this  expansive 
nature),  and  yet  possessing  a  strong  mutual  attraction  when  not  opposed 
by  any  obstacle.  They  therefore  combine,  when  favorably  situated  so 
to  do  ;  and  when  equally  combined,  their  expansive  and  repellent  forces 
are  neutralized,  and  electrical  quiescence  results.  Each  of  these  kinds 
of  electricity  may  exist  separately ;  they  are  then  in  a  state  of  antago- 
nism, and  exhibit  polarity,  and  other  electrical  effects.  Every  sub- 
stance becomes  thus  excited  whenever  any  part  of  its  natural  electricity 
is  (Jecomposed  by  friction  or  otherwise.  If  a  plate,  it  may  possess  the 
two  electricities  on  its  opposite  sides,  one  being  vitreous,  and  the  other 
resinous  ;  if  a  rod,  the  decomposition  of  a  part  of  its  natural  electricity 
will  make  the  rod  vitreous  at  one  end  and  resinous  at  the  other.  When 
the  cause  of  excitement  ceases,  the  two  fluids  reunite,  and  quiescence  is 
restored.  By  this  hypothesis,  all  electrical  phenomena  arise  from  the 
tendency  of  the  two  fluids  when  separated  to  reunite  and  neutralize 
each  other. 

Either  of  these  two  views  is  capable  of  explaining  most  electrical  phenomena, 
but  the  weight  of  scientific  opinion  is  now  in  favor  of  the  last.  Neither  view 
can  be  actually  true,  since  the  term  fluid  is  only  a  convenient  expression  for  an 
unknown  cause,  and  there  is  no  reason  why  we  should  assume  the  existence  of 
a  separate  fluid  or  ether,  as  a  medium  for  light,  heat,  or  magnetic  electricity, 
when  it  is  more  in  accordance  with  a  sound  philosophy  to  assume  that  these 


ELECTRICITY.  537 

separate  manifestations  are  but  functions  of  the  ethereal  medium  which  fills  the 
universe,  and  from  whose  correlations  to  the  particles  of  matter,  all  physical 
phenomena  proceed.  Compare  $$  765-772. 

817.  Electrical  tension.— -This  term  is  employed  to  express  that 
condition  of  bodies  in  which  the  electricity  is  free — a  condition  the 
reverse  of  electrical  quiescence.  This  condition  is  well  illustrated  in 
the  phenomena  of  the  Leyden  jar,  g  847,  where  there  is  perfect  equi- 
librium between  the  excitement  of  the  outer  and  inner  surfaces,  due  to 
their  antagonism.  The  energy  with  which  the  decomposed  electricities 
reunite,  when  communication  is  made  between  them,  shows  the  state 
of  tension  in  which  they  existed.  This  may  be  regarded  as  analogous 
to  the  tension  of  a  bent  spring,  in  which  equilibrium  is  regained  by  a 
reaction  equal  to  the  compressing  force.  Electrical  tension  is  a  condi- 
tion of  constrained  equilibrium,  and  when  the  free  electricities  to  which 
it  is  due,  reunite,  an  electrical  current  is  produced  from  the  reaction  of 
the  opposing  fluids,  analogous  to  mechanical  motion  from  the  recoil  of 
a  spring.  From  this  state  of  electrical  tension  are  derived  the  primary 
effects  of  electricity,  and  from  electrical  currents  arise  its  secondary 
effects.  All  electrified  bodies  manifest  electrical  tension  ;  they  attract 
other  bodies,  decomposing  their  natural  electricity,  deriving  from  them 
a  portion  of  the  opposite  fluid.  If  this  is  insufficient  to  satisfy  the 
antagonism  of  the  excited  electric,  the  attracted  bodies  are  next  re- 
pelled (812).  Hence,  two  bodies  equally  excited,  but  of  opposite  names, 
attract  each  other,  and  reunion  of  the  two  fluids  with  electrical  indiffer- 
ence results.  If  one  contained  an  excess  of  either  fluid,  both  remain 
excited  after  contact,  with  that  description  of  electricity  which  was  in 
excess ;  the  excess  being  divided  in  the  ratio  of  their  surfaces. 

Electrical  currents  are  either  momentary  or  permanent. — The 
first  occur  when  contact  is  formed  between  substances  oppositely  ex- 
cited by  friction  or  otherwise,  and  their  effects  are  instantaneous  and 
transient. 

Permanent  electric  currents  arise  only  from  the  sustained  action  of 
some  continuous  cause  ;  as,  from  the  continued  motion  of  the  electrical 
machine,  or,  more  simply,  from  the  chemical  action  of  unlike  substances, 
as  in  the  voltaic  battery,  in  which  the  electrical  current  is  kept  up  as 
long  as  any  chemical  action  exists. 

818.  Path  and  velocity  of  electric  currents. — If  several  con- 
ducting paths  are  open  to  an  electric  current,  it  will  always  choose  the 
shortest,  and  that  in  which  it  meets  the  least  resistance.  If  the  cur- 
rent is  powerful,  and  the  conductor  inadequately  small,  its  passage  will 
be  marked  by  light,  and  perhaps  by  the  combustion  and  deflagration 
of  the  conductor.  The  velocity  of  static  electricity,  by  Wheatstone's 
48 


538 


PHYSICS    OF    IMPONDERABLE   AGENTS. 


experiments,  over  a  copper  wire,  was  found  to  be  288,000  miles  in  a 
second — nearly  half  again  more  than  the  velocity  of  light  (g  404). 

It  appears  from  Dr.  Gould's  discussion  (Am.  Jour.  Sci.  [2]  XL,  161),  of  the 
very  numerous  telegraphic  observations  in  the  United  States,  made  under  the 
direction  of  Prof.  Bache,  for  the  Coast  Survey,  and  by  other  astronomers,  that 
the  velocity  of  a  voltaic  current,  when  the  earth  forms  part  of  the  circuit,  does 
not  exceed  16,000  miles  per  second,  and  it  has  been  measured  as  low  as  11,000 
miles  per  second ;  showing  a  great  retarding  force  in  a  conductor  of  1500  miles 
circuit.  In  the  famous  Atlantic  cable,  the  electrical  retardation  was  much 
greater  than  this,  being  mixed  with  the  accompanying  phenomena  of  induction. 

II.    LAWS  OF  ELECTRICAL  FORCES  AND  DISTRIBUTION  OF  ELECTRICITY  UPON 
THE  SURFACE  OF  BODIES. 

819.  Coulomb's    laws. — Coulomb    (died    1806),    a    distinguished 
French  physicist,  by  the  use  of  the  torsion  balance,  first  demonstrated 
the  following  laws  of  electrical  attractions  and  repulsions : — 

1st.  Two  excited  bodies  attract  and  repel  each  other  with  a  force  propor- 
tional to  the  inverse  square  of  their  distances  from  each  other. 

2d.  The  distances  remaining  the  same,  the  attractions  and  repulsions 
are  directly  as  the  quantities  of  electricity  possessed  by  the  two  bodies. 

Coulomb's  laws  of  torsion  have  already  been  demonstrated  (266). 
He  happily  applied  these  principles,  first  established  by  himself,  to  the 
measurement  of  electric  forces  in  his  tor-  553 

sion  electrometer. 

820.  Torsion    electrometer.— This 
instrument,  fig.  558,  consists  of  an  ex- 
terior glass   cage,  protecting  a  slender 
needle,  no.  of  gum   lac,  suspended  by 
a  fine  wire  of  silver  or  platinum,  cen- 
trally attached  to  the  under  side  of  the 
cap,  e,  upon  the  tube  d. 

This  cap  is  graduated,  and  turns  like  the 
cover  of  a  box.  The  graduation  is  read  at 
the  vernier,  a.  A  small  weight,  o,  of  brass, 
keeps  the  wire  tense,  while  through  it  the 
gum  lac  needle  passes.  At  one  end  of  the 
needle,  n,  is  a  small  gilded  ball  of  pith,  or  a 
disk  of  tinsel  paper.  The  cover  of  the  glass 
case  is  perforated  for  the  free  passage  of  a 
glass  insulating  rod,  ?,  carrying  a  polished 
brass  ball  at  m.  The  glass  cage  is  graduated 
in  a  zone  at  C,  into  .360  degrees,  to  measure 
the  angular  spaces  traversed  by  the  needle. 
The  zero  of  the  graduation,  and  of  the  arc  on  the  cap,  are  both  made  to  corre- 
spond (by  revolving  the  tube,  d,)  with  the  normal  position  of  the  needle  when 
at  rest,  and  unexcited.  To  avoid  the  loss  of  electricity,  the  air  in  the  cage  ia 
kept  dry  by  a  little  quick-lime,  placed  in  a  dish  for  that  purpose,  on  the  bottom. 


ELECTRICITY.  539 

821.  Demonstration  of  the  first  law. — The  apparatus  being  thus 
arranged,  the  insulated  rod,  i,  is  withdrawn,  and  the  ball,  w,  placed  in 
contact  with  some  excited  surface — as  the  electrical  machine.     Thus 
excited,  m  is  immediately  returned  to  its  place  by  the  insulating  handle, 
taking  care  that  it  touches  nothing.    Forthwith  the  disk,  n,  is  attracted 
to  m,  is  oppositely  electrified,  and  then  repelled  with  a  force  propor- 
tioned to  the  intensity  of  m.     After  a  few  oscillations,  n  comes  to  rest 
say  at  30  degrees  on  the  graduated  circle.     This  angle  then  represents 
the  repellent  force  of  the  electricity  on  m,  since  the  torsion  of  a  wire 
is  directly  as  the  twisting  force.     But  what  would  be  the  force  requi- 
site to  hold  the  disk,  n,  in  equilibrium  at  half  this  angular  distance,  or 
15°?     Revolving  the  movable  circle,  e,  in  the  direction  of  the  arrow, 
we  find  it  is  necessary  to  carry  it  from  0  to  105°,  in  order  that  the 
needle  may  point  to  15°.     The  wire  is  then  twisted  at  top  with  a  force 
of  105°,  and  at  bottom  with  a  force  of  15°,  giving  120°  as  the  angle 
representing  the  force  with  which  the  two  electrified  bodies  repel  each 
other,  at  the  distance  of  15° — or,  at  half  the  distance,  we  have  quad- 
ruple the  force ;  at  one-third  the  distance,  or  7£°,  the  force  would  be 
472°'5  -f  7°'5  =  480°,  according  to  the  law  of  inverse  squares. 

In  like  manner,  reversing  the  electricities,  we  prove  that  the  force 
with  which  two  electrified  bodies  attract  each  other,  is  inversely  pro- 
portional to  the  square  of  the  distance  by  which  they  are  separated. 

822.  Demonstration  of  the  second  law. — Having  repelled  the 
needle,  n  o,  by  the  excited  ball,  m,  withdraw  the  latter,  and  touch  it  to 
a  second  metallic  ball  of  the  same  size,  insulated  on  a  glass  handle. 
The  ball,  m,  parts  with  half  its  electricity  to  the  second  ball  (827). 
Now  return  it  to  the  torsion  balance ;  it  will  be  found  that  the  needle, 
n  o,  is  repelled  to  a  distance  equal  to  its  former  distance  multiplied  by 
the  square  root  of  one-half,  D'  =  D\/%.    Touch  m  again  to  the  second 
ball,  as  before,  and  it  will  then  repel  the  needle  to  a  distance  equal  to  the 
first  distance  multiplied  by  the  square  root  of  one-fourth,  D//  =  D~[/ £, 
and  so  on. 

Sir  Wm.  S.  Harris,  of  England,  by  the  use  of  a  bifilar  electrometer, 
which  substitutes  the  force  of  gravity  for  that  of  torsion,  has  shown  that  the 
two  laws  of  Coulomb  are  not  strictly  accurate,  unless  the  two  excited  bodies 
have  the  same  size  and  form,  or  unless  the  sections  of  the  opposing  parts  are 
equal.  The  result  of  his  determinations  is,  that  the  attraction  is  directly  propor- 
tional to  the  number  of  points  immediately  opposed  to  each  other,  and  inversely 
to  the  square  of  their  respective  distances. 

823.  Proof-plane. — For  the  purpose  of  determining  the   relative 
quantities  of  electricity  that  are  found  on  the  different  parts  of  the  sur- 
face oi  an  electrified  conductor,  a  contrivance  called  a  proof-plane  is 
used.    It  is  nothing  but  a  s  nail  disk  of  tinsel,  or  metal,  insulated,  as  in 


540 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


the  ball,  m,  of  the  torsion  balance,  fig.  558.  This  is  touched  to  the 
surface  whose  electricity  is  to  be  examined,  and  receives  therefrom  a 
quantity  of  electricity  equal  to  the  sum  of  both  of  its  own  surfaces.  It 
may  then  be  inserted  in  the  balance  of  torsion,  or  used  on  any  other 
electroscope.  The  electricity  on  the  body  touched  is  diminished  to  the 
same  extent,  but  when  the  proof-plane  is  small,  compared  with  the  area 
of  the  excited  conductor,  no  sensible  error  can  arise  from  this  loss. 
The  most  important  source  of  error  to  be  guarded  against  in  the  use 
of  this  instrument,  arises  from  the  effects  of  induction,  presently  to  be 
explained. 

824.  Electricity  resides  only  on  the  outer  surfaces  of  excited 
bodies,  and  not  in  their  substance,  or  on  their  interior  surfaces.  This 
fact  is  attributed  in  part  to  the  repulsive  power  of  the  electric  fluid 
acting  upon  the  particles  of  matter  interiorly,  thus  driving  the  excite- 
ment to  the  outer  surface,  where  it  meets  the  non-conducting  air,  and 
is  arrested.  It  is  also  due  to  the  inductive  influence  of  the  electricity 
of  surrounding  bodies,  and  of  the  walls  of  the  room.  The  following 
experiments  will  illustrate  this  law.  559 

A.  Electrify  the  metal   sphere,  a,  fig.  559,  on  an 
insulating  stand,  6,  and  approach  to  it  the  two  hollow 
hemispheres  of  brass,  c  c,  insulated,  and  made  accu- 
rately to  cover  the  sphere.    On  removing  them,  a  will 
be  found  without  the  least  trace  of  electrical  excite- 
ment, as  may  be  proved  by  a  delicate  electroscope, 

while  the  two  hemispheres  are  fully  excited.     To  remove  the  enveloping  hemi- 
spheres is  to  remove  the  surface  of  the  sphere,  560 
and  with  them  its  electricity. 

B.  Fig.  560  shows  an  insulated  hollow  sphere, 
with  a  hole  in  the  top.     When  this  is  electri- 
fied, the  proof-plane  may  be  introduced  by  the 
opening,  and  placed  in  contact  with  its  inner 
surface,    without    acquiring    any    excitement 
(provided  care  be  taken  to  avoid  the  inducing 
effect  of  the  edges  of  the  opening,  which  may 
otherwise  decompose  the  neutral  electricity  of 
the  gum-lac  handle),  while  from  contact  with 
any  point  of  the  outside,  the  proof-plane  ac- 
quires abundant  excitement. 

C.  Faraday  has  described  a  muslin  bag  in 
the  form  of  a  net,  fig.  561,  sustained  on  an 
insulated  ring  of  wire,  and   provided  at   the 
point   of    the    cone   with   two   insulated   silk 
strings,  c  c',  so  that  it  may  be  turned  inside 
out  at  pleasure,  without  touching  it.     When 
this  is  electrized  exteriorly,  it  may  be  turned 
inside  out  by  means  of  the  strings,  without  a 
trace  of  electricity  being  found  on  the  inside 

(which  an  instant  before  was  the  outside),  and  this  may  be  repeated  several  times 


ELECTRICITY. 


541 


before  the  electricity  is  dissipated.  He  is  in  the  habit  of  covering  his  most  deli- 
cate electroscopes  with  muslin  bags,  to  protect  them  from  the  influence  of  excited 
electrical  machines,  with  entire  561  562 

success. 

Fig.  562  shows  a  ribbon  of 
metallic  paper  wound  around  a 
metallic  axis,  insulated  by  the 
silk  threads  rr;  two  pith-balls,  c 
e  e',  are  suspended  by  linen 
threads,  at  one  end  of  the  rib- 
bon. When  the  ribbon  is  wound 
up,  and  the  whole  is  electrized, 
the  balls  of  the  electroscopes  di- 
verge powerfully.  If  the  ribbon 
is  now  unwound  by  drawing  the 
insulating  string  below,  the  electroscope  balls  gradually  fall,  and  finally  come 
almost  in  contact ;  but  when  the  ribbon  is  again  wound  up,  the  balls  diverge  as 
before.  This  may  be  repeated  several  times.  This  beautifully  illustrates  the 
relation  of  surface  «ua  intensity.  As  the  surface  is  increased,  the  same  quan- 
tity of  electricity  is  spread  out  over  a  larger  surface,  and  its  energy  declines,  but 
is  increased  again  as  the  surface  is  diminished  by  re-winding  the  ribbon. 

D.  It  appears  from  these  experiments  that  a  ball  of  wood  or  pith,  covered  with 
tin  foil  or  gold  leaf,  can  accumulate  on  its  surface  as  much  electricity  as  if  it  was 
of  solid  metal. 

It  is  thus  proved  that  all  the  electricity  with  which  a  conducting 
body  is  charged,  is  disposed  on  its  surface. 

825.  Distribution  of  electricity. — The  form  of  conductors  influ- 
ences the  distribution  of  electricity  on  their  surface.     In  a  sphere,  the 
distribution  is  uniform,  as  would  be  anticipated  from  the  known  pro- 
perties of  the  solid.    The  proof-plane,  applied  to  any  part  of  an  excited 
sphere,  acquires,  as  tested  by  the  balance,  553 

the  same  power.  In  an  ellipsoid  of  revo- 
lution, like  fig.  563,  the  proof-plane  ap- 
plied at  a,  gives  a  much  larger  angle  of 
torsion  in  the  balance  than  at  any  other 
point,  while  the  minimum  is  in  the  vicinity 
of  e ;  showing  a  tendency  in  electrical  ex- 
citement to  accumulate  about  the  extremi- 
ties of  any  solid  having  unequal  axes. 

In  cylinders,  the  concentration  of  force  is  within  about  two  inches  from  each 
end,  and  is  feeble  at  the  middle.  So  in  plates,  the  maximum  of  accumulation  is 
about  an  inch  from  the  edge.  The  same  is  true  of  the  edges  and  solid  angles 
of  prismatic  bodies. 

826.  The  power  of  points  (first  investigated  by  Franklin)  in  con. 
centrating  electricity  is  such  that  the  excitement  passes  off,  as  rapidly 
as  it  accumulates,  to  the  nearest  bodies,  or  is  diffused  into  the  ambient 
air  in  an  electrical  brush  or  rencil,  visible  in  the  dark  (842  (6)  ).   This 


542  PHYSICS    OF    IMPONDERABLE    AGENTS. 

fact  follows  as  a  consequence  of  the  tendency  of  electricity  to  accumu- 
late at  the  smaller  end  of  an  ellipsoid.  The  ellipsoid  may  be  so  elon- 
gated that  the  electricity  escapes — it  then  becomes  a  blunt  point.  These 
facts  are  of  the  greatest  importance  in  the  construction  of  electrical 
machines. 

827.  The  loss  of  electricity  in  excited  bodies,  even  when  insu- 
lated in  the  best  manner,  is  constant,  chiefly  from  two  causes,  viz. :  1st, 
the  moisture  of  the  air ;  and  2d,  the  imperfection  of  the  insulation. 
The  loss  from  the  first  cause,  in  still  air  of  average  dryness,  is  propor- 
tioned to  the  state  of  electrical  tension.    Bodies  feebly  excited,  and  per- 
fectly well  insulated  in  dry  air,  retain  their  state  of  tension  for  weeks 
or  months,  while  those  highly  excited,  and  not  carefully  preserved,  are 
soon  deprived  of  all  electrical  excitement.     The  rate  of  loss  by  imper- 
fect conduction  is,  of  course,  dependent  on  the  non-conducting  material 
used,  the  perfection  of  workmanship,  and  care  of  the  apparatus. 

The  loss  of  electricity  by  an  excited  conductor,  when  placed  in  con- 
tact with  an  unexcited  body,  insulated  from  the  earth,  is  in  proportion 
to  the  relative  surfaces  of  the  two  bodies.  One  gains,  the  other  loses. 
Two  equal  spheres  will  divide  the  whole  quantity  between  them.  If 
they  remain  in  contact,  the  distribution  is  unequal,  being  least  at  the 
point  of  contact,  and  increasing  to  a  maximum  at  20°  to  30°  from  the 
point  of  contact.  The  proof-plane  determines  exactly  all  such  questions. 

In  a  vacuum,  a  high  state  of  electrical  tension  is  impossible,  since  the  re- 
straining power  of  the  air  is  wanting.  But  a  feeble  tension  can  be  preserved  in 
an  exhausted  receiver  for  a  long  time.  The  movement  of  the  mercury  against 
the  walls  of  the  tube  of  a  barometer,  excites  electrical  tension,  ^nd  even  lumi- 
nous electricity,  as  was  shown  by  Cavendish. 

III.     INDUCTION  OF  ELECTRICITY. 

828.  Electrical  influence  or  induction. — Every  electrified  body 
is  surrounded,  so  to  speak,  by  an  atmosphere  of  influence,  analogous  to 
that  surrounding  a  magnet  (783),  within  which  every  insulated  con- 
ductor becomes  also  excited.    Bodies  so  affected  are  said  to  be  electrified 
by  induction,  having  their  neutral  electricity  decomposed  by  the  tension 
of  the  excited  conductor,  exercised  through  the  intervening  air. 

Let  the  conductor,  V,  fig.  564,  of  an  electrical  machine,  be  approached  within 
say  six  inches  of  an  insulated  metallic  con- 
ductor, A  B.  The  small  electroscopes,  a  a', 
suspended  beneath  its  ends,  instantly  diverge, 
and  at  the  same  time  are  respectively  attracted 
to  V,  at  A,  and  repelled  from  it  at  B.  If  V 
is  -f-  A  is  — ,  and  the  remote  end,  B,  is  plus. 
The  intermediate  electroscopes,  b  b',  also  di- 
verge, but  in  a  less  degree,  while  those  near 
the  middle,  c  c',  do  not  diverge  at  all.  If, 
while  thus  excited,  A  B  is  withdrawn  from  V  (care  being  taken  not  to  touch  the 


ELECTRICITY.  543 

conducting  surface),  the  electroscopes  will  present!}'  cease  to  indicate  any  ex- 
citement. The  explanation  of  these  facts  is,  that  the  neutral  fluid  of  A  B  has 
heen  decomposed  by  the  influence  of  V,  the  -)-  fluid  being  repelled  to  B,  and  the 
—  -  attracted  to  A,  while,  near  the  centre  (never  exactly  in  the  centre),  a  neutral 
point  is  found,  where  no  decomposition  exists.  When  V,  the  disturbing  cause, 
is  withdrawn,  the  two  electricities  of  A  B  unite  again,  and  leave  the  conductor 
entirely  passive.  If,  however,  the  conductor,  A  B,  is  made  in  two  parts,  joined 
at  the  neutral  point,  and  each  on  a  separate  glass  leg,  when  it  is  inductively 
excited,  the  two  parts  may  be  separated,  and  each  part  will  then  be  found,  when 
removed  from  influence,  to  possess  the  same  excitement  developed  in  it,  under 
the  inductive  power  of  V. 

By  means  of  a  glass  tube,  or  stick  of  resin  gently  excited,  and  approached  to 
one  of  the  electroscopes,  it  is,  of  course,  easy  to  determine  the  description  of 
excitement  in  V,  which  we  now  assume  to  be  -(-. 

829.  The  laws  of  induction  may  be  thus  stated: — 1st.  A  body 
electrized  by  induction,  possesses  no  more  electricity  than  before.   This 
is  shown  by  the  fact,  that  as  soon  as  the  inducing  influence  ceases,  the 
two  fluids  reunite  in  A  B,  and  no  trace  of  excitement  remains. 

2d.  If  a  conductor,  excited  by  induction,  is  touched,  or  made  to  com- 
municate with  the  earth  in  any  part  of  its  surface,  it  parts  with  a  por- 
tion of  electricity,  always  of  the  same  name  with  the  inducing  body, 
and  it  retains  the  fluid  of  opposite  name.  If  the  inducing  cause  is 
then  withdrawn,  the  insulated  conductor  remains  excited,  with  the  fluid 
of  opposite  name  to  that  of  the  inducing  body. 

Thus,  we  note  the  important  distinctions  between  a  body  electrized  by  induc- 
tion and  by  conduction.  Induction  occasions"  no  transmission  of  free  electricity 
to  the  other  body ;  but  only  a  decomposition  of  the  ^  electricities  of  the  insu- 
lated conductor.  Induction  produces  dissimilar  conduction,  similar  electricity 
to  that  of  the  exciting  body;  and  the  distance  to  which  electricity  of  induction 
extends,  greatly  exceeds  that  to  which  it  can  be  propagated  by  conduction, 
where  absolute  contact  or  very  close  proximity  is  required.  A  strong  analogy 
exists  between  electric  and  magnetic  induction.  Both  magnetism  and  electricity 
by  contact,  are  of  the  same  name  with  the  body  touched.  By  influence,  the 
neutral  fluid  of  the  excited  body  is  decomposed,  and  the  polarities  are  in  accord- 
ance with  laws  already  stated. 

830.  Induction  is  an  act  of  contiguous  particles. — Dr.  Faraday 
has  modified  the  usual  view  of  induction  just  stated,  by  showing  that 
induction  never  takes  place  at  a  distance,  without  polarizing  the  mole- 
cules of  the  intervening  non-conductor,  causing  them  to  assume  a  con- 
strained position,  which  they  retain  as  long  as  they  are  under  the 
influence  of  the  inductive  body. 

Because  air  and  other  non-conductors  permit  the  passage  of  electrical 
influence  in  this  manner,  Faraday  calls  them  dielectrics,  in  distinction 
from  electrics,  or  conductors  which  can  become  polarized  only  when 
insulated  by  some  dielectric.  Dielectrics  differ  in  their  specific  induc- 
tive capacity,  air  being  the  lowest  in  the  scale,  as  follows,  viz. :  air,  1 


544  PHYSICS    OF    IMPONDERABLE    AGENTS. 

resin,  177  ;  pitch,  1-80 ;  wax,  1-86 ;  glass,  1'90 ;  sulphur,  1'93  ;  shellac, 
1-95. 

The  apparatus  used  by  Faraday  in  determining  the  relative  inductive  capacity 
of  air  and  other  gases,  is  seen  in  fig.  565,  consisting,  essentially,  of  two  metallic 
spheres,  C  and  P  Q,  of  unequal  diameter,  the  smaller  placed  555 

in  the  centre  of  the  larger,  and  insulated  from  it  by  a  stem 
of  shellac  or  gutta  percha,  A.  The  two  halves  of  the  outer 
sphere  join  in  an  air-tight  joint,  like  the  Magdeburg  hemi- 
spheres (257).  The  space,  m  n,  may  be  emptied  of  air  by  an 
air-pump,  controlled  by  a  cock  in  the  foot,  and  filled  with 
any  other  gas  or  fluid.  This  apparatus  resembles  the  Ley- 
den  jar  (847),  with  the  advantage  of  changing  the  intervening 
dielectric  at  pleasure.  The  balls,  C  and  B,  constitute  the 
charged  conductor,  upon  the  surface  of  which  all  the  electric 
force  is  resident  by  virtue  of  induction.  As  the  medium  in 
m  n  may  be  changed  at  pleasure,  while  all  other  things  re- 
main the  same,  then  any  changes  manifest  by  the  proof- 
plane  and  torsion  balance,  will  depend  on  changes  made  in 
the  interior.  The  same  end  would  be  reached  by  having  two 
exactly  similar  inductive  apparatus,  with  different  insulating 
media.  When  one  was  charged  and  measured,  the  charge.  J 
being  divided  with  the  other,  the  ultimate  conditions  of  both  indicate  by  the 
torsion  balance  whether  or  not  the  media  had  any  specific  differences.  (For 
further  details,  see  Faraday's  Exp.  Res.  1197.) 

831.  The  attractions  and  repulsions  of  light  bodies  (811)  can 
be  explained  only  in  view  of  the  phenomena  of  induction.  The  excited 
tube  or  resin,  decomposes  the.  neutral  electricity  in  the  pith-balls  or 
bits  of  paper,  repelling  the  electricity  of  opposite  name,  and  being  thus 
left  of  an  opposite  excitement  to  the  rod  or  resin,  they  become  attracted 
to  the  exciting  body,  in  obedience,  to  electrical  laws.  All  cases  of  elec- 
trical repulsion  are  equally  referable  to  attraction  under  inductive 
influence.  Thus  the  apparent  repulsion  of  the  two  pith-balls  in  an 
electroscope,  is  really  the  effect  of  the  attraction  of  surrounding  bodies, 
whose  electrical  equilibrium  is  disturbed  by  the  inductive  influence  of 
the  exciting  cause. 

The  following  experiment  illustrates,  in  an  interesting  manner,  the  develop- 
ment of  electricity,  and  the  attractions  and  repulsions  of  light  bodies  by  induc- 
tion. Support  by  its  edges  a  pane  of  dry  and  warm  window-glass,  about  an 
inch  from  the  table,  on  two  pieces  of  dry  wood,  and  place  beneath  it  several 
pieces  of  paper  or  pith-balls.  Excite  the  upper  surface  by  friction  with  a  silk 
handkerchief,  the  electricity  of  the  glass  becomes  decomposed,  its  negative  fluid 
adheres  to  the  silk,  and  its  positive  to  the  upper  surface  of  the  glass  plate ;  this, 
by  induction,  acts  on  the  lower  surface  of  the  glass,  repelling  its  positive  elec- 
tricity, and  attracting  its  negative,  the  intervening  dielectric  being  polarized  as 
explained,  and  the  lower  surface  of  the  glass  electrified  by  induction  through 
its  substance,  attracts  and  repels  alternately,  the  light  bodies,  like  the  excited 
tube  (811).  (Bird.)  Numerous  experiments,  illustrative  of  induction,  are  given 
under  the  electrical  machine. 


ELECTRICITY. 


545 


832.  Electrometers.— Cavallo's,  Volta's,  and  Bennett's  —The 

electroscopes  mentioned  in  section  813,  serve  to  indicate  the  presence 
and  name  of  the  electricity.  Electrometers  are  designed  to  give  ap- 
proximate measures  of  the  quantity  of  elec- 
tricity. 

Fig.  566  shows  Cavallo's  electrometer — a  bell- 
jar  with  a  metallic  rod  and  button,  B,  sustaining 
two  pith-balls,  m,  at  the  ends  of  two  wires.  Volta 
substituted  for  the  two  pith-balls,  two  delicate 
blades  of  straw,  p.  Bennett  replaced  these  by 
two  strips  of  gold  leaf,  o,  placed  face  to  face. 
When  the  knob,  B,  receives  electricity,  the  pith- 
balls,  straws,  or  gold  leaves,  diverge,  and  by  the 
degree  of  their  divergence,  measured  on  a  graduated  arc,  the  intensity  of  the 
electricity  is  judged  of.  Two  strips  of  tin  foil,  c  c',  are  567 

pasted  to  the  inside  of  the  glass  bell,  to  discharge  the 
diverging  leaves,  when  they  are  repelled,  so  as  touch  the 
sides.  Otherwise  the  inside  of  the  glass  jar  would  be  elec- 
trified by  induction,  and  render  the  apparatus  useless ;  and 
to  avoid  dampness,  the  top  of  the  bell  is  varnished,  and  the 
air  within,  dried  by  quick  lime.  Approaching  an  excited 
body  towards  B,  the  gold  leaves  diverge,  because  the  posi- 
tive fluid,  if  the  excitant  is  positive,  is  driven  into  them, 
while  the  negative  is  attracted  to  B.  Touching  B  with  the 
linger,  the  positive  fluid  passes  off  to  the  earth,  but  on 
withdrawing  the  finger,  the  leaves  diverge  under  the  influ- 
ence of  the  negative  electricity  remaining  in  the  apparatus. 

Fig.  567  is  a  sensitive  form  of  gold  leaf  electrometer,  with 
brass  condensing  plates,  \  846,  and  a  cup  at  top  to  illustrate  the  effect  of  evapora- 
tion in  producing  electrical  excitement. 

Hare's  single  leaf  electrometer,  and  the  condensing  electrometer,  are  mentioned 
in  section  846,  and  Bohnenberger's  under  the  dry  pile,  g  873. 

IV.     ELECTRICAL  MACHINES. 

&J3.  The  electrophorus. — Any  apparatus  by  which  electrical  phe- 
nomena may  be  obtained  at  pleasure,  is  an  electrical  machine.  The 
simplest  apparatus  of  this  sort  is  Volta's  electrophorus,  or  carrier  of 
electricity,  invented  in  1775.  668  569 

A  cake  of  resin,  or  a  disk  of  whalebone- 
india-rubber,  or  gutta  percha,  eight  or 
ten  inches  in  diameter,  is  excited  by  a 
fur  or  warm  flannel,  and  a  smaller  disk  of 
brass,  or  tin  plate  (with  rounded  edges),  is 
placed  on  it  by  an  insulating  handle.  Touch 
the  upper  surface  of  the  metallic  disk  with 
the  finger  (fig.  568),  in  order  to  allow  the 
escape  to  the  common  reservoir  (815)  of  the 
negative  electricity,  resulting  from  the  decomposition  of  the  neutral  fluid  in  the 
metallic  plate  by  the  excited  resin.  Now  removing  the  finger,  raise  the  disk  by  tb 


546 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


insulating  handle,  and  approach  its  edge  to  any  conductor,  as  the  knuckle,  fig. 
569 ;  immediately  a  strong  spark  is  seen,  due  to  the  free  positive  electricity 
existing  in  A.  Place  A  on  B  again,  touch  it  as  before,  and  the  same  result 
may  be  obtained  as  often  as  desired.  If  A  is  left  in  repose  upon  B,  it  will  remain 
charged  a  long  time,  even  for  weeks,  and  a  Leyden  jar  may  be  charged  with  it  at 
any  time:  on  the  table  of  the  laboratory  it 
may  be  more  conveniently  used  than  an  ordi- 
nary electrical  machine  for  exploding  gases. 
The  section  of  the  electrophorus,  seen  in  fig. 
570,  shows  how  the  inductive  action  of  the 
excited  resin  acts,  in  affecting  the  electrical 
nomenclature  of  each  surface,  as  indicated  by 
the  signs  -f-  and  — .  tea^mmmil^Sfiails^ 

The  phenomena  involved  in  the  electrophorus  are  identical  with 
those  explained  in  \  829.  Of  course,  if  the  plate,  A,  were  raised 
without  touching,  it  would  manifest  no  electrical  excitement ;  the  two 
luids  re-combining  as  in  the  insulated  conductor,  fig.  563. 

834.  The  cylinder  electrical  machine. — When  larger  quantities 
:f  electricity  are  required  than  can  be  obtained  from  the  means  already 
described,  resort  is  had  to  machines  of  larger  size,  and  more  power,  all 
3f  which,  however  various  in  form,  consist  principally  of  three  parts, 
viz. :  1st,  a  non-conductor,  usually  of  glass,  revolving  on  a  horizontal 
axis,  and  producing  friction ;  2d,  a  rubber,  against  which  the  non- 
conductor presses.  The  rubber  is  a  soft,  elastic  non-conducting  body, 
as  a  cushion  of  leather,  usually  armed  with  amalgam,  to  be  described 
hereafter.  3d,  two  conductors,  usually  of  brass,  mounted  on  glass  sup- 
ports, one  to  receive  the  -f-  and  the  other  the  —  electricity. 

In  the  cylinder  machine,  fig.  571,  a  smooth  cylinder,  M,  of  glass,  insulated 

571 


and  filled  with  perfectly  dry  air,  is  revolve  1  by  the  winch  before  the  rubber 


ELECTRICITY.  547 

sustained  on  the  insulated  prime  conductor,  A,  and  covering  about  one-eighth 
of  its  surface :  an  apron  of  silk  is  usually  attached  to  the  upper  -edge  of  the 
rubber,  and  extends  as  far  as  the  points,  P,  on  the  second  conductor,  B,  designed 
to  receive  the  -j-  electricity  excited  at  C.  If  the  connecting  rods,  E  D,  are 
approached  as  in  the  figure,  and  the  cylinder  is  revolved,  and  there  is  no  con- 
nection with  the  earth,  then  the  -(-  electricity  accumulated  on  the  positive  con- 
ductor, will  reunite  with  a  spark  with  the  —  electricity  of  the  negative  conductor, 
A,  again  to  be  decomposed  as  before  at  C.  If  the  negative  conductor,  A,  is 
connected  with  the  earth  by  a  chain  or  metallic  thread,  then,  when  the  machine 
is  worked,  a  continuous  flow  of  sparks  of  positive  electricity  will  pass  from  the 
positive  conductor,  B,  to  any  conductor  near  enough  to  receive  them.  But  if  A 
is  insulated,  and  B  is  connected  with  the  earth,  then  from  E,  a  continuous  flow 
of  negative  electricity  is  obtained.  In  this  case  a  flow  of  positive  electricity 
takes  place  from  the  cushion,  C,  through  the  conductor,  B,  to  the  earth,  thus 
leaving  the  conductor  A  charged  with  negative  electricity.  This  form  of  cylinder 
machine  was  designed  by  an  Englishman  named  Nairne. 

Amalgam.— No  considerable  quantity  of  electricity  can  be  evolved 
from  an  electrical  machine  of  glass,  unless  the  rubber  is  excited  with 
an  amalgam  composed  usually  of  four  parts  mercury,  eight  zinc,  and 
two  tin,  mixed  with  some  unctuous  matter  and  spread  on  silk  or  leather. 
The  zinc  is  first  melted ;  the  tin  is  added,  and  the  mixture  stirred,  and 
poured,  not  too  hot,  into  a  wooden  box,  coated  inside  with  chalk,  and 
into  which  the  heated  mercury  has  been  first  poured.  The  lid  is  put 
on,  and  the  box  violently  shaken,  until  the  amalgam  becomes  cool.  It 
is  then  finely  pulverized  in  a  mortar,  and  becomes  as  soft  as  butter. 

835.  Ramsden's  plate  machine,  as  its  name  indicates,  has  a  plate 
or  plates  of  glass  substituted  for  the  cylinder.  This  form  of  apparatus 
is  seen  in  fig.  572.  The  plate,  F  F,  is  revolved  by  the  winch,  M,  sus- 
tained in  a  frame,  0  0,  of  baked  wood.  Two  pairs  of  spring  cushions, 
a  c,  armed  with  amalgam,  produce  friction.  The  conductors,  C  C,  collect 
the  electricity  from  the  glass  by  the  points  seen  on  the  inside  of  their 
curved  branches,  placed  near  the  surface  of  the  plate.  Each  of  the 
cushions  is  connected  with  the  earth  by  the  conductor,  D ;  strips  of 
tin  foil  pasted  upon  the  edges  of  the  frame,  0,  and  shown  in  573 
the  figure  unshaded,  communicate  between  the  four  sets  of 
cushions  and  the  chain  D. 

Ramsden's  apparatus  originally  gave  only  positive  electricity. 
It  was  so  modified  by  Von  Marum  as  to  obviate  this  defect.  This 
form  of  electrical  machine  was  contrived  by  Ramsden,  of  London, 
in  1776. 

The  earliest  electrical  machine  was  made  by  Otto  V.  Guericke 
(who  invented  the  air-pump),  and  was  a  globe  of  sulphur  or  resin, 
driven  by  a  motor  wheel,  the  hand  being  used  for  friction.  A  cone  of  sulphur, 
fig.  573,  cast  in  a  wine-glass,  and  provided  with  a  glass  rod  as  a  handle,  serves 
to  illustrate  this  early  electrical  apparatus.  But  hard  india-rubber  is  a  more 
convenient  and  certain  source  of  negative  electrical  excitement. 

In  the  United   States,  our  mechanicians  have  brought  all  apparatus 


548 


PHYSICS    OP   IMPONDERABLE   AGENTS. 


for  electrical  illustrations  to  a  degree  of  perfection  leaving  little  to  be 

desired. 

572 


836.  The  American   plate   electrical   machine. — The  form  of 
plate  machine  commonly  adopted  in  the  United  States  is  seen  in  fig. 
574  (from  Ritchie).     It  is  arranged  for  the  exhibition  of  both  electrici- 
ties at  pleasure,  and  has  a  prime  conductor  on  a  movable  stand. 

DR.  HARE  has  very  ingeniously  met  the  difficulty  of  obtaining  both 
electricities  from  the  plate  machine  by  making  the  plate  revolve  hori- 
zontally, and  thus  allowing  the  positive  and  negative  conductors  to 
stand  like  arches  in  two  vertical  planes  at  right  angles  to  each  other 
above  the  plate.  Am.  Jour.  Sci.  [1]  VII.  108.)  Dr.  Hare  was  an 
ardent  supporter  of  the  Franklinian  hypothesis,  and  this  apparatus 
was  contrived  to  sustain  his  arguments  in  favor  of  that  view. 

837.  Large   electrical  machine. — Ritchie's  double    plate  ma- 


ELECTRICITY.  549 

thine. — The  largest  electrical  machine  hitherto  constructed,  so  far  as  we  are 
advised,  is  that  made  for  the  University  of  Mississippi,  at  Oxford,  under  th« 

674 


direction  of  President  Barnard,  by  Ritchie,  of  Boston.  The  general  construction 
of  this  gigantic  electrical  apparatus  may  be  understood  from  fig.  575  (frontis- 
piece), in  which,  however,  the  prime  conductors  are  not  shown.  These,  for 
greater  convenience  of  manipulation,  are  made  movable  on  separate  supports. 

This  machine  has  two  plates  of  French  glass,  each  six  feet  in  diameter,  sus- 
tained by  an  insulated  steel  axle,  upon  eight  cut-glass  supports,  on  a  frame  of 
rosewood.  The  plates  are  excited  by  four  pairs  of  rubbers,  made  of  brass,  and 
lined  with  fine  wool  felt  three-eighths  of  an  inch  thick,  such  as  is  used  for  the 
dampers  of  the  gn*nd  piano.  These  are  covered  with  firm  India  silk,  upon 
which  the  amalp;am  is  spread.  Rubbers  of  this  construction  are  found  to  be  far 
more  efficient  th/m  those  in  general  use.  The  prime  conductors  of  this  machine 
expose  fifty  square  feet  of  polished  brass  cylinders  in  three  sections,  about  one 
foot  in  diametei  by  seven  in  length,  sustained  also  on  cut-glass  insulating  pil- 
lars. One  turn  Df  this  machine  fills  the  apartment  with  an  overpowering  odor 
of  ozone.  It  is  so  arranged  as  to  afford  negative  electricity  from  four  rubbers. 
One  battery  for  this  machine  contains  one  hundred  and  twenty  glass  bells, 
arranged  in  detachments,  whose  coated  surfaces  expose  about  ninety  square  feet 
of  area.  No  detailed  description  of  the  performance  of  this  superb  machine 
has  yet  been  mude  public.  It  cost  over  three  thousand  dollars  without  its  bat- 
teries. 

The  Tyler Lan  machine. — The  largest  and  most  famous  plate  machine 
mentioned  in  the  books  before  that  of  Ritchie,  of  Boston,  both  on  account  of  its 
pize  and  performance,  was  made  by  Cuthbertson  for  Von  Marum  in  1755,  and 
was  plated  ii  ,.he  Tylerian  Museum,  at  Haarlem,  in  Holland.  It  was  a  double 


650  PHYSICS    OF    IMPONDERABLE    AGENTS. 

plate  machine,  each  plate  sixty-five  inches  in  diameter,  with  eight  cushions, 
nearly  sixteen  inches  in  length,  and  twenty-three  and  a  half  feet  surface  in  the 
conductor.  It  gave  three  hundred  sparks  twenty-four  inches  long  in  a  minute 
forked  like  lightning,  and  with  rays  six  or  eight  inches  long,  branching  from  the 
angles  of  the  flash.  It  deflected  a  thread  six  feet  long,  six  inches  from  a  per- 
pendicular, at  a  distance  of  thirty-eight  feet,  and  the  balls  of  Cavallo's  electro- 
scope (832)  diverged  half  an  inch  asunder  when  forty  feet  distant  from  it.  The 
prime  conductor  was  supported  on  three  glass  pillars  sending  out  collecting 
branches  between  the  plates.  Two,  and  sometimes  four  men,  were  employed 
to  turn  it.  When  in  full  force,  a  single  spark  from  the  conductor  sufficed  to 
burn  and  dissipate  a  strip  of  gold-leaf  twenty  inches  long,  and  one  and  a  half 
lines  wide.  A  pointed  wire  exhibited  the  appearance  of  a  luminous  star  wheji 
held  twenty-eight  feet  from  the  conductor. 

All  glass  is  not  equally  fit  for  electrical  plates ;  that  which  is  white,  hard,  and 
free  from  bubbles,  is  most  esteemed.  If  too  much  alkali  is  used  in  the  compo- 
sition of  the  glass,  its  surface  attracts  moisture,  and  soon  becomes  damp  and 
rough.  Such  a  plate  is  worthless.  The  preference  given  to  old  plates  is  due, 
probably,  to  the  fact,  that  their  composition  has  enabled  them  to  preserve  their 
properties  uninjured. 

838.  Care  and  management  of  electrical  machines. — Perfect 
insulation  and  freedom  from  dust  and  roughnesses,  are  essential  to  the 
good  condition  of  all  electrical  machines.     For  this   end,  the  glass 
columns  are  varnished,  to  avoid  the  deposition  of  moisture,  and  all  the 
polished  surfaces  of  metal,  as  well  as  the  glass,  must  be  kept  quite 
clean,  and  free   of  dust.      If  the  surface   of  the   cylinder   or   plate 
becomes  streaked  with  amalgam,  it  must  be  wholly  removed.     It  is 
better  not  to  put  any  amalgam  into  immediate  contact  with  the  glass, 
but  to  spread  it  upon  the  cushion  pretty  thickly,  and  then  to  cover  it 
with  a  piece  of  silk ;  a  sufficient  quantity  will  pass  through  the  silk, 
as  the  machine  is  worked. 

If  the  glass  becomes  greasy,  it  is  best  washed  with  rectified  camphene,  burn- 
ing fluid,  or  ether.  It  is  indispensable  that  the  surface  of  the  amalgam  should 
be  in  good  metallic  communication  with  the  earth,  which  is  accomplished  by  the 
use  of  tin  foil,  or  tinsel.  Cushions  stuffed  with  metal  filings  are  preferred  by 
some,  chiefly  for  this  reason.  A  cushion  or  rubber  made  of  two  or  three  folds 
of  cotton-flannel,  between  which  is  laid  a  continuous  strip  of  tin  foil,  of  the 
same  size  with  the  rubber,  works  exceedingly  well.  Ritchie  prefers  piano  felt. 
Aurum  mitssivum  (the  bisulphuret  of  tin),  a  yellow  bronzy  powder,  is  an  excel- 
lent substitute  for  amalgam.  It  is  supposed  to  suffer  chemical  decomposition 
when  in  use,  and  _so  to  quicken  the  activity  of  the  machine.  Finally,  a  dry 
winter  air  is  indispensable  for  the  best  working  of  an  electrical  machine  ;  hence, 
radiant  heat,  falling  on  the  machine,  or  an  apartment  heated  by  a  dry  furnace 
air,  is  especially  favorable.  In  carpeted  rooms,  it  is  desirable  to  connect  the 
rubber  with  a  gas-fixture,  to  secure  a  good  communication  with  the  common 
reservoir. 

839.  Electricity  from  steam. — Armstrong's  hydro-electric  machine, 
fig.  576,  is  designed  to  illustrate  the  development  of  powerful  electrical 
effects  from  high  steam ;  a  fact  well  known  to  all  concerned  in  the 


ELECTRICITY.  551 

management  of  locomotive  steam-engines,  but  first  scientifically  noticed 
in  1840,  by  Mr.  Armstrong,  at  Newcastle-on-Tyne.  The  apparatus 
which  he  contrived  to  show  these  effects,  576 

is  a  common  high  pressure  steam  boiler, 
about  three  feet  long  and  twenty  inches  in 
diameter,  mounted  on  insulating  pillars, 
and  strong  enough  for  a  pressure  of  200 
Ibs.  to  the  inch.  The  steam  is  suffered  to 
escape  by  jets,  A,  of  a  peculiar  form,  on 
the  side  of  the  box,  B,  into  which  it  is  ad- 
mitted by  the  cock,  C.  Faraday,  in  inves- 
tigating the  electricity  of  steam,  found 
that  dry  steam  gave  no  excitement,  and 
that  the  electricity  resulted  from  the  fric- 
tion of  vesicles  of  water  against  the  sides 
of  the  orifice.  Hence,  B  contains  a  little 
water,  over  which  the  steam  escapes,  and  is  partially  condensed.  The 
jet  has  an  interrupted  passage,  seen  at  M,  to  produce  friction,  and  its 
nozzle  is  lined  with  dry  box  or  partridge  wood.  The  vapor  escapes 
against  a  plate,  P,  covered  with  metallic  points,  to  collect  the  electricity, 
and  ending  in  a  brass  ball,  D,  insulated  from  the  earth.  The  boiler  is 
negative,  and  positive  electricity  is  collected  at  D,  provided  the  water 
is  pure  and  free  from  grease.  Turpentine,  and  other  volatile  essences, 
reverse  the  polarity,  while  grease,  or  steam  from  acid,  or  saline  water, 
destroys  all  excitement.  If  the  nozzle  of  the  jet  ends  in  ivory  or  metal, 
there  is  also  no  excitement.  A  boiler,  such  as  is  described,  will  develop 
in  a  given  time,  as  much  electricity  as  four  plate  machines  forty  inches 
in  diameter,  making  sixty  turns  a  minute ;  a  truly  surprising  result. 

840.  Other  sources  of  electrical  excitement. — 1.  The  bands  of 
leather,  India-rubber,  or  gutta-percha,  used  to  drive  machinery,  some- 
times become  powerful  sources  of  resinous  electrical  excitement,  giving 
sparks  of  negative  electricity  over  twenty  inches  in  length. 

In  cotton-mills,  so  much  electricity  is  thus  set  free,  that  it  becomes  necessary 
to  let  steam  into  the  carding  and  roving  rooms,  to  avoid  inconvenience  from  the 
repulsions  and  attractions  of  the  cotton.  A  leathern  band,  mentioned  by  Mr. 
Bachelder  (Am.  Jour.  Sci.  [2]  III.,  250),  gave  sparks  to  the  finger  at  three  feet, 
and  a  luminous  brush,  to  a  steel  point,  at  seven  feet.  The  discharge  from  leathei*, 
as  from  all  bad  conductors,  is  local,  or  danger  would  attend  it. 

Dr.  Franklin,  in  a  letter  to  Bowdoin,  suggested,  for  a  portable  electrical  ma- 
chine, a  crossed  band  of  stuffed  leather,  moved  by  a  winch  over  drums. 

2.  The  friction  of  shoe-leather  on  woollen  carpets,  in  houses  warmed 
by  hot-air  furnaces,  or  steam,  in  cold  weather,  is  a  fertile  and  curious 
source  of  negative  electrical  excitement. 


552  PHYSICS    OF    IMPONDERABLE    AGENTS. 

The  young. people  in  the  author's  house  find  an  unfailing  source  of  amuse- 
ment in  cold  weather,  in  giving  eloctrical  shocks,  by  kisses  and  otherwise,  to 
unwary  people,  or  in  lighting  the  gas  by  a  spark  from  the  finger,  or  a  key- 
handle,  after  running  briskly  over  the  carpet.  Prof.  Loomis  has  noticed  these 
effects  in  detail  in  the  Am.  Jour.  Sci.  [2]  X.,  821,  and  XXVL,  586.  They 
appear  to  be  unknown  in  Europe,  owing  probably  to  the  fact  that  European 
houses  are  seldom  warmed  and  dried  by  hot-air  furnaces. 

841.  Theory  of  the  electrical  machine. — The  phenomena  of  the 
electrical  machine  may  be  explained,  either  on  the  theory  of  one  or  two 
fluids.      The   explanations  of   induction  (828),   already  given,   apply 
equally  to  the  development  of  free  electricity,  upon  the  prime  conduc- 
tors of  electrical  machines.     When  the  machine  is  turned,  the  neutral 
electricity  of  the  rubber  is  decomposed,  the  positive  fluid  follows  the 
glass,  until  coming  opposite  the  points  on  the  prime  conductor,  the 
negative  electricity  of  the  conductor  flows  out,  to  unite  with  the  posi- 
tive of  the  glass,  while  the  positive  fluid  of  the  conductor  is  repelled  to 
the  other  end,  thus  leaving  the  prime  conductor  powerfully  positive. 
Reaching  the  rubber,  the  neutral  fluid  of  the  glass  is  there  decomposed, 
its  negative  portion  seeks  the  common  reservoir,  and  the  positive  fol- 
lows the  revolving  glass  to  the  points  as  before.     The  conductor  does 
not  acquire  positive  electricity  from  the  plate,  but  gives  its  negative 
thereto,  thus  becoming  itself  positive. 

It  is  still  an  open  question  whether  the  action  of  the  amalgam  is  chemical  or 
mechanical  (834).  It  is  certain  that  an  amalgam  of  silver,  or  gold,  does  not  act 
to  excite  electricity,  like  amalgams  of  oxydizable  metals;  and  Dr.  Wollaston 
demonstrated,  that  the  latter  did  not  act  in  an  atmosphere  of  carbonic  acid  or 
nitrogen,  free  of  oxygen. 

In  all  cases,  the  discharge  of  an  electrical  conductor,  by  a  spark  or  otherwise, 
is  accompanied  by  the  induction  of  an  opposite  excitement  in  the  body  receiving 
the  shock,  whose  opposite  electricity,  uniting  with  that  of  the  conductor  by  a 
forcible  disruption  of  the  intervening  dielectric,  produces  the  sound  and  flash 
of  the  electric  discharge. 

842.  Experimental  illustrations  of  electrical  attractions  and 
repulsions. — A  multitude  of  instructive  and  amusing   experiments 
may  be  made  with  the  electrical  machine,  illustrating  the  law  of  attrac- 
tion.    A  few  must  suffice.  577 

1.  The  insulating  stool  is  a  bench  with 
glass  legs,  fig.  577  (a  board  on  four  black  bottles 
answers  perfectly),  on  which  a  person  may  stand  f. 
or  sit,  while  in  communication  with  the  electri- 
cal machine.  Being  thus  insulated,  the  free 
electricity  can  escape  only  through  the  sur- 
rounding air, — approaching  the  knuckle  to  any 
part  of  the  person  or  dress  of  one  so  situated, 
a  strong  spark  is  received.  Except  for  the  hair  being  repelled,  the  person 
charged  is  not  conscious  of  any  change  from  an  ordinary  state.  A  doll's  head, 
with  paper  hair,  set  upon  one  of  the  conductors,  is  a  common  electrical  toy. 


ELECTRICITY. 


553 


580 


2.  Henley's  electioscope,  fig.  578,  serves  to  mark  the  degree  of  tension 
in  the  machine  by  the  repulsion  of  a  pith-ball  at  the  end  of  a  straw  :    it  is 
mounted  on  one  of  the  conductors,  and   in    dry       578  579 
weather   remains  extended   a   long   time,  but  in 

damp  weather  falls  immediately,  when  the   ma- 
chine stops. 

3.  Electrical  bells,  fig.  579;  the  bells,  A 
and  B,  are  suspended  by  a  metallic  thread,  from 
the  ends  of   a  cross-bar  of  metal    hung    on    the 
machine ;  the  bell,  C,  and  the  two  clappers,  are 
hung  by  insulating  threads.     C  is  connected  with 
the  earth ;  and  when  the  machine  is  worked,  A  and 
B  become  positive,  and  by  induction  C  becomes 
negative,  and  the  little  clappers  being  alternately 

attracted  and  repelled,  a  constant  ringing  is  kept  up  as  long  as  the  excitement 

lasts.    If  the  machine  is  too  active,  luminous  sparks  pass,  and  the  bells  remain  still. 

The  bells  may  be  conveniently  arranged  on  an  independent  foot,  as  in  fig.  580. 

4.  Volta's  hail-Storm  is  a  contrivance  designed  to  show  how  (in  Volta's 
view)  hail  might  be  produced.     It  is  a  larger  way  of  581 
ehowing  the  same  facts  already  explained  in  $  811.     A 

glass  bell  communicates  with 
the  machine,  fig.  581,  above, 
and  rests  on  a  metal  plate  in 
communication  with  the  earth. 
When  the  machine  is  worked) 
the  pith-balls  on  the  plate  are 
violently  agitated,  being  drawn 
up  and  repelled  again  actively, 
while  the  excitement  lasts.  A 
simple  bell-glass,  or  large  tum- 
bler, electrized  by  contact  of  its 
interior  surface  with  the  con- 
ductor of  an  electrical  machine, 
answers  quite  as  well,  and  may 
be  placed  over  a  heap  of  pith- 
balls  on  the  table;  they  are 
violently  thrown  about  as  long 
as  the  excitement  continues.  The  dance  of  puppets,  fig.  582,  is  only  a  substi- 
tution of  little  figures  of 'dancing  peasants,  made  of  cork  or  582 
pith,  and  placed  between  two  metallic  plates. 

5.  The    electrical    wheel    is    composed   of    several 
points  fixed  in  a  centre,  so  balanced  as  to  rest  on  an  upright, 
sustained  on  one  of  the  conductors,  fig.  583;  as  the  machine 
is  workedy  the  escape  of  the  electricity  from  the  points  reacts 
on  the  air  with  sufficient  force  to  revolve  the  wheel  with  acti- 
vity.    The  existence  of  such  a  current  of  air,  caused  by  the 
escape  of  electricity  from  points,  is  further  shown  : — 

6.  By  a  candle  flame  ;  a  candle,  fig.  584,  held  before 
the  point,  has  its  flame  blown  aside  by  the  rush  of  air  accom- 
panying the  electricity.    If  the  candle  is  placed  as  a  conductor, 

uid  a  point  is  held  out  to  it,  the  direction  of  the  flame  is  altered  by  the  reverse 
fluid  induced  vu  the  point,  fig.  585. 
49* 


554 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


This  experiment  has  been  called  the  electrical  blow-pipe.  The  rush  of  air  from 
the  points  may  be  so  energetic  from  an  active  machine,  as  to  extinguish  the 
flame.  In  the  dark,  all  points  on  an  electrical  583 

machine  emit  a  stream  of  light,  called  the  elec- 
trical brush.   Of  course  584 
no  sparks  can  be  drawn 
585 


from  points,  but  a  Leyden  jar  may  be  silently  charged  from  them.  Masts  and 
yards  of  ships  are  often  seen  thus  tipped  with  fire  (called  St.  Elmo's  fire)  in  a 
thunder  storm.  If  the  point  is  covered  with  a  ball  an  inch  or  two  in  diameter, 
its  peculiar  action  ceases,  and  the  ball  emits  sparks. 

7.  Franklin's  spider,  Ellicott's  electrical  water-pot,  the  inclined  plane,  and  the 
electrical  planisphere,  are  other  well-known  forma  of  apparatus,  designed  to 
show  the  same  principle.  The  catalogues  of  all  leading  instrument-makers, 
contain  numerous  additional  illustrations  to  the  same  end. 

V.     ACCUMULATED  ELECTRICITY  AND  ITS  EFFECTS. 

843.  Disguised  or  latent  electricity. — The  phenomena  of  induc- 
tion, already  explained,  have  a  curious  and  most  important  extension 
in  the  subject  of  this  chapter.     When  two  equal  and  insulated  conduc- 
tors, equally  excited  by  the  two  opposite  electricities,  are  separated 
from  each  other  by  only  a  thin  plate  of  glass,  or  other  dielectric  mate- 
rial, no  signs  whatever  of  any  electrical  excitement  are  communicated 
by  either  to  an  electroscope  connected  with  them.     The  dielectric  pre- 
vents the  union  of  the  opposing  electricities,  but  not  their  mutual 
inductive  action,  whereby  their  presence  is  entirely  masked  to  sur- 
rounding bodies. 

Removed  to  some  distance  from  each  other,  each  manifests  free  elec- 
tricity, by  the  divergence  of  its  electroscope.  But  if  they  are  once 
more  brought  together,  this  evidence  of  excitement  again  disappears, 
and  so  on,  until  the  imperfect  inhalation  of  the  air  gradually  neutral- 
izes all  free  electricity. 

When  so  situated,  the  electricities  are  said  to  be  latent  or  disguised,— 
paralyzed  by  their  mutual  attractions. 

844.  The  condenser  of  JEpinus.— The  phenomena  of  disguisev. 
electricity  are  illustrated  by  the  use  of  various  condensers,  consisting 
essentially  of  two  extended  metallic  surfaces,  and  an  insulating  Mie- 


ELECTRICITY  555 

dium.  They  are  sometimes  adapted  to  accumulate  electricity  of  high 
tension,  and  sometimes  their  aid  is  invoked, to  render  sensible,  quanti- 
ties of  electricity  otherwise  insensible. 

The  condenser  of  ^Epinus,  figs.  586,  587,  is  designed  for  the  former  purpose, 
fwo  polished  metallic  surfaces,  AC,  with 
electroscopes,  a  b,  and  an  intermediate 
thin  glass  plate,  B,  fig.  587,  are  all 
mounted  on  insulating  glass  pillars,  and 
slide  in  a  groove  cut  in  the  base.  In  fig. 
586,  the  two  disks  are  placed  in  close 
contact  with  the  intervening  dielectric, 
B,  while,  by  the  chain,  n,  positive  elec- 
tricity flows  into  A,  from  the  excited 
conductor  of  an  electrical  machine. 

Did  A  stand  alone,  it  could  only  receive  so  much  electricity  as  would  raise  its 
surface  to  the  same  tension  with  the  prime  conductor  of  the  machine.  But  this 
condition  is  wholly  changed  by  the  presence  of  the  second  plate,  C,  cut  off  from 
actual  contact  with  A,  by  the  dielectric,  B,  but  entirely  within  its  inductive  in- 
fluence. A  part  of  the  natural  fluid  of  C  is  at  once  decomposed  by  this  influ- 
ence of  A,  attracting  its  negative  fluid  to  the  inner  surface  of  C,  and  holding  it 
there,  while  the  corresponding  positive  fluid  from  C,  is  expelled  by  the  conduc- 
tor, m,  to  the  earth.  No  free  electricity  would  remain  if  it  were  possible  for  B 
to  exist  and  act  as  a  dielectric  without  thickness  :  but,  as  this  is  evidently  im- 
possible, it  happens  that  a  little  less  negative  fluid  is  drawn  to  the  surface  of  C, 
than  exists  of  positive  on  A,  by  reason  of  the  thickness  of  B.  Consequently, 
the  electroscope  on  A  remains  slightly  elevated  (residual  charge),  even  after 
some  time,  while  that  on  C  continues  wholly  passive. 

But  the  neutralization  of  A's  positive  fluid  by  the  decomposition  of  an  equiva- 
lent of  natural  electricity  in  C,  results  in  diminishing  the  tension  of  A,  to  the 
low  degree  corresponding  to  its  residual  free  electricity.  Hence,  A  can  receive 
a  fresh  charge  from  the  machine,  raising  its  tension  to  its  first  condition,  and 
inducing  the  decomposition  of  a  fresh  portion  of  neutral  electricity  in  C  as 
before,  and  thus  the  action  proceeds,  until  the  whole  of  the  natural  fluid  of  both 
plates  is  decomposed  and  disguised,  or  rendered  latent,  excepting  that  small 
portion  which  at  each  instant  constitutes  ihefree  electricity,  equivalent  to  the 
difference  due  to  the  thickness  of  B,  and  which,  as  we  have  seen,  would  be  null, 
if  B  could  be  conceived  of  as  having  no  thickness.  It  is  this  small  residue 
which  constitutes  the  residual  charge  in  the  Ley  den  jar. 

In  performing  this  experiment,  the  knuckle  may  serve  as  a  conductor  to  the 
earth,  in  place  of  »>,  when  a  rapid  series  of  sparks  will  be  received  (positive 
electricity),  constantly  diminishing,  and  ceasing  with  the  maximum  charge  of 
A  and  C.  This  p.oint  of  maximum  charge  is  dependent  on,  1st,  the  extent  of 
surface  in  A  B ;  2d,  on  the  tension  of  the  prime  conductor;  and  3d,  on  the 
thickness  of  B. 

When  the  point  of  saturation  in  A  and  B  is  reached,  and  all  the  electricities 
possible  are  disguised  in  the  condenser,  the  pendulum  on  A  still  shows  only  a 
feeble  excitement,  although  both  A  and  B  are  in  a  state  of  extreme  tension. 
Withdraw,  now,  A  and  C  from  B,  as  shown  in  fig.  587 ;  now,  the  electroscopes, 
A  and  B,  both  show  high  excitement :  restore  the  plate  again  as  at  first,  and  b 
becomes  again  entirely  passive,  while  a  shows  the  same  feeble  excitement  as 
before.  The  opposing  fluids  on  A  and  C  are  wholly  occupied  with  their  mutual 


550  PHYSICS    (F    IMPONDERABLE    AGENTS. 

attractions,  and  only  the  small  excess  of  -|-  fluid  is  free,  as  already  explained 
to  affect  the  electroscope,  B.  The  plates,  A  and  C,  are  now  fully  i-harged  witj 
disguised  electricity,  rendered  latent  by  mutual  inductions,  and  the  polarization 
of  the  dielectric  B.  Although  apparently  passive,  they  are  actually  in  a  stat« 
of  high  tension,  as  may  be  proved  by.thtir  discharge. 

845.  The    discharge    of  the    condenser   may   happen   in   three 
ways: — 1st,  insensibly;  by  the  imperfect  insulation  of  the  supports, 
especially  if  the  air  is  damp  ;  but  always  gradually. 

2d,  by  the  disruptive  discharge.  If  the  plate,  B,  is  too  thin  in  refer- 
ence to  the  extent  of  surface  in  A  and  C,  the  tension  of  the  opposing 
fluids  will  overcome  the  cohesion  of  the  glass,  B,  and  it  will  be  shivered 
in  pieces,  with  a  loud  explosion,  and  brilliant  spark.  The  same  spark 
and  explosion  may  take  place  without  destroying  the  dielectric,  if  we 
use  a  discharging  rod,  to  effect  communication  between  A  and  C.  Thia 
apparatus  is  either  single,  as  in  fig.  533  5S9 

588,  or  double,  as  in  fig.  589.  If 
this  rod  is  provided  with  glass  in- 
sulating handles  (as  in  the  figures), 
the  experimenter  feels  no  sensation  ; 
but  otherwise,  or  if  A  and  C  are 
brought  into  connection  by  the 
naked  hands,  then  a  powerful  shock 
is  experienced,  convulsing  the  whole 
frame.  The  same  sensation,  in  a 
feeble  degree,  is  felt  when  the 
knuckle  receives  the  sparks  of  an  excited  machine. 

3d,  and  lastly,  the  charged  plates  may  be  slowly  discharged  by  alter- 
nate connection  with  the  earth.  While  the  condenser  is  in  the  condition 
indicated  by  fig.  586,  touch  C  with  the  finger ;  no  effect  follows  ;  touch 
A,  and  a  feeble  spark  is  received ;  the  electroscope,  a,  falls,  while,  at 
the  same  instant,  that  on  C  is  raised  to  the  same  degree,  showing  that 
what  A  has  lost  in  free  positive  electricity,  C  has  gained  in  free  nega- 
tive fluid.  Touch  C  ;  a  slight  shock,  a  feeble  spark,  and  the  fall  of  the 
electroscope,  B,  ensue,  while  the  electroscope  on  A  again  manifests  it8 
original  excitement.  Thus,  by  the  alternate  discharge  of  A  and  C,  the 
whole  of  their  disguised  fluids  are  gradually  set  free  and  discharged. 

846.  Volta's   condensing   electroscope. — This    instrument   de 
pends  on  the  principles  just  explained,  and  is  used  to  render  sensible 
by  condensation,  electricity  of  too  feeble  a  tension  to  affect  the  ordinary 
gold-leaf  electrometer. 

The  plate  A.  fig.  590,  is  covered  with  waxed  silk,  slightly  larger  than  the 
disks;  this  takes  the  place  of  the  dielectric,  B,  fig.  586.  .  When  the  instrument 
is  used,  the  upper  plate  is  placed  in  the  position  shown  in  fig.  591,  and  its  sur- 


ELECTRICITY. 


555 


face  is  touched  with  the  body  whose  excitement  we  would  measure;  e.  g.  a 
crystal  of  tourmaline.      At  the  same  time,  the  under  590 

surface    of    the    lower     plate  591 

(in  connection  with  the  gold 
leaves),  is  touched  by  the 
moistened  finger  of  the  other 
hand.  The  influence  of  the  ex- 
cited electric  acts  in  this  case 
exactly  as  has  been  already 
explained  in  the  condenser  of 
ZEpiuus.  No  divergence  is 
seen  in  the  gold  leaves,  until 
the  upper  plate  of  the  conden- 
ser is  raised,  as  in  fig.  590, 
when  the  gold  leaves  promptly 
diverge :  this  action  being 
heightened  by  the  inductive 
influence  of  two  little  balls  of 
polished  brass,  rising  within 
the  glass  as  high  as  the  lower 
edge  of  the  gold  leaves. 

Dr.  Hare's  single  gold- 
leaf     electrometer. — In 

this  instrument,  a  single  gold  leaf,  about  three  inches  long,  by  one-third 
of  an  inch  broad,  is  hung  by  a  brass  rod  from  the  top  of  a  bell  or  globe, 
as  in  the  last  instrument.  Immediately  opposite  to  the  lower  end  of 
the  leaf,  a  similar  rod  of  metal  passes  through  an  opening  in  the  side 
of  the  vessel  carrying  a  gilded  disk  of  wood  or  paper  half  an  inch  in 
diameter.  This  lateral  rod  is  graduated  to  measure  small  distances. 
To  use  this  instrument,  the  lateral  rod  is  put  in  communication  with 
the  earth,  and  an  electric  is  brought  in  contact  with  the  upper  disk, 
when,  if  the  distance  between  the  leaf  and  the  lower  disk  is  small,  the 
most  minute  attractive  force  is  detected.  In  the  original  592 
instrument,  Dr.  Hare  employed  a  plate  of  zinc,  on  an 
insulating  handle,  and  one  of  copper  on  the  instrument 
arranged  as  in  Volta's  electrometer,  when  the  simple 
separation  of  these  two  disks  would  evince  a  tenfold  deli- 
cacy of  action  compared  to  Volta's  condenser.* 

847.  The  Leyden  jar. — Accident  led  to  the  discovery 
of  this  remarkable  piece  of  apparatus,  long  before  its 
principles  were  made  clear  by  the  condenser  of  ^Bpinus, 
and  the  explanations  of  Franklin.  It  consists  of  a  thin 
glass  jar,  fig.  592,  coated  inside  and  outside  with  tin  foil, 
as  far  as  the  bend  of  the  neck.  The  inner  surface  is  extended  by  the 


*  Hare's  Mechanical  Electricity,  Philadelphia,  1835,  p.  29. 


558  PHYSICS    OF    IMPONDERABLE   AGENTS. 

wire,  carrying  a  brass  knob  at  top,  touching  the  inner  coating  by  a 
piece  of  chain  or  wire,  and  sustained  in  its  place  by  passing  through 
a  non-conducting  cover  of  dry  wood. 

The  relations  of  the  jar  and  the  two  metallic  coatings,  will  be  seen  by  fig.  593, 
showing  in  section  a,  Ley  den  jar,  the  parts  of  which  are  separable,  and  its  wire  bent 
conveniently  into  a  hook,  to  suspend  it  on  the  machine.  It  will  be  seen  at  a  glance 
that  this  arrangement  is  identical  in  principle  with  the  condenser  of  ^Epinus,  and 
the  electrical  plates  of  Franklin.  If  the  knob,  b,  of  the  Leyden  jar,  insulated 
upon  a  stand,  fig.  594,  is  presented  to  the  conductor,  a,  of  the  electrical  machine 
in  action,  only  a  single  spark  or  so,  will  enter  it,  unless 
a  way  is  provided,  as  by  the  conductor,  c,  for  the  escape  of 
the  similar  electricity  from  the  exterior  coating,  593 
while  its  opposite  is  then  fixed  as  in  C,  fig.  587. 
The  charging  of  the  jar  then  proceeds,  and  for 
every  spark  which  darts  from  a  to  b,  a  correspond- 
ing one  of  similar  electricity,  is  seen  to  escape 
from  the  outer  coating  to  c.  When  it  is  held  in 
the  hand,  the  same  effect  follows  through  the  arm, 
accompanied  by  a  slight  twinge  in  the  nerves. 
Presently  the  point  of  saturation  is  reached,  and  the  two  decomposed  electricities 
are  latent.  Either  coating  may  be  fearlessly  touched  alone,  but  as  soon  as  by  the 
discharger  or  otherwise,  communication  is  made  between  them,  a  loud  snap  and 
brilliant  spark  follow  with  a  violent  shock. 

The  invention  of  the  Leyden  jar,  or  vial,  is  commonly  attributed  to  Cun^eus 
or  Muschenbroek  of  Leyden,  in  1746.  Von  Kleist,  dean  of  the  chapter  at  Comin, 
in  Pomerania,  also  independently  discovered  this  important  instrument  by  a 
similar  accident. 

With  a  view  to  fix  electricity  in  some  insulated  substance,  Cunseus,  in  1746, 
led  electricity  into  a  small  vial  containing  water,  by  a  bent  nail  thrust  through 
the  cork,  and  hung  upon  the  prime  conductor.  Endeavoring,  in  one  of  these 
trials,  to  detach  the  vial  and  nail  from  the  electrical  machine,  Cunreus,  to  his 
great  amazement,  received  a  violent  shock.  Von  Kleist,  in  the  course  of  a 
valuable  series  of  experiments  (1745)  on  electricity,  led  the  fluid  by  a  brass 
wire  or  pin  into  a  bottle  containing  mercury.  "As  soon,"  he  says,  "as  this 
little  glass,  with  the  pin,  is  removed  from  the  electrical  machine,  a  flaming 
pencil  issues  from  it  so  long,  that  I  have  been  able  to  walk  sixty  paces  in  the 
room  with  this  little  burning  machine;  and  if  the  finger  or  a  piece  of  money  be 
held  against  the  electrified  pin,  the  stroke  coming  out  is  so  strong  that  both 
arms  and  shoulders  are  shaken  thereby." 

This  discovery  of  so  wonderful  a  power  in  nature,  before  unsuspected,  created 
immense  excitement  over  the  civilized  world,  and  it  was  precisely  at  this  time 
that  Franklin  immortalized  himself  by  his  contributions  to  the  new  science.  He 
explains  the  action  of  the  Leyden  vial  by  his  single  fluid  hypothesis,  in  his 
"  Observations  and  Experiments  on  Electricity,"  in  a  manner  which  must  ever 
win  for  him  the  reputation  of  a  profound  philo-  595 

sopher. 

848.  Electricity  in  the  Leyden  jar 
resides  on  the  glass. — In  fig.  595,  the 
jar,  A,  is  composed  of  the  three  separable 
pieces ;  B,  the  glass,  C,  its  outer,  and  D, 
its  inner  metallic  coatings.  When  this  jar  is  charged,  and  set  on  an 


ELECTRICITY.  559 

insulating  surface,  it  may  be  separated  into  its  three  parts  without 
being  discharged ;  but  C  and  D  will  then  be  found  by  the  electroscope 
entirely  free  from  excitement,  while  B  remains  strongly  excited.  Put- 
ting the  parts  together  again  as  in  A,  the  jar  will  be  found  charged  as 
at  first,  if  the  air  is  dry,  and  too  much  time  has  not  passed. 

849.  The  electric  battery.— As  the  charge  of  the  Leyden  jar  is, 
other  things  being  equal,  directly  as  its  surface,  large  jars  are  plainly 
of  more  power  than  small  ones.  But  a  limit  of  size  is  soon  reached, 
which  the  thickness  of  glass  required  for  strength,  and  other  circum- 
stances, render  it  unprofitable  to  pass.  Hence  several  coated  jars,  of 
moderate  size,  are  united  by  joining  all  their  inner  coatings  by  metallic 
rods,  and  all  their  outer  coatings  by  a  common  conducting  base,  as 
shown  in  fig.  596.  Such  an  arrangement  596 

is  called  an  electrical  battery.  When 
charged  from  a  common  source,  and  dis- 
charged in  the  usual  way,  they  all  act  as 
one  great  jar,  the  result  being  not  quite 
in  the  ratio  of  the  number  of  jars,  but 
nearly  so.  Hence,  the  smaller  the  num- 
ber, the  thinner  the  glass,  and  greater  the 
size  of  the  jars,  the  better,  and  several 
batteries  of  seven  and  nine  jars,  united  to  the  charging  rods  of  the 
central  jars,  are  preferable  to  more  extended  single  series.  They  are 
charged  by  connecting  the  interior  with  the  prime  conductor  by  t, 
and  the  exterior  with  the  earth.  If  the  battery  is  extensive,  and  the 
machine  powerful,  great  caution  is  requisite  to  avoid  receiving  its 
shock ;  a  i  accident  which  might  be  serious  in  its  consequences. 

The  bat:  :ry  used  by  Von  Marum,  with  the  machine  already  noticed  (837),  em- 
braced one  hundred  jars,  each  thirteen  inches  in  diameter  and  two  feet  high.  The 
coated  surface  was  five  hundred  and  fifty  square  feet  (five  and  a  half  feet  to  each 
jar).  When  fully  charged,  its  force  was  irresistible.  A  bar  of  steel  nine  inches 
long,  half  an  inch  wide,  and  one-twelfth  of  an  inch  thick,  was  rendered  power- 
fully magnetic  by  the  discharge.  A  small  iron  wire,  twenty-five  feet  long,  was 
deflagrated,  and  various  metals  were  dissipated  and  raised  in  vapor,  when 
placed  in  the  circuit  of  discharge.  A  book  of  200  pages  was  pierced  by  it,  and 
blocks  of  hard  wood,  four  inches  square,  split  into  fragments. 

850.  Discharge  in  cascade. — A  series  of  two  or  three  Leyden  jars 
may  be  placed  horizontally  upon  insulating  stands,  so  that  the  interior 
of  each  succeeding  one  may  receive  the  spark  from  the  outer  coatings 
of  the  one  preceding. 

This  mode  of  charging  cannot  be  carried  beyond  two  or  three  jars,  owing  to 
the  accumulated  resistance  soon  vitiating  the  result.  But  Mr.  Baggs,  of  London, 
has  very  ingeniously  contrived  an  electric  battery,  the  jars  of  which  are  charged 
together,  but  are  discharged  consecutively.  Each  jar  is  supported  in  a  horizontal 
position  on  a  vertical  spindle,  their  kno'os,  while  being  charged,  pointing  out- 


060 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


ward,  like  the  radii  of  a  circle,  and  when  the  battery  is  to  be  discharged,  the 
knobs,  by  a  quarter  revolution,  are  brought  opposite,  each  to  the  bottom  of  the 
next  jar.  In  this  way  the  disruptive  power  or  intensity  of  the  spark  is  multi- 
plied as  the  jars,  the  quantity  remaining  the  same.  Mr.  Boggs  is  said  to  have 
discharged  his  battery  of  twelve  jars  through  a  space  of  three  feet.  (Am. 
Jour.  Sci.  [2]  VII.  418.) 

851.  The  universal  discharger. — Various  contrivances  are  in  use 
for  regulating  or  measuring  the  discharge  of  the  electric  battery,  and 
the  single  jar.    Of  these,  Henley's  597 

universal  discharger,  fig.  597,  is, 
perhaps,  the  most  useful.  By 
means  of  this  simple  apparatus, 
the  electrical  fluid  may  b«  made  to 
pass  through  any  substance  placed 
upon  the  table,  t.  Two  rods,  slid- 
ing in  the  joints  a  of ,  end  in  balls, 

c  c',  covering  points  which  can  be 

exposed  by  their  removal.  The  rod,  a',  connects  with  the  positive  side 
of  the  battery,  for  example,  while  by  the  discharging  rod,  fig.  589, 
communication  can  be  made  at  pleasure  between  a  and  the  negative 
side  of  the  battery,  by  a  chain  or  metallic  thread. 

The  charge  of  the  battery  may  be  prevented  from  passing  a  given  limit,  by 
using  the  discharging  electrometers  of  Lane  or  Cuthbertson,  in  which  a  ball  ig 
sustained  at  such  a  distance  from  the  discharging  knob  of  the  battery,  that  when 
its  charge  reaches  the  proper  tension,  it  discharges  itself. 

A  beautiful  illustration  of  the  slow  discharge  of  a  charged  jar  is 
seen  in  fig.  598,  where  a  charged  Leyden  jar,  with  a  small  bell  in 
place  of  the  knob,  is  set  upon  a  board,  598 

near  to  a  little  brass  ball,  hung  from  a 
silken  thread,  upon  a  wire,  carrying  a 
second  bell  in  connection  with  the  earth 
by  A  B.  The  effect  is,  that  the  -f  elec- 
tricity of  the  jar  attracts  the  little  ball, 
lut  after  striking  the  bell,  the  ball  is  re- 
pelled, until,  coming  in  contact  with  the 
other  bell,  it  is  discharged,  and  so  on  for 
many  hours,  this  little  chime  is  rung  by 
the  electrical  pendulum. 

852.  The  electric  spark.— The  elec- 
tric light  and  spark  result  from  the  re- 
union of  the  two  electricities  in  the  air. 
In  a  vacuum  there  is  no  spark  (fig.  601). 

The  zigzag  path  of  the  spark  and  of  lightning  is  due  to  the  resistance 
of  the  air  Every  electrical  discharge  produces  expansion  of  the  air, 


ELECTRICITY. 


561 


and  the  form  and  color  of  the  spark  are  materially  influenced  by  the 
density  and  chemical  composition  of  the  gaseous  medium  through 
which  it  passes.  The  character  of  the  sparks  depends  also  on  the  form, 
area,  and  electrical  intensity  of  the  discharging  surfaces,  likewise  on 
the  kind  of  electricity  on  the  conductor  in  which  the  spark  originates ; 
from  the  negative  conductor  the  sparks  are  far  less  dense  and  powerful 
than  those  from  positive  electricity.  599 

Kinnersley's  thermometer,  fig.  599,  shows  the 
agitation  and  expansion  of  the  air  following  an  electrical 
explosion.  A  portion  of  water  in  the  larger  vessel,  which 
is  air-tight,  communicates  freely  with  the  small  open  tube, 
attached  to  the  foot,  and  ending  in  a  narrow  glass  tube. 
When  an  electrical  discharge  takes  place  through  the  ap- 
paratus, the  consequent  expansion  of  the  air  violently  raises 
the  column  in  the  smaller  tube,  but,  after  the  commotion  is 
over,  the  fluid  gradually  regains  its  original  level,  as  the 
air  in  the  larger  vessel  cools.  The  electrical  mortar  dis- 
charges its  ball  by  the  force  of  air  expanded  at  the  moment 
of  the  electrical  discharge. 

The  color  of  the  electrical  spark. — Faraday 
observed  that  in  air,  oxygen,  and  dry  chlorohydric 
acid  gas,  the  spark  was  white,  with  a  light  bluish 
shade,  especially  in  air.  In  the  heavy  thunder- 
storms common  in  an  American  summer,  the  light 
of  a  powerful  flash  of  lightning  is  distinctly  purple, 
and  sometimes  violet.  In  nitrogen  it  is  blue  or 
purple,  and  gives  a  remarkable  sound ;  in  hydrogen 
it  is  crimson,  and  disappears  when  the  gas  is  rare- 
fied ;  in  carbonic  acid  the  color  is  green,  and  the  form  of  spark  very 
irregular ;  in  oxyd  of  carbon  it  is  sometimes  green  and  sometimes  red  ; 
in  chlorine  it  is  green.  600 

The  little  apparatus,  fig.  600,  is 
well  calculated  to  show  these  effects 
by  contrast  at  one  view.  The  three 
tubes,  a  a'  a",  are  respectively  filled 
with  various  gases  and  sealed.  Each 
tube  has  two  short  platinum  wires,  nn, 
soldered  into  its  sides,  through  which 
the  electric  spark  from  b  must  pass 
on  its  way  to  the  ground  by  c. 

The  electrical  discharge  in 
a  vacuum,  becomes  an  ovoidal 
tuft  of  light,  uniting  the  con- 
ductors. The  apparatus,  fig.  601,  is  designed  to  show  these  effects. 
A  large  egg-shaped  glass  vessel  is  mounted  at  the  lower  extremity 
with  a  stop-cock,  for  attaching  it  to  the  air-pump,  in  order  to  re 
50 


062 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


move  the  whole  or  a  part  of  the  air,  or  to  replace  it  by  vapor  of 
alcohol,  ether,  or  any  other  gas  not  acting  on  601 

brass.  By  the  rod,  A,  connection  is  established 
with  the  electrical  machine,  while  the  distance 
between  the  electrical  poles,  B  C,  may  be 
adjusted  by  sliding  the  upper  rod  in  its  air- 
tight socket.  This  apparatus  is  called  the 
electrical  or  philosophical  egg.  The  rarer  the 
air,  the  more  globular  becomes  the  spheroid, 
and,  at  the  same  time,  less  brilliant.  The 
auroral  tube  is  only  a  modification  of  the  same 
apparatus. 

This  apparatus  is  also  used  with  splendid  effect 
with  the  Induction  coil. 

Difference  between  the  positive  and 
negative    spark.— The    tuft   of   light   from 
positive  electricity  is  far  more  beautiful  than 
that  from  negative,  as  seen  from         602 
the   ends   of    two    points.     Thus, 
while  positive  electricity  gives  an 
opening  sheaf  of  light,  negative 
electricity  gives  only  a  small  star, 
fig.   602.     In   rarefied    air,    these 
differences   are   much  less    appa- 
rent.   Faraday  suggests  that  they  are  due,  chiefly,  to  the  greater  facility 
with  which  negative  electricity  escapes  in  air,  than  603 

positive,  as  conductors  negatively  charged,  lose  their 
excitement  sooner  than  those  positively  charged. 

The  diamond  jar.— To  show  that  the  coatings  of 
the  jar  convey  the  electricity  collected  on  the  glass 
to  the  point  where  it  meets  the  cause  of  discharge,  a 
jar  may  be  coated  with  metallic  filings,  fig.  603,  or 
patches  of  tin-foil,  fig.  604,  cut  in  lozenges        604 
(a  diamond  jar).    The  wire  of  the  jar  is 
bent  over,  as  in  fig.  003,  so  as  to  bring  the 
ball  near  the  outer  coating,  which  connects 
l»y  a  chain  with  the  earth.     When  the  ma- 
chine (on  whose  arm  this  jar  is  hung)  is 
worked,  a  brilliant  spark  is  seen  at  inter- 
vals to  dart  from  the  knob  to  .the   outer 
coating,   and  thence   to  spread  *  in    zigzag 
courses  over  the  whole  surface. 
Scintillating  tube  and  magic  squares.  _ 
—Every  collection  of  electrical  apparatus  contains  these  familiar  pieces 


ELECTRICITY. 


563 


of  apparatus,  illustrative  of  the  phenomena  of  the  electric  spark.     The 
scintillating  tube,  fig.  605,  like  the  jar,  fig.  604,  has  rows  of  lozenge- 

605 


shaped  pieces  of  tin-foil  pasted  on  its  interior,  usually  in  a  spiral,  and, 
when  held  by  the  hand,  as  shown  in  the  figure,  the  electricity  flashes 
from  point  to  point  at  the  same  apparent  instant,  producing  a  most 
agreeable  effect.  606 

The  magic  squares  are  panes  of 
glass  on  which  are  interrupted  strips 
of  tin  foil,  cat  to  represent  some 
design,  to  be  made  visible  only  when 
a  spark  passes.  These  squares  are 
mounted  on  a  foot,  in  connection 
with  the  earth,  and  are  set  near  the 
ball  of  the  prime  conductor.  By 
scattering  metallic  filings  over  a 
varnished  surface  of  glass,  the  same 
effect  is  produced  as  upon  the  jar, 
fig.  603. 

853.  Effects  of  the  electric 
discharge.— The  effects  of  the 
electric   discharge    are    chiefly, 
1st,    physiological ;    2d,    physi- 
cal ;  3d,  mechanical ;  4th,   che- 
mical.    The  passage  of  the  electricities  through  bodies,  is  sometimes 
impeded  by  their  bad  conducting  power,  or  by  want  of  proper  dimen- 
sions ;  and,  in  either  case,  a  powerful  electric  discharge  manifests  itself 
in  one  of  those  modes. 

854.  Physiological  effects. — These  are  seen  in  the  shock  experi- 
enced by  all  living  beings,  in  the  passage  of  electricity  through  any 
of  their  members.     Any  number  of  persons,  joined  hand  to  hand,  will 
receive,  at  the  same  instant,  the  shock  of  an  electric  battery.     Abb6 
Nollet  imparted  it  to  over  six  hundred  persons  in  his  convent  at  one 
time — those  in  the  middle  of  the  chain  being  little  less  affected  than 
those  near  the  conductors. 

A  person  charged  on  the  insulating  stool,  feels  a  prickly  heat  and  glow  of  the 
ekin,  resulting  in  perspiration.     Many  useful  applications  have  been  devised  of 


564 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


this  agent  in  medicine.*  It  needs  hardly  to  be  said,  that  the  full  shoe*  of  a 
powerful  battery  will  destroy  life  in  man.  Sparks,  fifteen  or  eighteen  inches 
lomr  begin  to  be  unsafe,  if  from  large  surfaces.  Small  animals,  as  birds,  are 
easily  killed  by  a  moderate  discharge,  on  the  table  of  the  universal  discharger. 
Fig.  597. 

855.  Inflammation  of  combustibles.— Although  no  sense  of  heat 
is  felt  when  the  knuckle  receives  strong  sparks  from  an  active  machine, 
yet  the  smallest  spark  serves  to  inflame  ether,  whether  from  a  Leyden 
jar,  from  the  finger,  or,  more  strikingly,  from  an  icicle  held  in  the 
fingers  of  one  mounted  on  an  insulating  607 

stool. 

The  ether  is  placed  in  a  metallic  cup,  and  the 
spark  should  be  drawn  on  its  edge  moistened  with 
ether,  fig.  607.  Gunpowder  placed  on  the  table 
of  the  universal  discharger,  over  the  points  of 
the  rods,  a  a',  fig.  597,  is  simply  thrown  about, 
without  being  fired;  but  if  a  wet  string,  in 
place  of  one  of  the  conducting  wires,  forms  part 
of  the  connection,  its  retarding  power  is  such  as 
to  fire  the  powder.  The  lighting  of  gas  from 
the  finger  of  one  charged  by  running  on  a  car- 
pet has  already  been  mentioned  (840,  (2).)  Lycopodium,  alcohol,  a  newly 
extinguished  candle,  and  many  other  combustibles,  are  also  easily  inflamed  by 
the  s-iark  Gold  leaf  confined  between  two  glass  plates  with  the  edges  hang- 
ing out,  will  burn  with  the  explosion  of  the  glass,  and,  if  held  between  cards, 
will  stain  them  with  purple  oxyd  of  gold.  Silhouette  likenesses  of  Franklin 
are  thus  printed:  a  powerful  current  from  a  battery  is  needed  for  this. 

856.   Chemical  union  effected  by  electricity.— A  mixture  of 

hydrogen  two  volumes,  and  of  oxygen  one  volume,  or  of  hydrogen  with 

seven  or  eight  times  its  volume  of  common  air,  is  exploded  by  a  spark 

passing  through  the  containing  vessel,  e.  g.  609 

the  tin  air-pistol,  called  "  Volta's  pistol," 

fig.  608,  is  provided  with  an  insulated  con- 
ductor, ending  near  the  inner  608 

surface  of  the  pistol  at  B. 

Its  mouth  is  closed  tightly 

by   a  cork,  and   the    spark 

caused  to   pass   by  holding 

it  near  the  prime  conductor, 

fig.  609,  or  to  the  electro- 

phorus.     The   cork  is  then 

violently  expelled,  by  the  expansion  of  steam,  with  a  loud  explosion. 


*  Consult  Garratt's  Electro-physiology,  Boston,  1860,  8vo.,  pp.  708  j  or  Chan- 
ning's  Medical  Electricity. 


ELECTRICITY. 


565 


610 


Volta's  electrical  lamp.— A  self-regulating  hydrogen  apparatus  is 
seen  in  fig.  610,  similar  in  its  action  to  the  common  hydrogen  lamp, 
with  platinum  sponge.  In  its  base  drawer 
is  an  electrophorus,  r  P,  the  plate,  P,  of 
which  is  always  charged.  A  silk  cord 
connects  the  upper  plate  P,  with  the  gas 
cock,  R,  in  such  a  way  that  when  the  gas 
in  T  is  drawn,  the  communication  is  ef*- 
fected  at  o,  with  the  insulated  wire,  t/, 
and  the  electricity  thus  finds  its  way  in 
a  spark  between  the  buttons  at  0,  and 
escapes  to  the  earth  by  t.  As  the  hydro- 
gen is  flowing  at  that  moment  from  the 
jet,  it  is  inflamed,  and  kindles  a  little 
candle  standing  in  its  path.  Every  time 
the  cock,  R,  is  moved,  the  plate,  P,  rises, 
and  communicates  a  spark.  With  care, 
this  instrument  remains  in  action  for  weeks,  from  a  single  excitement. 
857.  The  mechanical  effects  of  the  electrical  discharge.— Any 
thin  non-conducting  substance  placed  between  the  balls  of  the  univer- 
sal discharger,  is  either  pierced  or  broken  where  the  fluid  passes.  The 
phenomena  attending  these  experiments  are  curious  and  instructive  in 
point  of  theory. 

When  a  thin  piece  of  glass,  v,  is  placed  in  the  position  seen  in  fig.  611, 
between  the  points  of  the  conductors,  a  b,  a  small  hole  will  be  made  through 
the  glass,  as  if  with  a  drill,  provided  the  effect  of  the  fluid  is  concentrated  by 
placing  a  drop  of  oil  at  the  point  to  be  pierced.  The  hole  is  circular,  starred, 
and  its  edges  smooth,  and  sometimes  it  remains  filled  with  the  powdered 
glass  in  fine  dust,  easily  removed.  It  requires  a  powerful  battery  to  pierce 
glass  one-twelfth  of  an  inch  thick.  gj2 

If  a  card  is  placed  in  the  path  of  the  fluid,  it  is  pierced  with 
a  raised  edge  (burr)  on  both  sides  of  611 

the  hole.  When  the  card  is  placed 
obliquely,  as  seen  in  fig.  612,  between 
the  points,  ac,  of  the  insulating  holder, 
the  hole  is  made  in  the  place  and  di- 
rection seen  at  o  in  the  section ;  that 
is,  nearer  the  negative  pole,  its  edges 
being  raised,  or  thickened,  a  circum- 
stance due,  probably,  to  the  decompo- 
sition of  the  neutral  fluid  in  the  card, 
occasioning  a  rush  of  electricity  in  both 
directions.  This  has  been  esteemed  a 
fact  inexplicable  on  the  single  fluid  hypothesis,  while  the  position  of  the  hole, 
always  near  to  the  negative  pole,  indicates  that  the  negative  fluid  passes  less 
readily  through  the  air  than  the  positive.  Many  othe-  examples  of  the  frac- 
50* 


566  PHYSICS    OF    IMPONDERABLE    AGENTS. 

ture,  or  dispersion  of  non-conducting  bodies,  may  be  gathered  from  tbe  largei 
treatises. 

858.  The  chemical  effects  of  statical  electricity  are  generally  fee- 
ble.    Besides  those  before  alluded  to  (856),  Wollaston,  with  very  fine 
points  of  gold  wire   immersed   in  water,  decomposed  water   in   very 
small  quantity.     A  paper  moistened  with  iodid  or  bromid  of  potassium, 
is  stained  brown  by  the  electrical  discharge  when  it  is  laid  upon  the 
scintillating  square  (fig.  606)*    defiant  gas,  sulphuric  acid,  chlorohy- 
dric  acid,  ammonia,  and  nitrous  oxyd,  are/decomposed  by  the  electric 
discharge,  with  the  separation  of  their  constituent  elements,  and  car- 
bonic acid  is  decomposed  into  oxygen,  and  oxyd  of  carbon.     The  ele- 
ments of  the  air  unite  under  a  prolonged  series  of  sparks  (Priestley), 
to  form  nitric  acid  (Cavendish),  and  lightning  in  the  atmosphere  forms 
the  same  compound,  as  the  analysis  of  rain-water  has  shown  (Liebig). 
Numerous  other  evidences  of  the  chemical  effects  of  electricity  have 
been  recorded ;  perhaps  the  most  important  of  these,  is  that  atmo- 
spheric effect,  called  ozone. 

859.  Ozone. — This  term  is  derived  from  the  Greek,  in  allusion  to 
the  peculiar  odor  which  is  always  perceived  after  an  electrical  discharge 
or  excitation  of  a  machine,  and  sometimes  improperly  compared  to  the 
odor  of  sulphur,  which  it  does  not  at  all  resemble.     It  is  due  to  a  re- 
markable state  or  condition  induced  in  oxygen  gas  by  electricity  (and 
by  several  other  causes  also).     Mr.  Schonbein,  of  Basle,  has  devoted 
himself  to  the  study  of  the  curious  properties  of  this  singular  product, 
the  record  of  which  belongs  rather  to  Chemistry  than  to  Physics. 

VI.     ATMOSPHERIC  ELECTRICITY. 

860.  Franklin's  kite. — We  owe  to  Dr.  Franklin  the  demonstration 
that  the  phenomena  of  a  thunder-storm  are  due  to  electricity,  identical 
with  that  excited  in  electrical  experiments.     He  proposed  two  modes, 
in  1749,  by  which  he  supposed  electricity  might  be  drawn  from  the 
clouds.   Dalibard,  at  his  suggestion,  erected  in  the  open  air  near  Paris, 
in  1752,  a  pointed  and  insulated  iron  rod,  40  feet  long.     On  the  10th 
of  May,  1752,  electrical  sparks  were  obtained  from  this  rod,  with  the 
usual  snapping  sound.     In  June  of  the  same  year,  Franklin,  tired  of 
waiting  for  the  erection  of  a  tall  spire  in  Philadelphia  on  which  to 
place  his  pointed  conductor,  conceived  the  idea  of  reaching  the  higher 
regions  of  the  air  by  a  kite.     This  h"e  formed  of  a  silk  handkerchief 
stretched  over  two  light  cedar  sticks.     It  had  a  pointed  wire  at  top, 
and  a  silken  cord  insulated  the  hempen  string,  at  the  lower  end  of  which 
he  tied  an  iron  key. 

Watching  the  approach  of  a  thunder-storm,  he  raised  the  kite,  and 
soon  had  the  satisfaction  of  seeing  the  fibres  of  the  hempen  string 


ELECTRICITY.  567 

bristle  and  repel  each  other,  and  finally  when  the  rain  had  rendered 
the  string  sufficiently  a  conductor,  he  enjoyed  the  unspeakable  satisfac. 
tion  of  seeing  long  electrical  sparks  dart  from  the  iron  key.  Thus  was 
realized  by  actual  experiment  one  of  the  boldest  conceptions  and  most 
interesting  discoveries  in  the  history  of  science. 

Efforts  have  been  made  to  rob  Franklin  of  the  honor  of  this  discovery,  but  il 
iri  one  thing  to  suggest  that  two  phenomena  may  be  identical,  and  quite  anothei 
thing  to  prove  it.  Dalibard's  experiments  were  undertaken  at  Franklin's  sug 
gestions  and  hardly  preceded  his  own  in  date. 

These  experiments  were  everywhere  repeated,  and  it  soon  became  evident  thai 
they  were  far  from  being  free  from  danger.  Romas,  in  June,  1753,  during  a 
thunder-storm  in  France,  drew  flashes  of  electrical  fire  ten  feet  long,  from  a  kite 
raised  by  a  string  550  feet  long.  The  experiment  was  accompanied  by  every 
evidence  of  intense  electrical  tension  in  the  attraction  of  straws,  the  sensation 
of  spiders'  webs  over  the  faces  of  the  spectators,  and  in  the  loud  reports  and 
roaring  sounds,  similar  to  the  noise  of  a  large  bellows.  In  August,  1753,  Prof. 
Richmann,  of  St.  Petersburgh,  lost  his  life  while  engaged  in  similar  experiments. 
Cavallo,  in  London,  in  1777,  obtained  enormous  quantities  of  atmospheric  elec- 
tricity by  an  electrical  kite,  and  noticed  that  it  frequently  changed  its  character 
as  the  kite  passed  through  different  layers  of  the  air.  In  telegraph  offices  during 
a  thunder-storm,  vivid  sparks,  often  very  inconvenient  and  not  without  danger, 
are  constantly  flowing  from  the  receiving  instruments,  being  induced  on  the 
telepraph  wires  from  the  atmosphere,  during  thunder-storms.  (Henry,  Am. 
Jour.  Sci.  [2]  III.  25.) 

861.  Free  electricity  in  the  atmosphere. — That  the  atmosphere, 
besides  the  combined  electricity  proper  to  it,  contains  also  at  all  times 
free  electricity,  is  proved  by  raising  an  insulated  conductor  a  few  feet 
into  the  air,  as  by  a  long  tishing-rod,  and  connecting  it  with  the  con- 
denser of  the  electrometer,  the  leaves  of  which  will  diverge  sensibly 
when  there  is  no  sign  of  any  thunder-storm.  Near  the  earth  (say  within 
three  or  four  feet),  no  evidence  of  free  electricity  can  be  detected,  but 
as  we  rise  in  the  air,  its  force  constantly  increases.  Becquerel  and 
Breschet,  sent  up  arrows,  attached  to  a  tinsel  cord  ninety  yards  long, 
from  the  top  of  the  Great  St.  Bernard,  while  the  other  end  was  con- 
nected with  the  condenser  of  an  electrometer ;  they  found  that  the  gold 
leaves  diverged  in  proportion  as  the  arrow  rose  higher. 

It  appears  from  experiments  like  these  and  others  made  chiefly  by  Ronalds, 
of  Kew,  that  the  atmospheric  electricity  increases  and  decreases  daily,  twice  in 
twenty-four  hours,  and  the  following  general  results  are  established. 

1st.  The  electricity  of  the  air  is  always  positive — is  fullest  at  night — increases 
after  sunrise — diminishes  towards  noon — increases  again  towards  sunset,  and 
then  decreases  towards  night,  after  which  it  again  increases. 

2d.  The  electrical  state  of  the  apparatus  is  disturbed  by  fogs,  rain,  hail,  sleet, 
or  snow.  It  is  negative  when  these  approach,  and  then  changes  frequently  to 
positive,  with  subsequent  continued  changes  every  three  or  four  minutes. 

3d.  Clouds  also,  as  they  approach,  disturb  the  apparatus  in  a  similar  way, 
and  produce  sparks  from  the  insulated  conductor  in  rapid  succession,  so  that 
an  explosive  stream  of  electricity  rushes  to  the  receiving  pole,  which  should  be 


568  PHYSICS    OF   IMPONDERABLE   AGENTS. 

passed  off  to  the  earth.  Similarly  powerful  effects  frequently  attend  a  driving 
fog  and  heavy  rain. 

Orosse,  of  England,  had  over  a  mile  of  insulated  wire  sustained  on  poles  one 
hundred  feet  high  above  the  tall  trees  of  his  park,  connecting  by  pointed  conduc- 
tors with  his  laboratory,  where  he  has  frequently  collected,  during  a  heavy  fog. 
electricity  enough  to  charge  and  discharge  a  battery  of  fifty  jars,  and  seventy- 
three  square  feet  of  coated  surface,  twenty  times  m  a  minute,  with  a  report  as 
loud  as  that  of  a  cannon. 

Numerous  hypotheses  have  been  put  forward  to  account  for  what  has 
been  considered  the  free  electricity  of  the  atmosphere.  Prof.  Henry, 
after  an  attentive  study  of  the  whole  subject,  feels  compelled  to  reject 
them  all  as  insufficient  except  that  of  Peltier,  which  refers  these  pheno- 
mena not  to  the  excitement  of  the  air,  but  to  the  inductive  action  of  the 
earth  on  its  non-conducting  aerial  envelope.  This  view  involves  the 
assumption  that  the  earth  was  in  some  way  primarily  electrified.  It  is 
a  fact  that  the  earth  is  always  in  a  state  of  negative  excitement,  as  was 
shown  by  Volta,  who  for  this  purpose  received  the  spray  from  a  cascade 
on  the  balls  of  a  sensitive  electrometer,  when  the  leaves  diverged  with 
negative  electricity.  (See  an  able  article  on  Atmospheric  Electricity 
by  Prof.  Henry.  Patent  Office  Report,  Agriculture,  1859,  p.  485.) 

The  subject  of  atmospheric  electricity,  especially  the  description  of 
electric  meteors,  is  more  properly  referred  to  Meteorology. 

§  3.  Dynamical  Electricity. 

I.     GALVANISM  AND  VOLTAISM. 

862.  Discovery  of  galvanism. — In  1786,  Luigi  Galvani,  professor 
of  anatomy  in  the  University  of  Bologna,  while  engaged  upon  a  long 
series  of  observations  on  the  effects  of  atmospheric  electricity  upon 
animal  organisms,  noticed  that  the  legs  of  some  frogs,  prepared  for 
experiments,  became  convulsed,  although  dead  and  mutilated — when 
the  vertebrae,  with  portions  of  the  lumbar  nerves,  were  pressed  against 
the  iron  railing  of  the  window  balcony  where  they  613 

were  placed,  awaiting  the  use  for  which  they  had 
been  designed.  Repeating  this  novel  and  curious 
observation  in  various  ways,  he  soon  found  that 
the  convulsions  were  strongest  when  he  made  con- 
nection by  means  of  two  metals  between  the  lumbar 
nerves,  and  the  exterior  muscles  denuded  of  the 
skin,  as  shown  in  fig.  613,  where  rods  of  copper  and 
zinc,  being  thus  held,  convulse  the  leg  into  the 
position  shown  by  the  dotted  line.  But  contact  of 
metals  with  the  animal  tissues  he  found  not  to  be 
essential  to  produce  these  convulsions,  since  they  occur  also  by  contact 
of  the  exterior  raucous  with  the  interior  nervous  surface. 


ELECTRICITY.  569 

To  repeat  Galvani's  experiment,  strip  the  skin  from  the  legs  of  a  vigorous 
frog  and  cut  the  animal  in  two,  an  inch  above  the  thighs.  Expose  the  lumbar 
nerves  within  and  on  either  side  of  the  backbone,  by  pushing  aside  the  muscles 
with  the  finger,  so  that  the  point  of  an  arc  of  the  two  metals  may  touch  the 
nerves  j  then  bring  the  other  metal  rod  into  contact  with  any  portion  of  the 
outer  surface,  and  strong  twitchings  will  be  developed  as  if  the  animal  was 
alive,  both  on  touching  and  removing  the  rod,  even  some  hours  after  death. 

The  galvanic  fluid. — Galvani  regarded  the  convulsions  of  the  frog 
as  excited  by  a  nervous  or  vital  fluid,  which  passed  from  the  nerves  to 
the  muscles  by  way  of  the.  exterior  communication  established  between 
them :  this  fluid,  in  his  view,  existed  in  the  nerves,  it  traversed  the 
metallic  arc,  and  falling  on  the  muscles,  it  contracted  them,  like  the 
electric  discharge. 

Galvani  was  an  anatomist  and  physiologist,  ;ind  not  a  chemist,  or  physicist. 
He  did  not  work  out  all  the  teachings  of  his  own  discovery,  being  more  inte- 
rested in  demonstrating,  as  he  did,  the  existence  of  a  true  animal  electricity, 
developed  between  the  outer  surface  and  the  nerves.  The  physical  branch  of 
the  subject  he  left  to  others,  and  chiefly  to  VOLTA,  devoting  the  few  remaining 
years  of  his  life  to  the  study  of  animal  electricity.  Volta's  doctrines  Galvani 
never  accepted,  and  died  in  1798,  before  the  Voltaic  Pile  was  given  to  the  world. 
In  the  department  of  vital  electricity,  Galvani's  labors  have  been  justly  appre- 
ciated only  in  our  time,  having  been  naturally  eclipsed  in  his  own  by  the  splendid 
discovery  of  the  Voltaic  Pile,  and  the  crowd  of  wonders  following  in  its  train. 

The  story  usually  found  in  text  books,  of  the  accidental  discovery,  in  1790, 
of  the  new  science  by  the  twitching  of  frogs'  legs,  prepared  for  the  repast  of 
Madam  Galvani,  is  a  fabrication  of  Alibert,  an  Italian  writer  of  no  repute. 
Galvani  had  then  been  for  eleven  years  engaged  upon  a  laborious  series  of 
electro-physiological  experiments,  using  frogs'  legs  as  electroscropes.  No  great 
truth  was  ever  discovered  by  accident,  and  years  of  laborious  research  had  pre- 
pared the  way  for  this  discovery.  It  is  undoubtedly  true  that  what  we  find  is 
often  more  important  than  what  we  seek,  but  it  is  research  and  not  accident 
which  makes  the  discovery.  Every  hypothesis  is  good  which  bears  fruit  in  dis- 
covery ;  but  to  accept  the  discovery  and  reject  the  hypothesis  when  no  longer 
fruitful,  requires  all  the  self-denial  of  the  highest  philosophy,  and  is  a  noble 
attribute  of  the  greatest  minds. 

•863.  Origin  of  Volta's  discovery. — Contact  theory. — Adopting 
at  the  outset  with  the  greatest  enthusiasm  the  vitalist  hypothesis  of 
Galvani,  Volta  came,  after  no  long  time,  to  the  conviction  that  the 
electrical  effects  attributed  by  Galvani  to  the  animal  electricity  of  the 
frog,  were  really  due  to  the  contact  of  dissimilar  substances,  and  that 
the  frogs'  limbs  were  only  the  sensitive  electroscope,  adapted  to  indicate 
the  electrical  current  developed  by  the  two  unlike  metals.  Each  disco- 
verer saw  but  half  the  truth.  Thus  originated  his  celebrated  "  contact 
theory;"  a  view  of  the  source  of  dynamic  electricity,  that  long  held 
almost  universal  sway  over  scientific  opinion  until  gradually  supplanted 
by  the  electro-chemical  theory,  which  refers  these  phenomena  to  chemical 
action. 


570  PHYSICS    OF   IMPONDERABLE   AGENTS. 

By  the  use  of  his  condensing  electrometer  (846),  Volta  sought  to  establish  the 
contact  theory  by  a  great  number  of  well-devised  experiments.  Being  assured 
of  the  passive  state  of  the  electrometer,  he  established  communication  between 
the  earth  and  the  upper  plate  by  the  moistened  fingers,  while  at  the  same  time 
a  bit  of  zinc  plate  held  also  in  the  moistened  fingers  of  the  other  hand  is  placed 
in  contact  with  the  lower  plate ;  after  a  single  instant,  contact  is  broken,  and 
on  raising  the  upper  plate,  the  gold  leaves  diverge.  Whence  the  electricity? 
Volta  replied,  "  from  the  contact  of  the  two  unlike  substances/'  overlooking  the 
fact  that  there  was  a  chemical  action,  due  to  the  effect  of  the  moist  fingers  on 
the  zinc.  As  the  plate  touched  by  the  zinc  became  positive,  and  the  copper 
negative,  he  assumed  that  there  was  an  "  electromotive  force"  capable  of  develop- 
ing these  electrical  states  in  the  two  metals  as  a  result  of  simple  contact.  This 
experiment  was  repeated  with  conductors  of  every  sort,  and  always,  when  one 
of  them  was  an  alterable  substance,  with  the  same  results.  He  divided  conduct- 
ing bodies  into  two  classes ;  the  first  class,  including  the  metals,  metallic  ores, ' 
and  carbon,  he  calls  electromotors;-  the  second  class  contains  liquids,  saline  solu- 
tions, animal  tissues,  <fec.  He  found  that  a  double  combination  of  three  elements, 
so  arranged  that  their  order  was  reversed,  neutralized  each  other,  and  produced 
no  spasm  in  the  frog's  legs,  which  he  uniformly  used  as  an  electroscope.  This 
was  in  1796,  four  years  in  advance  of  the  date  usually  assigned  as  that  of  the 
invention  of  the  Voltaic  pile. 

Passing  over  the  long  controversy  between  Volta  and  his  cotemporaries,  we 
come  to  the  essential  fundamental  fact  of  Volta's  discovery,  viz. :  that  certain 
metals,  and  particularly  the  oxydizable  metals,  disengage  electricity  and  charge 
the  condenser,  when  placed  in  the  conditions  just  described. 

This  discovery,  immediately  led  to  the  second,  and  by  far  the  most 
celebrated  of  Volta's  discoveries,  viz.,  the  Voltaic  pile,  or  battery. 

864.  Volta's  pile,  or  the  Voltaic  battery. — Every  form  of  appa- 
ratus designed  to  produce  a  current  of  dynamic  electricity  is  called  a 
battery  or  pile.  Volta's  original  apparatus  was,  as  its  name  implies,  a 
pile  of  alternate  silver  and  zinc  disks,  laid  up  as  in  fig.  614,  with  disks 
of  paper  or  cloth  between  them,  moistened  with  brine,  or  acid  water. 
This  arrangement  was  more  commonly  made  with  alternate  disks  of 
copper  (C)  and  zinc  (Z),  care  being  taken  always  to  observe  the  order, 
copper — cloth — zinc.  The  terminal  disks  were  provided  with  ears  for 
the  convenient  attachment  of  wires.  Thus  arranged,  the  following 
characteristic  results  are  observed.  1st.  The  pile  being  insulated  by 
glass  or  resin,  touch  Z  with  the  plate  of  the  condenser  (covered  with 
silk),  while  the  finger  rests  on  C,  and  then  apply  the  plate  to  the  con- 
denser ;  the  gold  leaves  will  indicate  strong  vitreous  electricity.  2d. 
Reverse  this  order,  touching  C  with  the  plate  while  the  finger  is  on  Z, 
and  a  strong  charge  of  resinous  electricity  is  received. 

The  pile  may  be  regarded  as  a  Ley  den  jar,  or  electrical  battery,  per- 
petually charged,  and  capable  of  re-charging  itself  as  long  as  the  given 
conditions  are  maintained. 

Th'>se  results  may  be  repeated  an  indefinite  number  of  times,  as  long 


ELECTRICITY. 


571 


as  the  cloths  remain  moist,  and  the  intensity  of  the  action  is  directly  as 
the  number  of  plates  in  the  pile. 

Each  touching  couplet  of  copper  and  zinc  may  be  soldered  together, 
and  is  then  called  a  couple,  pair,  or  voltaic  element.  Any  two  metals 
of  unlike  properties  may  be  substituted  for  the  614 

zinc  and  copper,  with  the  same  results. 

The  end  of  the  pile  which  yields  vitreous 
electricity  is  called  its  positive  pole,  and  that 
which  yields  resinous  electricity  is  called  the 
negative  pole ;  a  name  also  applied  to  the  wires 
or  conductors  connecting  the  two  poles. 

Arranged  as  in  fig.  614,  the  pile,  when  its 
poles  are  joined,  gives  a  decided  shock,  similar 
to,  but  less  intense  than,  that  from,  statical 
electricity.  On  breaking  contact  between  the 
poles,  a  brilliant  spark  of  voltaic  electricity  is 
seen ;  and  if  the  wires  end  in  points  of  gold  or 
platinum,  inserted  in  water,  without  mutual 
contact,  a  flow  of  ga§  bubbles  from  them,  an- 
nounces the  decomposition  of  the  water.  We 
thus  classify  the  effects  of  the  pile  into  physio- 
logical, physical,  and  chemical  phenomena. 

The  discovery  of  the  pile,  Volta  announced  in 
March,  1800,  to  Sir  Joseph  Banks,  both  in  the 
form  just  described  and  also  the  crown  of  cups 
(Couronne  des  tasses],  a  series  of  twenty  glass 
goblets  arranged  in  a-  circle,  with  wires  con- 
necting the  -f-  and  —  elements  of  each  cup  to 
the  opposite  of  the  next. 

This  last  is  the  type  of  all  modern  batteries 
writh  separate  cells.  He  classified  its  effects,  but  made  no  mention 
of  its  power  of  chemical  decomposition,  a  property  he  had  not  then 
observed.  This  last  power  was  immediately  discovered  by  Nicholson 
,md  Carlisle,  in  London,  on  the  2d  of  May,  1800.  Aside  from  Volta' s 
theoretical  notions,  history  will  ever  assign  him  a  high  place  as  a 
philosopher,  and  as  having  by  his  genius  blessed  the  world  by  one  of 
the  greatest  and  most  fruitful  discoveries  in  science. 

Distinction  between  Voltaism  and  Galvanism. — It  will  be  seen 
that  Voltaism  and  the  Voltaic  pile  are  terms  properly  applied  only  to  the 
discoveries  of  Volta,  and  that  the  term  galvanic  battery  is  a  misnomer,  Gal- 
vani  never  having  seen  such  an  instrument.  The  term  Galvanic  fluid  is 
justly  applied  to  animal  electricity,  which  Galvani  was  the  first  to  discover. 


572  PHYSICS    OF   IMPONDERABLE    AGENTS. 

865.  Quantity  and  intensity. — There  is  a  very  marked  difference 
between  the  tension  of  the  electricity  from  the  Voltaic  pile,  and  that  of 
friction.     No  sensation  follows  the  touch  of  either  pole  of  a  Voltaic 
battery  singly :  both  poles  must  be  touched  simultaneously  in  order  to 
perceive  the   shock.     The  projectile  force  in  Voltaic  electricity  is  so 
nearly  null,  that  in  the  most  energetic  and  extensive  series  of  cells,  the 
terminal  points  must  be  brought  indefinitely  near,  or  into  actual  con- 
tact, before  any  current  is  established,  unless  in  vacuo.     The  intensity 
of  the  battery  is  however,  under  some  circumstances,  increased  by  re- 
duplicating the  number  of  couples  of  a  given  size  (see  §  881).     The 
quantity  of  electricity  set  in  motion  in  the  Voltaic  battery  depends  not 
on  the  number  of  the  series,  but  on  the  extent  of  surface  brought  into 
action  in  each  pair,  the  conducting  power  of  the  interposed  liquid,  and 
also  upon  the  external  resistance. 

The  views  formerly  expressed  by  most  authors  on  the  subject  of  quantity  and 
intensity  have  been  modified  in  important  respects  by  the  application  of  the 
"  law  of  Ohm  ;"  for  a  discussion  of  which  compare  $  881. 

866.  Simple  Voltaic  couple. — Whenever  two  unlike  substances, 
moistened  by,  or  immersed  in,  an  acid  or  saline  fluid  are  brought  into 
contact,  a  Voltaic  circuit  is  established.     The  earliest  recorded  obser- 
vation on  this  subject  (Sulzer's),  was  the  familiar  experiment  of  a  silver 
and  copper  coin,  or  bit  of  zinc,  placed  on  the  opposite  sides  of  the  tongue, 
and  the  edges  brought  together,  when  a  sharp,  prickly  sensation  and 
twinge  is  felt,  and  if  the  eyes  are  closed,  a  mild  flash  of  light  is  also 
seen.     In  this  case,  the  saliva  is  the  saline  fluid,  exciting  a  Voltaic 
current  due  to  its  chemical  effect  on  the  zinc  or  copper ;  and  the  nerves 
of  sense  are  the  electroscope.     The  action  depends  on  contact,  and 
ceases,  or  is  renewed,  as  often  as  this  is  broken  or  made. 

In  fig.  615,  we  have  the  simplest  form  of  Voltaic  battery,  a  slip  of  amalga- 
mated zinc,  Z,  and  another  of  copper,  C,  immersed  in  a  glass  of  water,  acidulated 
by  sulphuric  acid.  When  these  strips  touch  (either  within  or  515 

without  the  fluid),  an  electrical  current  is  set  up,  passing  from 
the  zinc  to  the  copper  in  the  fluid,  and  from  the  copper  to  the 
zinc  in  the  air,  as  shown  by  the  arrows.  The  polarity  of  the 
ends  in  the  air  is  the  reverse  of  that  in  the  acid,  as  shown  by 
the  signs  plus  and  minus.  This  is  analogous  to  the  decompo- 
sition of  neutral  electricity  in  a  rod  of  glass  or  of  wax.  While 
contact  is  maintained,  either  directly  or  by  conducting  wires, 
evidence  of  chemical  action  is  seen  in  the  constant  flow  of  gas 
bubbles  (hydrogen)  from  the  zinc  to  the  copper,  from  the  sur- 
face of  which  they  are  given  off,  This  action  ceases  at  any 
moment  when  contact  ceases,  and  if  the  separation  of  the  metals  takes  place  in 
the  dark,  a  minute  spark  is  seen  at  the  moment  of  breaking  contact  in  the  air. 

The  direction  of  the  Voltaic  current  depends  entirely  on  th%  nature 
of  the  chemical  action  producing  it.  Thus  if  in  the  arrangement  just 


ELECTRICITY.  573 

described,  strong  ammonia  water  was  used  in  place  of  the  dilute  acid, 
all  the  electrical  relations  of  the  metals  and  the  fluid  would  be  reversed : 
since  the  action  would  then  be  on  the  side  of  the  copper,  and  the  zinc 
would  be  relatively  the  electro-negative  metal. 

867.  Electro-positive  and  electro-negative  are  relative  terms, 
designed  to  express  the  mutual  relations  of  two  or  more  elements  in 
reference  to  each  other.     Thus  zinc,  being  a  metal  very  easily  acted  on 
by  all  acid  and  many  saline  solutions,  becomes  electro-positive  to  what- 
ever other  element  it  may  be  associated  with,  unless,  as  in  the  last 
section,  the  other  element  is  acted  on,  and  the  zinc  is  not,  when  it 
becomes  electro-negative.    Oxygen  is  an  element  which  acts  upon  every 
other,  and  is  therefore  the  type  of  electro-negative  substances ;  gold, 
platinum,  and  silver,  being  among  the  least  easily  oxydized  metals, 
become  electro-negative  substances  to  all  others  more  easily  acted  on 
than  themselves,  and  therefore  these  are  fit  substances  for  the  negative 
element  of  Voltaic  couples.     In  chemical  works,  tables  will  be  found 
in  which  all  the  elements  are  grouped  in  this  relative  order  of  electro- 
positive and  electro-negative  power. 

868.  Amalgamation. — Commercial  zinc  is  seldom  or  never  pure, 
and  the  foreign  substances  which  it  contains  are  such  as  to  stand  in  an 
electro-negative  relation  to  the  zinc.     A  slip  of  common  rolled  zinc, 
immersed  in  dilute  sulphuric  acid,  is  actively  corroded  with  the  escape 
of  abundance  of  hydrogen,  while  if  a  strip  of  chemically  pure  zinc  was 
used,  no  action  would  happen.     (De  la  Rive.)     This  action  of  common 
zinc  is  called  a  local  action,  implying  the  existence  of  as  many  small 
local  Voltaic  circuits  as  there  are  particles  of  foreign  electro-negative 
substances  on  its  surface ;  each  of  which  constitutes,  with  the  contigu- 
ous particles  of  zinc,  a  minute  battery,  and  thus  the  whole  surface  is 
presently  corroded  and  roughened,  and  the  power  of  the  whole  couple 
reduced  just  in-proportion  to  the  extent  of  this  local  action. 

Rub  the  freshly  corroded  surface  of  such  a  piece  of  commercial  zinc 
with  a  little  mercury,  when  instantly  it  combines  with  and  brightens 
the  whole  surface,  covering  it  with  a  uniform  coating  of  zinc  amalgam. 
This  perfectly  protects  the  zinc  from  local  action  by  covering  up  the 
electro-negative  points,  and  makes  the  whole  surface  of  one  electrical 
name.  Zinc,  thus  amalgamated,  may  be  left  indefinitely  long  in  acid 
water,  without  injury,  and  when  brought  into  contact  with  the  electro- 
negative element  of  a  Voltaic  couple,  it  becomes  a  much  more  energetic 
source  of  electricity  than  before. 

The  discovery  of  this  property  (due  to  Mr.  Kempt)  is  hardly  less 
important  than  the  discovery  of  the  battery,  for  without  it,  sustained 
and  manageable  batteries  are  impossible. 
61 


574 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


II.     BATTERIES  WITH  ONE  FLUID. 

8G9.  Voltaic  batteries  are  constructed  for  use  either  with  one  or 
with  two  fluids. 

The  first  embraces  the  original  crown  of  cups  (864),  and  all  batteries  with  one 
fluid  and  a  single  cell.  The  batteries  with  two  fluids  and  two  cells,  of  whatever 
name,  involve  a  double  chemical  decomposition,  and  are,  hence,  more  compli- 
cated, but  also,  generally,  more  efficient ;  we  will  consider  these  separately, 
remarking,  that  the  interest  attached  to  the  first  class,  with  a  single  exception, 
ia  now  chiefly  historical. 

870.  Trough  batteries. — The  inconvenience  of  Volta's  original 
form  of  the  pile,  fig.  614,  led  to  placing  the  elements  in  a  trough,  as 
seen  in  fig.  616,  called,  from  the 
inventor,  Cruickshank's  trough. 
Each  compound  couple  of  zinc 
and  copper  was  cemented  water 
tight  into  a  groove,  all  the  zincs 
facing  in  one  direction.  The  filling  of  these  cells  with  dilute  acid  was 
a  tedious  operation,  with  extended  series,  and  as  the  zincs  were  not 
amalgamated,  the  best  force  of  the  apparatus  was  spent  before  it  could 
be  filled.  Davy  and  Nicholson  greatly  improved  the  trough  by  attach- 
ing the  couples  to  a  bar  of  wood 
by  straps,  conm,  as  in  fig.  617, 
and  Dr.  Wollaston  surrounded  each 
zinc,  z,  with  the  copper,  on  both 
sides,  thus  doubling  the  effective 
surface.  Thus  arranged,  the  whole 
series  could  be  plunged  at  one 
movement  into  glass  cells,  a  a,  or 
into  a  porcelain  trough  divided 
into  cells.  The  famous  battery  of  the  London  Royal  ^pstitution,  (first 
used  in  May  or  June,  1810,)  was  a  series  of  2000  couples  of  this  con- 
struction, arranged  in  200  glass  or  porcelain  troughs,  ten  couples  in 
each  trough,  each  plate  having  an  effective  surface  of  twenty-two  square 
inches.  This  battery  was  placed  in  the  vaults  under  the  Royal  Insti- 
tution, where  its  hydrogen  and  acid  vapors  did  not  annoy  the  experi- 
menter, and  its  power  was  led  up  by  conductors  to  the  laboratory  above. 

The  battery  with  which  Davy  made  his  immortal  discovery  of  the 
metallic  bases  of  the  alkalies  (October,  1807),  contained  250  pairs  of 
plates,  made  in  1803.  [See  Am.  Jour.  Sci.  [2],  XXVIII.,  279.] 

Hare's  calorimotor  consisted  of  twenty  plates  each,  of  copper  and  zinc, 
nineteen  inches  square,  and  so  combined  in  a  cubical  box  as  to  form  but  two 
large  elements  of  fifty  square  feet  each,  or  two  hundred  square  feet  of  active 
surface  in  both  members,  all  plunged  by  one  movement  in  a  vat  of  acid. 


ELECTRICITY.  575 

The  deflagrators  of  Dr.  Kare,  as  originally  constructed,  were  formed 
of  spirals  of  copper  and  zinc,  rolled  with  a  narrow  space  between  them,  and  the 
opposing  metals  held  from  contact  by  wooden  strips.  Each  zinc  was  9  X  6  in., 
and  each  copper  14  X  6  in- >  so  that  every  part  of  the  zinc  was  opposed  to  the 
copper  surface ;  eighty  of  these  coils  were  so  arranged  on  bars  of  wood  as  to 
plunge  by  an  easy  mechanism  into  glass  cylinders  containing  the  acid.  The 
facility  of  immersion  and  removal  of  these  coils  in  contact  of  the  acid  liquor, 
made  Hare's  deflagrators  as  much  superior  to  the  early  trough  batteries  as  the 
batteries  of  two  fluids  are  superior  to  Hare's.  In  a  very  efficient  form  of  Hare's 
deflagrator,  the  members  were  connected  in  a  box,  suspended,  to  revolve  on  an 
axle  having  another  box  placed  at  right  angles  to  the  first,  so  that  a  quarter 
revolution  of  the  apparatus  turned  on  or  off  the  exciting  acid  at  pleasure,  with- 
out deranging  the  connections,  which  were  established  through  the  axis  of  revo- 
lution. 

A  battery  constructed  for  Prof.  Silliman,  in  Boston,  in  1836,  on  the  plan  of 
Wollaston  and  Hare  combined,  contained  nine  hundred  couples  of  copper  and  zinc 
(10  X  4  in.  each),  exposing  five  hundred  and  six  square  feet  of  available  surface, 
arranged  in  twelve  parallel  series,  capable  of  being  used  consecutively  as  nine 
hundred  couples,  or  in  three  series  of  three  hundred  each.  One  plunge  immersed 
the  whole  battery,  and  when  this  instrument  was  new,  the  arch  of  flame  between 
its  poles  measured  over  six  inches. 

Mr.  Crosse,  and  also  Mr.  Gassiot,  have  constructed  very  extended  scries  of 
trough  batteries  for  physiological  experiments  ;  the  former  had  twenty-four 
hundred  pairs  of  plates,  the  cells  well  insulated  ;  the  latter  put  up  three  thousand 
five  hundred  and  twenty  cylindrical  pairs,  placed  in  cells  of  varnished  glass, 
and  insulated  by  glass  pillars  varnished.  The  batteries  were  excited  by  water 
only.  Except  for  the  purposes  of  low  intensity  and  long-continued  action,  bat- 
teries of  this  description  are  now  no  longer  constructed. 

The  want  of  sustained  and  regular  action  in  all  batteries  of  the  original  form, 
has  led  to  the  contrivance  of  other  and  more  scientific  batteries ;  some  of  the 
most  valuable  of  which  we  will  now  describe. 

871.  Smee's  battery  is  formed  of  silver  and  amagalmated  zinc,  and 
reeds  but  one  cell  and  one  fluid  to  excite  it.  The  618 

silver  plate,  S,  fig.  G18,  is  prepared  by  washing  in 
nitric  acid  to  roughen  it,  and  then  coating  its  surface 
with  platinum,  thrown  down  on  it  by  a  voltaic  cur- 
rent, in  that  state  of  fine  division,  known  as  plati- 
num-black. This  is  to  prevent  the  adhesion  of  the 
liberated  hydrogen  to  the  polished  silver.  Any  sur- 
face of  polished  metal  retains  a  film  of  gas  with 
singular  obstinacy,  thus  preventing,  in  a  measure, 
the  contact  between  the  fluid  and  the  plate.  The 
roughened  surface  produced  from  the  deposit  of  pla- 
tinum-black, entirely  prevents  this.  The  zinc  plates, 
22,  in  this  battery,  are  well  amalgamated,  and  face  both  sides  of  the 
silver.  The  three  plates  are  held  in  position  by  a  clamp,  b,  at  top, 
while  the  interposition  of  a  bar  of  dry  wood,  w,  prevents  the  passage 


576  PHYSICS    OP   IMPONDERABLE    AGENTS. 

of  a  current  from  plate  to  plate.  Water  acidulated  with  one-seventh 
its  bulk  of  oil  of  vitriol,  or,  for  less  activity,  with  one-sixteenth,  is  the 
exciting  fluid. 

The  surface  of  the  negative  plate  is  kept  clean  in  daily  use  by  occa- 
sional immersion  in  chlorid  of  iron,  which  removes  all  foreign  substances 
deposited  on  it.  For  large  sized  batteries,  the  silver  plates  are  made  by 
electro-casting,  to  secure  entirely  plane  surfaces.  (Mathiot.) 

The  quantity  of  electricity  excited  in  this  battery  is  very  great,  but  the  inten- 
sity is  not  so  great  as  in  the  compound  batteries  presently  to  be  described.  This 
battery  is  nearly  constant,  does  not  act  until  the  poles  are  joined,  and,  without 
any  attention,  will  maintain  a  uniform  flow  of  power  for  days  together.  A  thick 
plate  of  lead,  well  silvered,  and  then  coated  with  platinum-black,  will  answer 
equally  well,  and,  indeed,  better  than  a  thin  plate  of  pure  silver.  This  battery 
is  recommended  over  every  other  for  the  student,  as  comprising  the  great  requi- 
sites of  cheapness,  simplicity,  and  constancy.  This  is  the  battery  generally 
employed  in  electro-metallurgy.  Chester  has  patented  an  improved  form  of  this 
battery,  much  used  by  the  telegraph  companies.  It  is  the  only  single  fluid  bat  • 
tery  now  much  used  in  physical  experiments. 

Mathiot  has  described  the  form  of  Srnee's  batteries  used  in  the  large  electro- 
typing  operations  of  the  United  States  Coast  Survey  Office.  See  Am.  Jour. 
Sci.  [2],  XV.,  303.  619 

872.  The  sulphate  of  copper  battery  is  designed  to 
use  a  solution  of  sulphate  of  copper  in  dilute  sulphuric 
acid,  the  copper  element  being  made  to  contain  the  ex- 
citing fluid.  This  battery,  fig.  G19,  is  used  for  electro- 
magnetic experiments,  and  although,  it  soon  becomes 
encumbered  with  a  pulp  of  metallic  copper  thrown 
down  on  the  zinc,  its  cheapness  and  constancy  will  always  render  it  a 
valuable  instrument. 

III.     DRY  PILES. 

873.  Dry  piles  of  Zamboni  and  DeLuc. — These  piles  are  con- 
structed of  disks  of  metallic  paper,  as  of  copper  and  zinc  (called  gold 
and  silver  papers),  placed  back  to  back,  and  alternating,  as  in  the  pile 
of  Volta,  fig.  614,  all  the  coppers  facing  in  one  direction.  Some- 
times zinc  paper  gilded  on  one  side ;  or  zinc  paper  smeared  with 
black  oxyd  of  manganese  and  honey  on  the  other  side,  is  used, 
and  with  more  marked  effects.  Some  hundreds,  and  even  thousands 
of  these  disks,  as  large  as  a  quarter  dollar,  are  crowded  into  a  glass 
tube,  just  large  enough  to  receive  them,  varnished  within  and  without. 
Screw  caps  of  metal  compress  and  retain  the  disks,  forming  at  the  same 
time  metallic  connections  with  the  outer  pairs  to  propagate  the  electri- 
cal effect.  A  feeble  current  is  thus  set  up,  which  may  last  for  years ; 


ELECTRICITY. 


577 


but,  if  the  paper  has  been  artificially  dried,  so  as  to  free  it  from  all 
absorbed  moisture,  no  current  exists.  g2Q 

Zamboni  (1812),  and  DeLuc  (1810),  who  first  constructed  piles 
of  this  sort,  arranged  them  in  pairs  to  ring  bells  by  the  vibra- 
tion of  a  small  electric  pendulum  (fig.  598),  alternately  attracted 
and  repelled  between  the  columns,  which  are  in  the  condition  of 
a  perpetually-charged  Leyden  jar  of  low  tension.  A  set  of  these 
bells  rang  in  Yale  College  laboratory  for  six  or  eight  years 
unceasingly. 

Bohiieiiberger's  electroscope  is  constructed  on  this 
principle.  B  and  C,  fig.  620,  are  the  poles  of  two  dry  piles,  be- 
tween which  hangs  a  single  gold  leaf,  ending  in  the  knob,  D. 
When  any  feebly  electric  body  is  approached  to  D,  the  gold  leaf 
at  once  declares  its  electrical  name,  by  being  attracted  to  its 
opposite.  This  is  undoubtedly  one  of  the  most  delicate  electroscopes  known. 

IV.     BATTERIES  WITH  TWO  FLUIDS. 

874.  Daniell's  constant  battery. — This  truly  philosophical  instru- 
ment was  invented  in  1836  ;  up  to  which  time  the  improvements  in  the 
original  Voltaic  pile  had  been  only  mechanical.  Prof.  J.  F.  Danie',1, 
of  London,  first  discovered  and  applied  an  effectual  means  of  preserving 
the  power  and  continuing  the  action  of  the  apparatus  for  a  length  of 
time.  All  other  batteries  with  two  fluids  are  only  modifications  of  his 
original  instrument. 

It  consists  of  an  exterior  circular  cell  of  copper,  C,  fig.  621, 
which  serves  both  as  a  containing  vessel  and  as  a  negative  ele- 
ment; a  porous  cylindrical  cup  of  earthenware,  P  (or  the  gullet 
of  an  ox  tied  into  a  bag),  is  placed  within  the  copper  cell,  and  a 
solid  cylinder  of  amalgamated  zinc,  Z,  within  the  porous  cup. 
The  outer  cell,  C,  is  charged  by  a  mixture  of  eight  parts  of  water 
and  one  of  oil  of  Vitriol,  saturated  with  blue  vitriol  (sulphate  of 
copper).  Some  of  the  solid  sulphate  is  also  suspended  on  a  per- 
forated shelf,  or  in  a  gauze  bag,  to  keep  up  the  saturation.  The 
inner  cell  is  filled  with  the  same  acid  water,  but  without  the  cop- 
per salt.  For  the  most  constant  results,  he  used  a  saturated  solu- 
tion of  blue  vitriol,  made  slightly  acid  for  the  outer  cell,  and  for 
the  zinc,  twenty  parts  water  to  one  of  sulphuric  acid.  Eight  or 
ten  hours  is  about  the  limit  of  its  constancy.  Any  number  of 
cells  so  arranged  are  easily  connected  together  by  binding  screws, 
the  C  of  one  pair  to  the  Z  of  the  next,  and  so  on. 

The  hydrogen  from  the  decomposed  water  in  this  instrument  is  not 
given  off  in  bubbles  on  the  copper  side,  as  it  is  in  all  forms  of  the 
simple  circuit  of  zinc  and  copper;  but  the  sulphate  of  copper  there 
present  is  decomposed  in  the  circuit,  atom  for  atom,  with  the  decom- 
posed water,  and  the  hydrogen  takes  the  atom  of  oxyd  of  copper, 
appropriating  its  oxygen  to  form  water  again,  while  metallic  copper  is 
deposited  on  the  outer  cell.  If  the  zinc  is  well  amalgamated,  no  actioi? 
61* 


578 


PHYSICS    OF   IMPONDERABLE    AGENTS. 


622 


of  any  sort  results  in  this  battery  until  the  poles  are  joined,  and  it  gives 
off  no  fumes.  Ten  or  twelve  such  cells  form  a  very  active,  constant, 
and  economical  battery,  and  twenty  or  thirty  are  ample  fur  most  uses. 
Hot  solutions  increase  its  power,  while  the  extent  of  zinc  surface,  and 
not  the  diameter  of  the  copper,  limits  the  amount  of  electrical  effect. 

875.  Grove's  nitric  acid  battery. — Mr.  Grove,  of  London,  has 
successfully  applied  the  principle  of  Daniell's  battery,  to  produce  the 
most  powerful  and  intense  sustaining  battery 
known.  The  fluids  used  are  strong  nitric  acid 
and  dilute  sulphuric  acid,  kept  apart  by  a 
porous  jar.  The  metals  are  amal- 
gamated zinc,  placed  in  the  sul- 
phuric acid  of  the  outer  vessel, 
and  platinum  in  the  porous  vessel : 
fig.  623  shows  this  arrangement 
complete,  while  the  platinum  ele- 
ment, P,  is  seen  isolated  in  fig.  622.  p  i 
The  cover,  c,  upon  the  vase,  V,  fig. 
623,  tends  to  keep  down  the  strong 
vapors  of  nitrous  acid  evolved 
when  the  battery  is  in  action. 
The  binding  screws,  a  b,  serve  to 
unite  the  elements  of  separate  pairs.  The  zinc  here  surrounds  the 
platinum,  because  both  that  metal  and  the  nitric  acid  are  to  be  econo- 
mized as  much  as  possible,  being  the  costly  parts  of  the  arrangement. 
From  six  to  ten  parts  of  water  are  used  in  A,  to  one  of  acid 

The  action  of  this  battery  is  intense  and  splendid.  •  The  hydrogen  is 
immediately  engaged  by  the  nitric  acid,  which  it  decomposes  very 
readily.  There  is  therefore  a  double  chemical  action,  and  an  increased 
flow  of  electricity,  since  no  part  of  the  power  is  lost  in  combination. 
The  fumes  of  nitrous  acid  are  partly  absorbed  by  the  nitric  acid, 
turning  it  at  last  intensely  green  :  but  enough  are  evolved  to  render  it 
important  to  set  the  apparatus  in  a  clear  space,  or  good  draught.  Four 
cells,  with  platinum  three  inches  long  by  half  inch  wide,  decompose 
water  rapidly;  and  twenty  such  cells  form  a  battery  giving  intense 
effects  of  light. 

Platinum,  in  the  nitric  acid  battery,  is  estimated  as  sixteen  or  eighteen  times 
more  powerful  than  copper  in  Daniell's  battery ;  that  is,  six  square  inches  of 
platinum  is  as  efficacious  as  one  hundred  square  inches  of  copper ;  and  Peschel 
found  that  three  hundred  and  forty  times  is  much  surface  of  copper  was  needed 
in  a  spiral  battery  on  Hare's  construction,  as  of  platinum  in  Grove's,  to  insure 
equal  effects. 

A  Grove's  battery,  constructed  'by  Jacobi,  of  St.  Petersburgb,  contains  sixty- 


ELECTRICITY. 


579 


624 


four  platinum  plates,  each  thirty-six  square  inches  surface,  or  combined,  sixteen 
square  feet.  This  would  be,  by  comparison,  equal  to  a  Darnell's  battery  of  two 
hundred  and  sixty-six  square  feet,  or  a  Hare's  battery  of  about  five  thousand 
five  hundred  square  feet.  Grove's  battery  is  rather  costly,  and  very  trouble- 
some to  manage,  as  are  all  batteries  with  double  cells  and  porous  cups,  although 
the  trouble  involved  in  their  use  is  not  to  be  compared  with  the  vexation  involved 
in  the  earlier  single  fluid  batteries. 

376.  Carbon  battery. — The  great  cost  of  large  members  and  exten- 
sive series  of  Grove's  platinum  battery,  led 
Prof.  Bunsen,  of  Marburg,  to  use  the  carbon 
of  gas  coke  as  a  substitute  for  the  platinum. 
Prof.  Silliman,  Jr.,  in  1842,  described  a 
battery  (see  Am.  Jour.  Sci.  [1],  XLIII., 
393,  and  XLIV.,  180),  in  which  natural 
plumbago  was  used  in  place  of  the  plati- 
num of  Grove's  arrangement.  This  was 
before  Bunsen's  apparatus  was  known  of 
in  this  country. 

Fig.  624  shows  the  original  form  of  Bunsen's 
cells.  Where  the  carbon,  C,  is  contained  in  an 
exterior  vase,  V,  of  nitric  acid,  the  amalgamated 
zinc  is  in  a  porous  cup,  P,  of  dilute  sulphuric  |f 
acid.  The  objection  to  this  arrangement  is  the  '-^^ 
large  consumption  of  nitric  acid  and  smallness 
of  the  zinc.  In  the  Author's  plan,  afterwards  adopted  essentially  by  M.  Deleuil, 
the  carbon  was  in  the  porous  cup,  surrounded  by  the  zinc.  In  fig.  625,  this 
625  626 


arrangement  is  shown  in  detail.  P,  is  the  pile  complete.  P,  is  the  jar  of  hard 
pottery  to  contain  the  zinc,  Z,  and  the  dilute  sulphuric  acid;  V  is  the  porous 
vase,  to  contain  the  carbon,  C,  with  its  nitric  acid.  The  attachment  of  a  con- 
ductor to  the  carbon  is  accomplished  by  a  conical  hole  in  the  centre,  into  which 
a  plug  of  hammered  copper  is  crowded  with  a  wrenching  motion.  If  prisms  of 
the  hard  carbon  of  the  gas  retorts  are  used  (and  this  kind  of  carbon  is  unques- 
tionably the  best),  a  copper  baud  is  attached  to  the  top  by  electro-galvanic  sol- 
dering. The  carbon  of  Bunsen's  cells  is  prepared  by  pulverizing,  and  baking 
in  moulds,  the  coke  of  bituminous  coal.  Fig.  626  shows  a  series  of  ten  cups  of 
the  carbon  battery  arranged  for  use,  the  alternate  members  being  joined  by 
binding  screws,  as  made  by  Deleuil,  of  Paris,  each  zinc  being  twenty-two  centi- 
metres (eight  and  three-quarter  inches)  high.  As  the  electro-motive  energy  of 
the  battery  depends  on  size  as  well  as  number,  these  large  members  have  great 


580 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


advantages.  The  Author  demonstrated,  in  1842  (loc.  cit.),  that  carbon  was 
nearly  if  not  quite  as  good  as  platinum,  surface  for  surface.  A  battery  of  fifty 
cells,  like  fig.  626,  costs  fifty-five  dollars  in  Paris,  and,  with  such  a  series,  all  the 
most  splendid  effects  of  the  electric  light,  deflagrations,  and  chemical  decompo- 
sitions can  be  very  satisfactorily  shown. 

877.  Other  forms  of  Voltaic  battery  exist  in  great  variety,  but 
involving  no  principle  not  already  explained.    Some  have  special  adap- 
tation to  a  particular  use,  like  Chester's  form  of  Smee's  battery  for 
telegraphic  use ;.  Farmer's  copper  battery  ;  the  battery  of  Bagration, 
of  zinc  and  copper  in  moist  earth ;  or  Grove's  oxygen  and  hydrogen 
gas  battery,  so  instructive  theoretically.     But  further  descriptions  are 
excluded  by  want  of  space. 

V.     POLARITY,  RETARDING    POWER,  AND    NOMENCLATURE    OF    THE    VOLTAIC 

PILE. 

878.  Polarity  of  the  compound  circuit. — In  batteries  of  two  or 
more  couples,  connection  is  formed,  not  as  in  the  single  couple,  between 
members  of  the  same  cell,  but  between  those  of  different  names  in  con- 
tiguous cells,  as  in  fig.  627,  where  the  copper  of  1  joins  the  zinc  of  2, 
and  so  on.     The  current  flows  from  the  zinc  to  the  copper  in  the  fluid, 
but  from  the  copper  to  the  zinc  in  the  air  (fig.  628),  both  in  simple  and 

627 

628 


compound  circuits.  This  is  important  to  be  remembered,  since  the 
zinc  is  called  the  electro-positive  element  of  the  series,  although  out  of 
the  fluid  it  is  negative.  Consequently,  in  voltaic  decompositions,  the 
element  which  goes  to  the  zinc  pole  is  called  the  electro-positive,  and, 
for  the  same  reason,  that  which  goes  to  the  copper,  is  the  electro-nega- 
tive element.  The  terminal  plates,  Z  and  C,  in  1  and  5,  fig.  627,  are 
not  concerned  in  the  electrical 
effect,  being  in  fact  only  conduc- 
tors of  the  electricity,  and  hence 
they  may  be  removed  as  in  fig. 
628,  without  altering  the  power  or 
nature  of  the  battery.  They  serve, 
in  fact,  merely  as  a  convenient  mode 
of  join' ng  the  poles,  as  in  fig.  629.  The  apparent  polarity  of  the  simple 
circuit  is,  therefore,  the  reverse  of  that  of  the  compound  circuit;  but, 


ELECTRICITY. 


581 


an  attentive  observation  of  these  explanations,  and  of  the  figures,  will 
prevent  all  confusion  on  this  point. 

879.  Grouping  the  elements  of  a  pile,  in  various  numerical  rela- 
tions, is  an  important  means  of  modifying  its  power,  and  the  character 
of  its  effects,  already  explained. 

Take,  for  example,  six  cups,  as  in  fig.  630,  arranged  in  consecutive  order,  and 


630 


631 


632 


we  have,  owing  to  the  resistance  to  the  elec- 
tric flow,  the  maximum  intense  effects  pos- 
sible with  such  number.  Changed  to  two 
groups  of  three  each,  the  quantity  is  doubled, 
with  half  of  the  intensity,  fig.  631.  In  fig. 
632,  are  three  groups  of  two  cups  each,  so 
arranged  as  to  present  three  times  the  sur- 
face in  630,  with  a  proportionate  loss  of  in- 
tensity. Lastly,  in  fig.  633,  each  zinc,  and 
each  copper,  joins  one  common  conductor, 
each  on  its  own  side,  throwing  the  six 
couples  into  one  surface  of  six-fold  extent 
to  fig.  630.  The  arrangement  may  be  ex- 
pressed, assuming  the  resistance  of  a  single 
cup  as  unity,  thus  :  1.  f  =  1-5.  |  =  0-666. 
£  =  0-166,  and  so  for  any  number  of  couples. 

880.  Electrical    retarding   power 
of  the  battery. — Ohm's  law. — A  cer-    " 

tain  resistance  to  the  passage  of  a  voltaic  current  is  offered  by 
every  additional  element  placed  in  the  circuit  as  well  as  by  increased 
length  of  conductor.  The  new  properties  thus  acquired  by  the  com- 
pound circuit  have  been  already  alluded  to  (865). 

Ohm,  of  Berlin,  in  1827,  first  demonstrated  mathematically  the  law 
regulating  the  flow  of  electricity  in  the  compound  battery.  As  the  ap- 
paratus is  composed  solely  of  conductors  of  different  retarding  power, 
the  electric  current  must  proceed,  not  only  along  the  connecting  wire, 
from  pole  to  pole,  but  also  through  the  whole  apparatus ;  the  resistance 
offered  to  the  passage  of  the  current  consists  therefore  of  two  parts,  one 
exterior  to,  and  one  within,  the  apparatus. 

Let  the  ring,  a  b  c,  in  fig.  634,  represent  a  homogeneous  conductor,  and  let  a 
source  of  electricity  exist  at  A.  From  this  source  the  electricity  will  diffuse 
itself  over  both  halves  of  the  ring,  the  positive  passing  in  the  634 

direction  a,  the  negative  in  b,  and  both  fluids  meeting  at  c.  Now 
it  follows,  if  the  ring  is  homogeneous,  that  equal  quantities  of 
electricity  pass  through  all  sections  of  the  ring  in  the  same  time. 
Assuming  that  the  passage  of  the  fluid  from  one  cross  section  of 
the  ring  to  another,  is  due  to  the  difference  of  electrical  tension  at 
these  points,  an/1  that  the  quantity  which  passes  is  proportional 
to  this  difference  of  tension,  the  consequence  is,  that  the  two  fluids 
proceeding  from  A,  must  decrease  in  tension  the  farther  they  recede  from  the 
starting  point. 

This  decreasing  tension  may  be  represented  by  a  diagram.     Suppose  the  ring 


582          PHYSICS  OF  IMPONDERABLE  AGENTS. 

in  fig.  635,  to  be  stretched  out  to  the  line  A  A'.    Let  the  ordinate  A  B  rej  resent  the 
tension  of  positive  electricity  at  A,  and  A'  B'  the  nega-  635 

tive  tension  at  A',  then  the  line  B  B'  will  express  the   B 
tension  for  all  parts  of  the  circuit  by  the  varying  lengths 
ot  the  ordinates  A  B,  A'  B',  at  every  point  of  A  c  or  c  A'. 

E  A' 

Hence  Ohm's  formula  F  =  — ,  where  ^represents  the 


strength  of  the  current,  E  the  electro-motive  force  of 
the  battery,  or  the  attraction  of  zinc  for  oxygen,  and  R 
the  resistance.  Therefore,  the  greater  the  length  of  the  circuit,  the  less  will  be 
the  amount  of  electricity  which  passes  through  any  cross  section  in  a  given  time. 
In  exact  terms,  this  law  states  that  the  strength  of  the  current  is  inversely  propor- 
tional to  the  resistance  of  the  circuit,  and  directly  as  the  electro-motive  force. 

In  the  simplest  Voltaic  current,  we  have  not  a  homogeneous  conductor, 
but  several  of  various  powers.  To  illustrate  this,  let  the  conductor,  A  A',  fig. 
636,  consist  of  two  portions  having  different  cross  sec-  636 

tions.  For  example,  let  the  cross  section  A  d  be  n 
times  that  of  d  A' ;  then,  if  equal  quantities  pass 
through  all  sections  in  equal  times,  and  if  through  a 
given  length  of  the  thicker  wire  no  more  fluid  passes 
than  through  the  thinner  wire,  the  difference  of  tension 
at  both  ends  of  this  unit  of  length  of  the  thicker  wire 

1 

must  be  only  -th  of  what  it  is  in  the  latter.     Thus,  "  the  electric  fall,"  as  Ohm 
n 

calls  it,  will  be  less  in  the  case  of  the  thick  wire  than  of  the  thinner,  as  shown 
by  the  line  B  c  in  the  figure.  The  result  is  expressed  in  the  law  that  the  "  electric 
fall"  is  directly  as  the  specific  resistances  of  the  conductors,  and  inversely  as  their 
cross  sections.  Hence,  the  greater  the  resistance  offered  by  the  conductor,  the 
greater  the  fall.  The  very  simplest  circuit  must  therefore  present  a  series  of 
gradients  expressive  of  the  tension  of  its  various  points — as  one  for  the  con- 
necting wire,  one  for  the  zinc,  one  for  the  fluid,  and  one  for  the  copper.  Tho 
electro-motive  force  of  a  voltaic  couple  ("E"  of  Ohm's  formula)  may  be  experi- 
mentally determined,  and  is  proportional  to  the  electric  tension  at  the  ends  of 
the  newly  broken  circuit. 

881.  Formulae  of  electric  piles. — It  follows,  from  what  has  been 
stated,  that  the  intensity,  7,  of  a  current,  united  by  a  homogeneous 
wire  whose  length  is  L,  may  be  represented  by  the  formula 


in  which  r  designates  a  length  of  wire  representing  the  resistance  of 
the  pile  or  its  reduced  length,  and  E  the  electro-motive  force  measured 
by  the  tension  at  the  poles  when  the  circuit  is  broken. 

If  the  resistance  of  the  pile  is  nothing,  or  an  insensible  quantity,  as 
in  the  case  of  a  thermo-electric  couple  of  great  surface,  the  formula 

Tfl 

becomes  I  =  ~.     That  is,  the  intensity  of  the  current  is  in  the  inverse 
Li 

dtio  of  the  length  of  the  homogeneous  wire  joining  the  poles  of  the 


ELECTRICI TY.  583 

battery.  If,  however,  the  pile  itself  offers  sensible  resistance,  as  is  the 
case  with  hydro-electric  piles  composed  of  many  couples,  the  formula 
shows  that  tlie  intensity  of  the  current  is  in  the  inverse  ratio  of  the  length 
of  tlie  connecting  wire  increased  by  a  constant  quantity,  r,  which  repre- 
sents the  resistance  of  the  pile  itself. 

In  the  case  of  many  different  sources  of  resistance,  interposed  in  the 
circuit  of  the  connecting  wire,  L  represents  the  sum  of  the  reduced 
lengths  equivalent  to  these  resistances. 

E 
Intensity  given  by  many  couples. — In  the  formula,  /=     •        , 

let  E  be  the  electro-motive  force,  and  r  the  resistance  of  a  single  couple, 
L  and  r  being  always  reckoned  as  lengths  of  the  same  kind  of  wire 
taken  as  a  standard  of  comparison ;  we  may  then  consider  many 
couples  united  one  to  another  in  a  series  as  shown  in  fig.  630.  Ohm 
considers  that  each  couple  produces  an  electric  current  which  traverses 
the  pile  as  if  that  couple  was  alone,  so  that  the  electro-motive  force  of 
the  series,  or  the  tension  at  the  poles  which  measures  it, will  be  the  sum 
of  the  electro-motive  forces,  E  -f  E'  +  E"  -j-  .  .  .,  of  all  the  couples 
in  the  series.  In  the  same  manner  the  current,  produced  by  each  couple 
traversing  all  the  others,  meets  with  a  resistance  equal  to  the  sum, 
r  -\-  K  -f-  r//  -f-  .  .,  of  1;he  resistances  of  all  the  couples ;  hence, 

E  +  W  +  W  +  •  , 


If  the  couples  are  all  equal  to  each  other,  and  f,  represents  their  num- 

nE 

ber,  the  formula  becomes  /==  -^ — ; .     This  shows  that  the  intensity 

L  +  nr 

of  the  current,  from  a  series  arranged  one  by  one,  is  proportional  to 
the  sum  of  the  electro-motive  forces  of  all  the  couples,  and  inversely  as 
the  total  resistance  of  the  circuit  including  the  pile  itself. 

If  we  designate  by  c,  I,  s  the  conductibility,  the  length,  and  the  section 
of  a  wire ;  and  by  (/,  V,  sx  the  same  quantities  for  a  second  wire,  it 
follows  from  the  principles  already  established,  and  from  the  fact  that 
the  resistance  of  a  wire  is  in  the  inverse  ratio  of  its  conducting  power, 
that  two  wires  will  produce  equal  diminution  of  the  intensity  of  the 
same  electric  current  when : — 

-  =  — ,  or,  ZsV  =  Vs",  or,  I  =  V  ~. 
sc       s  c/  s'v 

The  third  equation  expresses  the  length  of  a  wire  whose  section  is  s, 
and  conductibility  c,  that  will  produce  the  same  effect  upon  the  current 
as  another  wire  whose  length  is  Zx,  section  s7,  and  conductibility  (/. 


•r>84  PHYSICS    OF    IMPONDERABLE   AGENTS. 

This  value  of  Z  is  called  the  reduced  length  of  the  first  wire  as  com- 
pared with  the  second. 

If  we  have  a  series  of  wires  united  together  by  their  ends  as  a 
compound  conductor,  the  equivalent  length  of  the  first  wire  will  be 
expressed  by  the  formula  :  — 


s'c'  ~^~  s"c"  ~^~  s"'c"'  )  ' 

/ 


Effect  of  increasing  the  number  of  couples  in  a  battery.  — 

The  consideration  of  the  formulas  given  above  shows  that, 

1.  The  intensity  of  the  current  increases  with  the  number  of  couples. 

E 
Dividing  both  terms  of  the  fraction  by  n,  it  becomes  I  =  £        ,  this 

«  +  r 

shows  that  the  value  of  I  increases  with  increase  of  n,  or  the  number 
of  couples. 

2.  The  increased  intensity  of  the  current,  by  increasing  the  number 
of  couples,  is  more  evident  when  L  is  great  in  comparison  with  r,  or 
when  the  external  resistance  to  be  overcome  is  much  greater  than  the 

resistance  of  the  battery.    If  on  the  contrary  L  is  very  small,  —  is  also 

very  small,  and  the  intensity  of  the  current  changes  but  very  little  with 
any  increase  of  the  number  of  couples. 

3.  If  there  is  no  exterior  resistance,  or,  L  =  0,  1  =  —  =  —  .     In 

this  case  the  intensity  is  not  varied  by  varying  the  number  of  couples, 
or  one  couple  gives  as  great  intensity  as  any  number  of  couples. 

4.  The  intensity  is  not  increased  by  increasing  the  number  of  couples 
when  each  couple  added  is  accompanied  by  an  exterior  resistance  equal 
to  L  ;  or,  in  other  words,  when  the  exterior  resistance  increases  in  the 
same  ratio  as  the  number  of  couples,  since  on  that  supposition  the 

nE  E 

formula  becomes  /  =  —  —  ,  -  =  —  —  ;  —  . 

nL  -f-  nr       L  -{-  r 

5.  If  the  exterior  resistance,  L,  is  very  great,  I  is  very  small,  unless 
n  is  made  very  great.     This  shows  that  it  is  necessary  to  employ  a 
great  number  of  couples  when  a  great  amount  of  resistance  is  to  be 
overcome,  as  in  the  voltaic  arch,  and  in  the  electrolysis  of  bodies  that 
are  imperfect  conductors,  or  in  sending  an  impulse  through  a  long 
telegraphic  circuit. 

Effect  of  enlarging  the  plates  of  a  battery.  —  If,  instead  of 
uniting  many  couples  in  a  series,  we  unite  a  number  of  couples,  m,  by 
poles  of  the  same  name  aa  in  fig.  633,  it  will  be  equivalent  to  enlarging 


ELECTRICITY.  585 

the  dimensions  of  the  plates  of  a  single  couple,  the  resistance  of  the 

r  E 

battery  will  be  — ,  and  the  formula  becomes  /= .    We  thus  see 

L  +  T- 
m 

that  if  L,  the  exterior  resistance,  is  very  great  in  proportion  to  r,  the 
resistance  of  the  battery,  the  intensity  will  be  but  little  increased  by 
uniting  the  couples  by  poles  of  the  same  name.  If  L  is  very  small  in  pro- 
portion to  r,  the  intensity  will  be  much  increased  by  this  method,  and  if  L 
is  so  small  that  it  may  be  neglected,  the  intensity  will  be  proportional  to 
the  extent  of  surface  acting  as  a  single  couple.  We  know  indeed  that, 
when  chemical  action  is  exerted  over  a  large  surface,  the  quantity  of 
electricity  which  traverses  the  connecting  wire  is  also  very  great. 

Eifect  of  enlarging  the  couples  and  increasing  their  number.— 
If  the  number  and  dimensions  of  the  couples  are  both  increased  at 

nE  E 

the  same  time,  the  formula  becomes  /  =    = 

*+•= 

shows  that  increasing  the  number  of  couples  produces  the  same  effect 
as  diminishing  in  the  same  proportion  the  resistance  of  the  exterior 
circuit,  and  increasing  the  surface  of  each  couple  has  the  same  effect  as 
diminishing  the  resistance  of  the  pile.  Hence: — 

If  L,  the  resistance  of  the  exterior  circuit,  is  great,  it  will  be  most 
advantageous  to  unite  many  couples  in  a  single  series :  But  if  the  resist- 
ance of  the  exterior  circuit  is  small,  greater  advantage  may  be  obtained  by 
uniting  the  couples  by  poles  of  the  same  name,  in  such  a  manner  as  to 
form  couples  of  large  extent  of  surface. 

A  most  interesting  application  of  these  principles  to  the  practical 
construction  and  use  of  batteries  will  be  found  in  a  paper  by  Mr.  G. 
Mathiot,  Electrotypist  of  the  United  States  Coast  Survey.  (Am.  Jour. 
Sci.  [2]  XV.  305.) 

882.  Faraday's  nomenclature. — Faraday  has  introduced  certain 
terms  into  the  language  of  electrical  science,  which  are  generally  adopted 
for  their  convenience,  and  their  absence  of  assumed  or  theoretical  notions. 

Electrode  is  used  in  place  of  pole,  to  which  latter  term,  meaning  the 
terminal  wires  of  a  battery,  Davy  and  others  seemed  to  attach  a  sense 
as  if  it  possessed  a  certain  attractive  force,  like  the  pole  of  a  magnet. — 
Electrode  (from  r/hexTpov,  and  6do<;,  a  way),  means  simply  the  way  or 
door  by  which  a  Voltaic  current  enters  or  leaves  a  substance. 

Anode  is  that  surface  of  a  body  receiving  the  current,  or  the  positive 
side  of  the  series,  from  ava,  upwards  (as  the  sun  rises),  and  udos,  a  way. 

Cathode  is  that  surface  of  a  body  from  which  a  current  flows  out 
towards  the  negative  side  of  the  series,  from  xard,  downwards,  as  the  sun 
62 


586          PHYSICS  OF  IMPONDERABLE  AGENTS. 

sets,  and  6dot;,  a  way).  The  observer  is  supposed  to  face  the  noith,  with 
the  positive  of  the  battery  on  his  right  hand,  and  its  negative  on  his  left. 

Electrolyte  is  any  substance  capable  of  separation  into  its  con- 
stituents by  the  influence  of  a  Voltaic  series  (from  ijAsxTpov,  and  /I6o, 
to  sel  loose;.  Electrolysis,  the  act  of  decomposition.  Electrolyzed,  and 
electrolyzable,  are  obvious  derivatives  from  the  same  words. 

Ions  (from  toy,  neuter  of  slp.i,  to  go),  are  the  elements  into  which  an 
electrolyte  is  resolved  by  the  current.  These  are  either  anions,  ele- 
ments found  at  the  anode,  or  catons,  ions  found  at  the  cathode. 
Hereafter  we  shall  employ  these  terms  when  they  are  appropriate. 

VI.     THE  EFFECTS  OF  THE  VOLTAIC  PILE. 

1.  Physical  effects. 

883.  The  Voltaic  spark  and  arch.— In  1809,  Davy,  with  the 
extensive  series  of  two  thousand  couples  at  the  Royal  Institution,  first 
demonstrated  the  full  splendors  of  the  Voltaic  arch  between  electrodes 
of  well-burned  charcoal.  However  powerful  the  series  may  be,  no 
effect  is  seen,  in  the  air,  until  the  points  of  the  carbon  electrodes  are 
brought  into  actual  contact,  or  at  least  insensibly  near.  Herschel 
noticed  that  an  electrical  spark  from  a  Leyden  637 

jar,  sent  through  the  carbon  points,  when  near 
each  other,  established  the  flow  of  the  Voltaic 
current,  by  projection  no  doubt  of  material  particles.  When  the  spark 
passes,  then  the  electrodes  may  be  withdrawn,  as  in  fig. 
637,  and  the  arch  of  electric  flame  connects  them  with  a 
white  and  violet  light  of  intolerable  brightness ;  several 
inches  in  length  if  the  pile  is  very  powerful.  This  arch 
of  seeming  flame  is  not  produced  by  the  combustion  of 
the  carbon  electrodes,  since  it  exists,  with  even  greater 
brilliancy,  in  a  vacuum,  or  in  an  atmosphere  of  nitrogen 
or  carbonic  acid.  Despretz  states  that  in  vacuo  with  a 
powerful  pile,  the  Voltaic  arch  may  be  formed  at  some 
centimetres  distance,  without  contact.  Fig.  638,  shows  a 
convenient  apparatus  for  this  experiment,  in  vacuo,  or  in 
various  gases,  as  in  Davy's  original  experiments.  The 
Voltaic  arch  is  accompanied  by  a  loud  hissing  or  rushing 
sound,  due  to  the  mechanical  removal  and  transportation 
of  particles  of  carbon  from  the  positive  to  the  negative 
electrode,  by  which  the  former  is  diminished  in  length,  or 
made  cup-shaped,  while  the  latter  is  sensibly  elongated, 
as  first  noticed  and  described  by  Prof.  Silliman,  in  1822 
(Am.  Jour.  Sci.  [1]  V.  108),  in  the  use  of  a  powerful  deflagrator  con- 
structed by  Dr.  Hare. 


ELECTRICITY. 


587 


Through  colored  glasses,  these  particles  of  carbon  can  be  conveniently  observed 
apparently  moving  slowly  from  pole  to  pole,  and  giving  unquestionably  that  oval 
form  to  the  arch,  seen  in  fig.  639,  when  the  electrodes  are  vertical,  and  the  nega- 
tive carbon  is  uppermost.  There  is  also  distinctly  to  be  seen,  a  certain  structure 
in  zones,  or  bands  o*  different  brilliancy.  When  the  image  of  the  carbon  electrodes 
is  projected  on  a  screen,  fig.  640,  as  was  first  done  by  Foucault  with  the  electric 
lantern,  the  growth  of  the  negative  640  641 

and  the  decrease  of  the  positive  elec- 
trode is  easily  observed,  without  in- 
jury to  the  eyes.   The  negative  carbon 
is  seen  to  glow  first,  as         539 
if    the    light    originated 
there,  but  as  the  experi- 
ment advances,  the  posi- 
tive carbon  becomes  the 
most  briliant,  and  main- 
tains this  superiority  du- 
ring the  experiment ;  be- 
coming at  the  same  time 
cup-shaped. 

The  Voltaic  arch  is  magnetic,  or  capable  of  influencing  the  magnet,  by  the 
approach  of  which  it  is  deflected,  as  seen  in  fig.  641,  or  it  is  made  to  revolve 
with  a  loud  hissing  noise ;  a  fact  first 
observed  by  Davy,  but  since  carefully 
studied  by  De  la  Rive,  Quet,  and  Des- 
pretz.  This  fact  is  far  more  conspicuous 
in  the  arc  from  the  induction  coil,  §  933. 

884.  Regulators  of  the  elec- 
tric light. — Since  the  introduc- 
tion of  powerful  constant  batteries, 
it  has  been  possible  to  use  the  elec- 
tric light  for  scientific  and  econo- 
mical purposes.  For  this  purpose 
regulators  have  been  devised  to 
render  the  light  constant,  by  ap- 
proaching the  electrodes  in  pro- 
portion as  they  are  consumed. 

In  fig.  642,  is  shown  that  of  Deleuil, 
of  Paris,  and  its  details,  in  fig.  643.  The 
two  carbon  points,  P  and  N,  are  held 
in  position  by  two  vertical  rods,  of 
which  the  lower  one,  P,  is  moved  up- 
wards by  the  mechanism  in  fig.  643  ; 
while  the  upper  one,  N,  passes  through 
the  ball,  D,  with  friction.  The  flow  of 
the  current  is  shown  by  the  arrows 
arriving  at  Gr,  and  departing  at  II. 
The  frame  of  the  apparatus  is  of  cast- 
iron.  The  slightly  concave  mirror,  E,,  is  for  certain  purposes  replaced  by  a  large 
parabolic  mirror.  When  the  zinc  electrode  is  connected  with  G,  and  the  carbon 


688 


PHYSICS    OF   IMPONDERABLE   AGENTS. 


643 


with  H,  communication  is  established  by  depressing  N  with  the  hand.  As  th« 
current  in  its  circuit  passes  through  a  coil  of  wire  surrounding  the  electro- 
magnet, E,  fig.  643,  the  soft  iron  armature,  m,  on 
the  lever  A,  is  drawn  up  to  E,  so  long  as  the  cur- 
rent flows,  but  if  it  is  interrupted,  then  m  falls, 
and  the  lever  A  is  drawn  upwards  by  the  spring, 
B,  acting  against  the  fulcrum,  L  :  the  effect  of  that 
motion  is  to  raise  the  electrode,  P,  by  a  tooth, 
I,  catching  in 
notches  on  the 
upright,  K.  In 
this  way  con- 
nection is  again 
established  with 


the  battery ;  and 
when  this  sim- 
ple mechanism 

is  once  adjusted,  it  will  act  for  hours  with  great  certainty, 
maintaining  the  light  constant. 

Duboscq's  photo-electric  lantern  is  seen  in  fig. 
644.  This  instrument  is  used  to  replace  the  sun  in 
all  optical  experiments  requiring  a  strong  white  light. 

The  poles  S  and  I  are  preserved  at  the  same  distance  by 
the  action  of  an  electro-magnet  in  the  foot  E,  upon  a  soft 
iron  bar  F  F  in  connection  with  an  endless  screw  V,  moving 
the  pulleys  P  P',  which  are  connected  by  cords  with  the  poles 
S  and  I.  The  contact  of  S  and  I  induces  magnetism  in  the 
electro-magnet  E,  while  the  springs  R  L  regulate  the  motion 
of  the  machinery.  The  apparatus  is  simple  and  portable, 
and  its  effect  is  to  make  the  electrical  light  so  steady  and 
constant  that  it  may  be  used  for  all  optical  experiments. 
The  positive  pole  consumes  much  more  rapidly  than  the 
negative,  both  from  a  more  intense  action  upon  it  and 
because  its  particles  are  carried  over  and  deposited  on  the 
negative  pole,  elongating  the  point  of  the  latter.  To  pro- 
vide for  this  difference,  the  pulley  P'  is  variable,  and  carries 
the  pole  I  up  proportionably  faster,  so  that  the  focal  posi- 
tion of  the  light  remains  unchanged. 

885.  Properties  of  the  electric  light.— Like  the 
solar  Jight,  it  is  unpolarized.  It  explodes  a  mixture  of  hydrogen  and 
chlorine,  and  acts  on  chloride  of  silver,  and  other  photographic  prepa- 
rations, like  the  sun.  Bodies  made  phosphorescent  by  the  sun,  are 
similarly  affected  by  the  electric  light.  In  1842,  Silliman  took  daguer- 
reotypes with  it  (Am.  Jour.  Sci.  [1]  XLIII.  185),  and  it  is  now  used  in 
preference  to  solar  light,  for  the  purpose  of  taking  microscopic  photo- 
graphs. (Duboscq.) 

Fizeau  and  Foucault,  have  compared,  by  photometric  measurement,  the  light 
from  ninety-two  carbon  couples,  arranged  in  two  series  of  forty-six  (879),  with 


ELECTRICITY.  589 

the  solar  team,  and  also  with  the  oxyhydrogen  or  Drummond  light.  In  a  clear 
August  day,  with  the  sun  two  hours  high,  the  electric  light,  assuming  the  sun 
as  unity,  bore  to  it  the  ratio  of  2-59  : 1,  i.  e.,  the  sun  was  twice  and  a  half  more 
powerful :  while  the  Drummond  light  was  only  the  one  one  hundred  and  forty- 
sixth  that  of  the  sun.  Bunsen  found  the  light  from  forty-eight  elements  of  carbon, 
equal  to  five  hundred  and  seventy-two  candles.  The  intensity  of  the  electric  light 
depends  far  more  on  the  size  of  the  individual  members  of  the  pile  than  on  their 
number.  The  effect  from  forty  large  sized  couples  was  found  by  Fizeau  and  Fou- 
cault  to  be  about  the  same  as  that  from  double  the  number,  when  the  eighty 
were  arranged  consecutively,  as  in  tig.  630,  while,  with  the  same  elements  in 
two  parallel  series,  there  was  a  very  great  increase  of  effect.  Fraunhofer  showed 
that  the  spectrum  of  the  electric  light  was  distinguished  from  that  of  the  sun 
by  a  very  bright  line  in  the  green,  and  a  somewhat  less  luminous  one  in  the 
orange  (461).  Dove  has  lately  shown  (Poggendorff  's  Annalen,  1857,  No.  6)  that 
this  light  has  two  distinct  sources  :  1st,  the  ignition  or  incandescence  of  the 
translated  particles,  passing  in  the  course  of  the  discharge :  2d,  the  proper 
electric  light  itself.  On  the  contrary,  Draper  has  shown  tnat  the  .  pectrum  from 
a  glowing  platinum  wire  heated  by  the  battery,  contains  no  dark  lines,  so  that, 
unlike  the  electric  light,  it  is  strictly  white  (Am.  Jour.  Sci.  [2]  VIII.,  340).  It 
is  not  only  particles  of  carbon  which  pass  in  the  Voltaic  arch,  but  of  whatever 
conductor  may  form  the  positive  electrode,  as  platinum,  of  any  metal,  and  the  light 
varies  in  its  optical  properties  with  every  change  of  the  electrode.  (Wheatstone.) 

886.  Heat  of  the  Voltaic  arch. — Deflagration. — When  the  posi- 
tive electrode  is  fashioned  into  a  small  crucible  of  carbon,         645 
as  in  fig.  645,  gold,  silver,  platinum,  mercury,  and  other 
substances,  are  speedily  fused,  deflagrated,  or  volatilized, 
with  various-colored  lights. 

The  fusion  of  platinum  (like  wax  in  a  candle)  before  the  Voltaic 
arch  is  significant  of  its  intense  heat,  and  still  more,  the  volatiliza- 
tion and  fusion  of  carbon,  a  result  first  announced  by  Prof.  Silliman 
in  1822,  and  since  confirmed  by  Despretz,  who,  by  the  union  of  the 
heat  of  six  hundred  carbon  couples  arranged  in  numerous  parallel  series,  and 
conjoined  with  the  jet  of  an  oxyhydrogen  blow-pipe,  and  the  heat  of  the  mid- 
day sun,  focalized  by  a,  powerful  burning-glass,  succeeded  in  volatilizing  the 
diamond,  fusing  magnesia  and  silica,  and  softening  anthracite.  The  diamond 
is  also  softened,  and  converted  into  a  black  spongy  mass  resembling  coke,  or, 
more  nearly,  the  black  diamond  found  in  the  Brazilian  mines. 

A  delicate  stream  of  mercury  being  allowed  to  flow  from  a  narrow  elongated 
funnel  (the  negative  electrode),  upon  a  surface  of  mercury  in  a  glass  vase  form- 
ing the  positive  electrode,  is  deflagrated  with  transcendent  splendor.  Many 
yards  of  number  twenty  platinum  wire,  held  between  the  electrodes,  may  be 
kept  in  the  full  glow  of  white  heat  for  a  long  time.  The  teacher  can  devise 
many  pleasing  additional  experiments,  as  drawing  the  arch  beneath  water,  oil, 
and  other  liquids,  from  points  of  carbon,  or  from  platinum  and  steel  wires. 

When  a  fine  platinum  wire  is  made  the  positive  electrode,  and  a  solution  of 
chlorid  of  calcium,  or  any  other  metallic  chlorid,  is  made  the  negative  elec- 
trode, on  touching  the  surface  of  the  liquid  with  the  point  of  the  fine  wire,  if 
the  series  is  powerful  the  wire  is  fused  on  the  surface  of  the  liquid,  evolving  a 
light  of  surpassing  beauty,  whose  color  is  that  appropriate  to  the  metal  in  solu- 
tion ;  e.  g.,  from  calcium  salts,  violet-red ;  from  sodium,  yellow ;  from  barium, 
52* 


590  PHYSICS    OF   IMPONDERABLE    AGENTS. 

reddish-yellow;  from  potassium,  violet;  from  strontium,  red,  Ac.     These  beau- 
tiful facts  were  first  noticed  by  Dr.  Hare. 

Dr.  Page  has  described  a  singular  motion  imparted  by  the  current  to  globules 
of  pure  mercury,  placed  in  a  shallow  dish,  and  covered  by  acidulated  water:  the 
globules  elongate  to  ovoids  and  move  actively  about,  one  end,  that  towards  the 
-j-  pole,  being  clouded  by  escaping  gas-bubbles.  If  the  mercury  contains  zinc, 
the  position  of  the  clouded  end  is  reversed.  (Am.  Jour.  Sci.  [2],  XI.,  192.) 

887.  Measurement  of  the  heat  of  the  Voltaic  current. — By 
means  of  a  long  wire  coiled  into  a  close  spiral,  and  enclosed  in  a  calo- 
rimeter of  glass,  containing  water,  Becquerel  and  others  have  established 
the  laws  regulating  the  flow  of  heat  in  the  electric  current,  by  its  effect 
in  elevating  the  temperature  of  the  water.     A  coil  of  platinum  wire 
contained  in  the  bulb  of  a  Sanctorio's  thermometer,  becomes  a  means 
of  estimating  the  heat  of  currents  too  feeble  to  be  otherwise  measured. 
The  results  are,  that  when  a  Voltaic  current  traverses  a  homogeneous 
wire,  the  quantity  of  heat  in  a  unit  of  time  is  proportional : — 

1.  To  the  resistance  which  the  wire  opposes  to  the  passage  of  the  elec- 
tricity : 

2.  To  the  square  of  the  intensity  of  the  current.     The  intensity  of  a 
current  is  measured  by  the  quantity  of  water  which  it  will  decompose 
in  a  given  time. 

For  a  given  quantity  of  electricity,  the  elevation  of  temperature  at 
different  points  on  a  conducting  wire,  is  in  the  inverse  ratio  of  the 
fourth  power  of  its  diameter. 

Draper  has  applied  the  coefficient  of  expansion  to  determine  the 
degree  of  heat  corresponding  to  a  particular  color  (585). 

2.   Chemical  effects  of  the  pile. 

888.  Historical. — The  chemical  effects  of  the  pile  are  most  wonderful, 
and  the  present  advanced  state  of  chemical  science  is  largely  attribu- 
table to  the  flood  of  light  shed  by  the  researches  of  Davy  and  Faraday 
upon  the  electrical  relations  of  the  elements  and  the  decomposition  of 
compounds  by  the  Voltaic  circuit. 

In  1800,  immediately  after  Volta's  announcement  to  Sir  Joseph  Banks  of  his 
discovery  of  the  pile,  Messrs.  Nicholson  and  Carlisle  constructed  the  first  pile 
in  England,  consisting  of  thirty-six  half  crowns,  with  as  many  discs  of  zinc  and 
pasteboard  soaked  in  salt  water  (864).  Observing  gas-bubbles  arise  when  the 
wires  of  this  pile  were  immersed  in  water,  Nicholson  covered  them  with  a  glass 
tube  filled  with  water,  and,  on  the  2d  of  May,  1800,  completed  the  splendid  dis- 
covery, that  the  Voltaic  current  had  the  power  to  decompose  water  and  other 
chemical  compounds.  Stimulated  by  so  fine  a  result,  chemists  and  physicists 
everywhere  repeated  the  experiment,  perfecting  the  methods  of  obtaining  the 
oxygen  and  hydrogen  gases  in  a  separate  condition.  The  chemical  theory  of 
the  pile,  originally  advanced  by  Fabbroni,  a  countryman  of  Volta's,  some  years 
before,  was  taken  up  and  ardently  advocated  by  Davy,  who,  in  1801,  had  suc- 
ceeded to  a  place  in  the  laboratory  of  the  Royal  Institution :  where,  on  the  6th 


ELECTRICITY. 


591 


of  October,  1807,  he  made,  by  the  Voltaic  pile,  the  memorable  discovery  of 
potassium,  the  metallic  base  of  potassa,  before  regarded  as  a  simple  substance ; 
and  soon  after  established  the  startling  truth,  that  all  the  earths  and  alkalies, 
until  then  esteemed  simple  substances — the^  whole  crust  of  the  globe,  in  fact — 
were  oxyds  of  metals,  whose  existence  had  hitherto  been  unsuspected. 

889.  Electrolysis  of  water. — Voltameter. — The  Voltaic  decom- 
position, or  electrolysis  of  water,  is  the  finest  possible  illustration  of 
the  chemical  power  of  the  pile.  Water  is  a  compound  of  oxygen  and 
hydrogen  gases,  in  the  proportions  of  one  measure  of  the  former  to  two 
of  the  latter.  When  two  gold  or  platinum  wires  are  connected  with 
the  opposite  ends  of  the  battery,  and  held  a  short  distance  asunder  ii> 
a  cup  of  water,  a  train  of  gas-bubbles  will  be  seen  rising  from  eacK 
and  escaping  at  the  surface.  If  the  electrodes  are  not  647 

of  gold  or  platinum,  the  oxygen  combines  with  one  of 
them,  and  only  hydrogen  escapes,  as  in  Nicholson's  ori- 
ginal experiment.  With  two  glass  tubes  placed  over  the 
platinum  poles,  fig.  646,  we  can  collect  646 

these  bubbles  as  they  rise.  The  gas 
(hydrogen)  given  off  from  the  negative 
electrode  is  twice  the  volume  of  that 
obtained  from  the  positive.  When  the 
tubes  are  of  the  same  size,  this  differ- 
ence becomes  at  once  evident  to  the 
eye.  By  examining  these  gases,  we 
shall  find  them,  respectively,  pure  hy- 
drogen and  oxygen,  in  the  proportion  __ 
of  two  volumes  of  the  former  to  one  of 
the  latter.  Agreeably  to  principles 
already  explained,  the  oxygen  (electro-negative)  appears  at  the  -j-  elec- 
trode, and  the  hydrogen  (electro-positive)  appears  at  the  —  electrode. 
The  rapidity  of  the  decomposition  is  greater  when  the  water  is  made  a 
better  conductor,  by  adding  a  few  drops  of  sulphuric  acid ;  and  for 
rapid  electrolysis  the  number  of  couples  in  the  series  should  be  in- 
creased to  overcome,  by  superior  tension,  the  low  con-  648 
ducting  power  and  chemical  affinity  of  the  electro- 
lyte. If  a  single  tube  only  covers  both  electrodes,  as 
in  fig.  647,  the  total  electrical  effect  is  easily  measured 
by  the  graduation  of  the  tube,  the  quantity  of  gases 
given  off  in  a  unit  of  time  being  directly  as  the  current. 
The  contents  of  this  tube  will  explode  if  a  lighted 
match  is  applied  to  them,  or  if  an  electric  spark  passes 
through  them.  Such  an  instrument  is  a  Voltameter. 

A  convenient  form  of  this  instrument  is  seen  in  fig.  648,  made  of  a  common 
bottle,  filled  with  acid  water;  the  platinum  electrodes  pass  through  the  cork  and 


592 


PHYSICS  OF  IMPONDERABLE  AGENTS. 


end  in  two   plates  of  platinum,  while  a  bent  gas  tube  of  glass  conveys  off  the 
accumulating  gases  as  fast  as  they  are  evolved  by  the  electrolysis. 

890.  Laws  of  electrolysis. — From  a  great  number  of  elaborate 
experiments,  the  accuracy  of  which  remains  unshaken.   Faraday  has 
deduced  the  following  general  laws  of  electrolysis. 

1st.  The  quantity  of  any  given  electrolyte,  resolved  into  its  constitu- 
ents by  a  current  of  electricity,  depends  solely  on  the  amount  of  elec- 
tricity passing  through  it,  and  is  independent  of  the  form  of  apparatus 
used,  the  size  or  dimensions  of  the  electrodes,  the  strength  of  the  solu- 
tion, or  any  other  circumstance.  Hence,  the  amount  of  water  decom- 
posed in  a  given  time  in  the  Voltameter,  is  an  exact  measure  of  the 
quantity  of  electricity  set  in  motion. 

2d.  In  every  case  of  electrolysis,  the  elements  are  separated  in 
equivalent  or  atomic  proportions,  and  when  the  same  current  passes  in 
succession  through  several  electrolytes  in  the  same  circuit,  the  whole 
series  of  elements  set  free  are  also  in  atomic  proportions  to  each  other. 
It  follows,  therefore,  that  the  amount  of  electricity  required  to  resolve 
a  chemical  combination,  is  in  constant  proportion  to  the  force  of  chemi- 
cal affinity  by  which  its  elements  are  united. 

3d.  The  oxydation  of  an  atom  of  zinc  in  the  battery,  generates 
exactly  so  much  electricity  as  is  required  to  resolve  an  atom  of  water 
into  its  elements.  Thus,  8'45  grains  of  zinc  dissolved  in  the  battery, 
occasions  the  electrolysis  of  2'35  grains  of  water.  But  these  numbers 
are  in  the  ratio  of  32'5  :  9  the  equivalents,  respectively,  of  zinc  and  of 
water.  Hence  follow  these  corollaries : — First,  The  sourve  of  Voltaic 
electricity  in  the  pile  is  chemical  action  solely.  Second,  T ke  forces  termed 
chemical  affinity  and  electricity,  are  one  and  the  same. 

One  or  two  additional  illustrations  of  these  laws  will  suffice  in  this 
place,  referring  the  student  to  chemical  649 

treatises  for  a  fuller  discussion  of  this 
very  important  topic. 

891.  Electrolysis  of  salts.— In  the 
bent  tube,  B  A,  fig.  649,  put  a  solution 
of  any  neutral   salt ;   i.  e.,  sulphate  of 
soda,  and  diffuse  the  blue  solution  from 
a  purple  cabbage  in  the  liquid.     Let  the 
current  of  a  Voltaic  pile  communicate 
with  this  saline  solution  by  two  platinum 
wires,  dipping  into  the  legs  of  the  tube — 
presently  the  blue  color  of  the  solution 

is  changed  on  the  positive  side  for  red,  and  on  the  negative  for  green, 
indicating  the  presence  of  an  acid  set  free  in  A,  and  of  an  alkali  in  B 


ELECTRICITY. 


593 


If  the  action  is  kept  up,  the  whole  of  the  blue  liquid  is  changed  to  red 
and  green.  Transpose,  then,  the  -J-  and  —  wires,  so  as  to  reverse  tho 
direction  of  the  current ;  presently,  the  red  and  green  change  back  to 
blue,  and,  in  a  short  time,  that  which  was  red  becomes  green,  and  vice 
versa.  This  is  a  case  of  electrolysis  in  which  the  electrolyte  (sulphate 
of  soda)  is  changed,  not  into  its  ultimate  elements,  but  only  into  the 
acid  and  alkali,  which  may  be  called  its  proximate  constituents ;  any 
other  saline  fluid  may  be  substituted  with  similar  results.  If  an  alka- 
line chloride  is  used,  i.  e.,  common  salt,  the  free  chlorine  evolved  on 
the  +  side,  discharges  all  color,  while  the  soda  produces  on  the  — 
side  its  appropriate  green  tint.  If  a  metallic  salt,  e.  g.,  sulphate  of 
copper,  or  acetate  of  lead,  is  used  in  A  B,  then,  on  the  —  side,  metallic 
copper  or  lead  is  evolved ;  while,  on  the  -f-  side,  is  the  free  acid  before 
in  combination  in  the  salt. 

A  more  surprising  example  of  the  apparent  transfer  of  elements  under  the 
power  of  the  Voltaic  current,  is  illustrated  in  fig.  650,  where  in  B,  the  centre  glass, 
of  the  three  wine-glasses,  A  B  C,  is  a  650 

solution  of  sulphate  of  soda,  while  A 
and  C  contain  only  pure  water,  blued 
with  cabbage  solution.  Filaments  of 
moist  cotton  wick  connect  the  three 
glasses,  and  the  electrodes  are  intro- 
duced into  A  and  C,  when  the  same 
series  of  changes,  already  described  in 
fig.  649,  takes  place,  with  the  same  re- 
versals when  the  electrodes  are  trans- 
ferred. B  remains  apparently  unchanged,  while  C  is  reddened,  and  A  becomes 
green,  or  vice  versa.  There  is,  in  fact,  nothing  more  wonderful  in  this  case  than 
iu  the  last,  only  the  dissection  of  the  process  into  three  parts,  makes  the  result 
still  more  striking.  In  place  of  A  B  C,  any  number  of  glasses,  with  different 
salts  and  compounds,  may,  with  a  powerful  series  of  Bunsen,  be  substituted, 
•\vith  results  conformable  to  the  law  in  $  890. 

892.  Electro-metallurgy. — The  electrotype. — The  cold  casting 
of  metals  by  the  Voltaic  current,  is  a  fine  example  of  651 

the  rich  gifts  made  by  abstract  science  to  the  practical 
arts  of  life.  Every  DanielFs  battery  is,  in  fact,  an 
electro-metallic  bath,  in  which  metallic  copper  of  a 
firm  and  flexible  texture  is  constantly  thrown  down 
from  solution. 


The  very  simple  apparatus  required  to  show  these  results 
«xperimentally,  is  represented  in  the  fig.  651.  It  is  nothing, 
in  fact,  but  a  single  cell  of  Daniell's  batttery.  A  gla«s  tum- 
bler, S,  a  common  lamp-chimney,  P,  with  a  bladder-skin 
tied  over  the  lower  end  and  filled  with  dilute  sulphuric  acid, 
is  all  the  apparatus  required.  A  strong  solution  of  sulphate 
of  copper  is  put  into  the  tumbler,  and  a  zinc  rod,  Z,  is  inserted  in  P ;  the  moulds, 
or  casts,  m  m,  are  suspended  by  wires  attached  to  the  binding  screw  of  Z.  Thus 


594 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


arranged,  the  copper  solution  is  slowly  decomposed,  and  the  metal  is  evenly  and 
firmly  deposited  on  mm.  A  perfect  reverse  copy  of  m.  is  thus  obtained  in  solid 
malleable  copper.  The  back  of  m  is  protected  by  varnish,  to  prevent  the  adhe- 
sion of  the  metallic  copper  to  it.  In  this  manner  the  most  elaborate  and  costly 
medals  are  easily  multiplied,  and  in  the  most  accurate  manner.  In  practice, 
reverse  casts  of  the  object  to  be  copied  are  first  made  in  fusible  metal  or  wax.  The 
art  is  now  extensively  applied  to  plating  in  gold  and  silver  from  their  solutions  ; 
the  metals  thus  deposited  adhering  perfectly  to  the  metallic  surface  on  which 
they  are  deposited,  provided  these  be  quite  clean  and  bright. 

Even  alloys,  as  bronze,  brass,  and  German  silver,  may  be  deposited  according 
to  electrolytic  law. 

The  positive  electrodes  should  be  of  the  same  metal  as  that  in  solution,  and 
as  large  as  the  surfaces  to  be  coated,  and  these  should  not  be  larger  than  the 
plates  of  the  battery  furnishing  the  current.  The  arrangement  of  apparatus 
commonly  used  in  this  art,  is  seen  in  fig.  652,  where  the  metallic  solution  is  held 

652 


T) 


in  a  separate  bath,  over  which  are  extended  two  stout  rods ;  B,  carrying  the 
objects,  m,  in  connection  with  the  negative  side  of  the  battery ;  and  with  the  posi- 
tive side,  the  rod  D,  on  which  is  suspended  a  plate  of  the  metal  proposed  to  be 
deposited,  to  maintain  the  uniform  strength  of  the  solution,  which  is  preferably 
kept  at  a  somewhat  higher  temperature  than  that  of  the  air.  Wood-cuts  and 
printers'  types  are  thus  copied  in  copper,  the  moulds  taken  in  wax  from  them 
being  made  conductors  by  dusting  over  the  surface  with  extremely  fine  plum- 
bago. All  the  copper-plates  for  the  charts  of  the  United  States  Coast  Survey, 
are  reproduced  by  the  electrotype — the  originals  never  being  used  in  the  press, 
but  only  the  copies ;  and  any  required  number  of  these  may  be  produced  at 
small  expense.  For  an  instructive  account  of  these  extensive  electrotype  opera- 
tions, the  student  is  referred  to  a  paper  by  the  Electrotypist  of  the  Coast  Sur- 
vey, Mr.  G.  Mathiot  (Amer.  Jour.  Sci.  [2],  XV.,  305). 

893.  Crystallization  from  the  action  of  feeble  currents. — It 
was  known  to  the  alchemists,  very  early  in  chemical  history,  that  cer- 
tain metals,  as  gold,  silver,  copper,  lead,  tin,  &c.,  were  deposited  in  a 
pure,  or  "  reguline"  condition,  from  their  solutions,  when  another  metal 
was  present,  or  even  sometimes  without  that  condition.  Thus  the  lead 
tree  (arbor  Saturnce),  the  tin  tree  (arbor  Jovis],  the  silver  tree  (arbor 
Diance),  were  so  calljd  by  the  alchemists,  from  the  apparent  growth 


ELECTRICITY.  595 

of  theso  metals  out  of  their  solutions,  and  in  tree-like  forms.  This 
growth  we  now  know  to  be  due  to  Voltaic  crystalline  deposition. 

Examples. — A  solution  of  chlorid  of  gold  in  ether,  by  slow  change,  deposits 
spontaneously,  crystals  of  fine  gold,  in  elegant  moss-like  growths ;  and  Liebig  has 
shown  us  how  to  prepare  a  silver  solution,  which,  by  the  aid  of  an  essential  oil  as  a 
reducing  agent,  will  coat  glass  with  a  film  of  silver  so  thin  as  to  be  transparent, 
and  still  so  brilliant  as  to  reflect  light  more  perfectly  than  the  best  mercurial 
mirrors. 

A  dilute  solution  of  acetate  of  lead  (half  an  ounce  to  a  quart  of  rain  water), 
surrenders  all  its  lead  to  a  strip  of  zinc  hung  in  the  containing  bottle,  in  elegant 
crystalline  plates  (the  arbor  Saturnce);  this,  and  the  next  case,  are  true  Voltaic 
circuits,  while  in  the  first  two  cases,  hydrogen  appears  to  supply  the  want  of  the 
second  element  of  Voltaic  couple.  In  like  manner,  a  dilute  solution  of  nitrate 
of  silver,  placed  over  mercury,  .soon  deposits  all  its  silver  in  an  arborescent  form 
(arbor  Diance)  on  the  mercury. 

But  the  most  instructive  case  of  this  kind  is  when  a  bar  of  pure  tin  is  placed 
upright  in  a  tall  vessel,  the  lower  half  of  which  is  filled  with  a  saturated  solution 
of  protochlorid  of  tin,  while  above  it  rests  a  dilute  solution  of  the  same  salt. 
The  bar  is  therefore  in  two  solutions  chemically  identical,  but  physically  unlike. 
The  result  is  a  Voltaic  current,  by  which  metallic  tin,  in  beautiful  brilliant  plates, 
is  deposited  upon  the  upper  part  of  the  bar,  while  the  lower  part  is  correspond- 
ingly dissolved  by  the  free  electro-negative  element  of  this  electrolysis. 

The  earliest  recorded  experiments  with  this  species  of  Voltaic  circuit  are  those 
of  Bucholz  (1807),  whence  this  slow-acting  pile  is  sometimes  called  the  "  Bucholz- 
pile."  Becquerel  has  greatly  extended  our  knowledge  of  the  actions  thus  pro- 
duced, forming  thereby  many  non-metallic  crystalline  products.  Cross  thus 
formed  crystals  of  carbonate  of  lime  in  two  days  in  the  light,  or  in  six  days  in  the 
dark.  Mallett  thus  produced  crystals  of  copper,  and  of  red  oxyd  of  copper,  in 
a  single  night  from  the  nitric  solution.  (Am.  Jour.  Sci.  [2]  XXX.  253.) 

894.  Deposit  of  metallic  oxyds  and  Nobili's  rings. — Becquerel 
has  shown  that  oxyd  of  lead  and  oxyd  of  iron  may  be  deposited  in 
a  thin  film  on  the  surface  of  oxydizable  metals  by  using  an  alkaline 
solution  of  the  metallic  oxyd,  and  making  the  plate  to  be  oxydized  the 
negative  electrode  of  a  constant  battery  ;  a  deep  brown  coating  of  the 
oxyd  is  thus  deposited  in  a  few  minutes  so  firmly  as  to  withstand  the 
action  of  the  burnisher,  and  perfectly  protect  the  iron  or  steel  from 
atmospheric  action. 

If  the  film  of  oxyd  of  lead  is  very  thin,  it  presents,  over  a  surface 
of  polished  silver  or  steel,  a  most  pleasing  exhibition  of  colored  rings, 
analogous  to  the  colored  rings  of  Newton  from  thin  plates  (530).  For 
this  purpose  the  negative  electrode  is  made  of  a  thin  platinum  wire, 
protected  from  the  solution  by  a  glass  tube,  except  at  the  extremity, 
where  a  mere  point  is  presented.  A  rim  of  wax  on  the  edges  of  the 
plate  retains  the  solution  of  potassa,  saturated  with  oxyd  of  lead,  while 
it  is  connected  on  the  positive  pole,  and  the  negative  point  is  held  for  a 
few  seconds  within  a  line  of  the  polished  surface.  These  colored  rings 
were  first  noticed  by  Mr.  Nobili,  whence  their  name. 


696          PHYSICS  OF  IMPONDERABLE  AGENTS. 

3.  Physiological  effects  of  the  pile. 

895.  The  physiological  effects  of  the  Voltaic  pile. — Galvani's 
original  experiment,  and  the  earlier  observations  of  Swammerdam  and 
Sulzer,  of  two  metals  on  the  tongue,  deserve  to  be  remembered  as  being 
our  earliest  knowledge  of  this  subject.   From  a  single  cell,  or  even  a  small 
number  of  pairs,  the  dry  hands,  grasping  the  electrodes,  receive  no  sen- 
sation ;  number,  and  not  size  of  elements,  is  requisite  for  the  physio- 
logical effect.    Thus,  from  a  column  of  fifty  elements,  or  still  more  from 
fifty  cups  of  Bunsen,  or  a  Cruickshank's  trough  (870),  a  smart  twinge  is 
felt,  reaching  to  the  elbows,  or  if  the  hands  are  moistened  with  saline 
or  acid  water,  the  shock  will  be  felt  in  the  shoulders.     This  shock  is 
unlike  the  sharp  and  sudden  commotion  from  statical  electricity,  being 
a  more  continued  sensation,  accompanied,  during  the  continuance  of  the 
current,  by  a  sense  of  prickly  heat  on  the  surface.     But  it  is  only  at 
the  making  and  breaking  of  contact  that  a  shock  is  felt.    If  the  battery 
contains  some  hundreds  of  Couples  actively  excited,  the  shock  becomes 
painful,  or  even  fatal.     It  may  be  passed  through  any  number  of  per- 
sons whose  moistened  hands  are  firmly  joined,  but  it  is  sensibly  less 
acute  at  the  middle  of  such  a  circuit  than  to  those  at  the  electrodes. 
Even  after  death,  this  power  produces  spasmodic  muscular  contrac- 
tions, efforts  to  rise,  and  contortions  of  the  features  frightful  to  behold.* 
Persons  in  whom  animation  was  suspended,  have  been  restored  by  the 
influence  of  the  hydro-electric  current  on  the  nervous  system. 

The  senses  of  sight,  hearing,  and  taste,  are  all  affected  by  a  Voltaic  current; 
a  flash  of  light,  a  roaring  sound,  and  a  sub-metallic  savor  being  received  when 
the  shock  of  a  small  battery  is  passed,  successively,  through  the  eyes,  the  ears, 
and  the  tongue. 

Prom  the  experiments  of  Becquerel,  it  appears  that  seeds  subjected  to  a 
gentle  electric  current,  germinate  sooner  than  otherwise.  Von  Marum  observed 
that  plants  with  a  milky  juice,  like  the  Euphorbiacece,  do  not  bleed  after  a 
powerful  electrical  shock,  owing,  he  suggests,  to  the  loss  of  contractile  power  in 
the  plant. 

For  a  detailed  account  of  the  application  of  electricity  to  medical  uses,  con- 
sult the  works  of  Dr.  G.  Bird  (of  London),  "W.  F.  Channing  (of  Boston),  and  the 
late  elaborate  volume  of  Dr.  Garrett. 

The  magnetic  effects  of  the  pile  belong  to  electro-dynamics, 
while  its  electrical  effects  have  already  been  considered  in  $$  863,  864. 

VII.     THEORY  OF  THE  PILE. 

896.  Three  views.— 1.  It  has  already  been  stated  (863),  that  Volta 
and  his  school  ascribed  the  effects  of  the  pile  to  the  simple  contact  of 
unlike  metals,  each  decomposing  the  neutral  electricity  of  the  other. 

*  See  a  notice  of  Dr.  lire's  experiments  on  a  newly  executed  criminal,  at 
Glasgow,  in  1818.  HARRIS,  Galvanism,  123,  J.  Weale. 


ELECTRICITY.  597 

He  argued  that  the  chemical  action  of  the  battery  was  requisite  only 
to  afford  conductors  for  the  electricity,  while  the  metallic  substances 
remaining  in  every  way  unchanged,  they  are  supposed  to  discharge 
into  each  other.  According  to  this  hypothesis,  the  two  metals  are  in 
opposite  electrical  states,  one  being  positive,  the  other  negative ;  these 
states  becoming  at  once  destroyed  by  the  intervening  fluid.  This  theory 
assumed  that  the  whole  effect  of  the  apparatus  is  but  a  disturbance 
and  reproduction  of  electrical  equilibrium.  This  view,  however,  can- 
not be  maintained,  since  it  involves  an  impossibility : — the  production 
of  a  continual  current,  flowing  on  against  a  constant  resistance,  with- 
out any  consumption  of  the  generating  force. 

2.  On  the  other  hand,  Fabbroni,  Davy,  Wollaston,  and,  above  all,  in 
our  day,  Faraday,  De  la  Rive,  and  Becquerel  have  sought  to  establish 
that  the  Voltaic  excitement  was  only  the  reciprocal  of  the  chemical 
action  ;  and  as  this  was  more  intense,  and  properly  directed,  so  was 
the  pile  more  powerful.     In  addition  to  the  statements  and  arguments 
already  adduced,  it  is  proper  here  to  consider  the  ground  of  these  two 
views,  and  somewhat  more  in  detail. 

3.  A  third  view  or  theory  of  the  pile  has  been  advanced  by   Peschel, 
which  he  calls  the  molecular  theory,  and  which  rests  on  a  sort  of  middle 
ground  between  the  contact  and  the  chemical  theories. 

897.  Volta's  contact  theory, — The  advocates  of  this  mode  of  ex- 
plaining the  action  of  the  pile  (embracing  nearly  the  whole  body  of  the 
German  physicists),  contend  that  they  have  experimentally  established 
the  following  points  in  support  of  Volta's  theory,  viz. :  1st,  That  Volta's 
original  experiments  demonstrate  the  fact  beyond  question,  that  the 
simple  contact  of  heterogeneous  metals  does  produce  an  electrical  cur- 
rent (846).  2d,  That  in  some  cases,  when  a  purely  chemical  action 
exists  between  a  fluid  and  one  of  the  two  metals  immersed  in  it,  the 
contact  of  the  metals  arrests  this  action,  and  an  opposite  action  com- 
mences. 3d,  That  there  are  even  cases  of  hydro-electric  combinations, 
in  which  electrical  action  exists,  without  any  chemical  action  whatever 
on  the  electromotors.  4th,  The  advocates  of  this  view  further  contend 
that  chemical  action  is  never  the  primitive  cause  of  electrical  excite- 
ment ;  although  some  do  not  question  the  influence  of  chemical  action 
in  promoting  and  increasing  the  excitement  originally  due  to  contact. 

Since  scarcely  any  chemical  action,  or  none  at  all,  occurs  in  a  con- 
stant battery  without  contact,  it  is,  with  reason,  urged  that  contact  of 
the  heterogeneous  metals  is  the  one  indispensable  prior  cause  of  the 
Voltaic  current.  Hence  the  real  difficulty  seems  to  be,  to  decide  what 
share  chemical  influence  really  has  in  exciting  the  electrical  action. 
Want  of  space  prevents  our  giving  the  evidence  in  detail  upon  which 
58 


698  PHYSICS    OF   IMPONDERABLE   AGENTS. 

the  advocates  of  the  contact  theory  rely  for  the  support  of  the  above 
propositions. 

898.  The  chemical  theory  assumes  the  electrical  current  to  be  the 
reciprocal  of  the  chemical  action  in  the  cells  of  the  battery,  and  that 
chemical  action  is  essential  to  the  production  of  such  a  current. 

De  la  Rive  demonstrated  this  latter  point  in  the  following  manner : 
A  pair,  formed  of  two  plates,  one  of  gold,  the  other  of  platinum,  was 
plunged  into  pure  nitric  acid,  without  the  development  of  any  current ; 
by  the  addition  to  the  nitric  acid  of  a  single  drop  of  chlorohydric  acid, 
a  very  decided  current  was  obtained  from  the  gold  to  the  platinum 
through  the  liquid.  In  the  first  case  there  was  no  chemical  action  ;  in 
the  second  case,  the  gold  was  attacked,  and  the  platinum  was  not,  or 
more  feebly. 

The  laws  of  electrolysis,  first  demonstrated  by  Faraday,  as  already 
stated  (890),  lend  the  evidence  of  mathematical  certainty  to  the  chemi- 
cal theory  of  the  pile.  Since  we  thus  reach  the  unavoidable  conclusion 
that  an  equivalent  of  electricity  is  a  chemical  equivalent,  and  so  bring 
the  discussion  down  to  the  rigid  test  of  the  balance,  the  ultima  ratio 
of  chemists  and  physicists. 

In  addition  to  the  laws  of  Faraday,  already  rehearsed,  are  the  fol- 
lowing:— 

Laws  of  the  disengagement  of  electricity  by  chemical  action, 
first  stated  by  M.  Becquerel : — 

1st.  In  the  combination  of  oxygen  with  other  bodies,  the  oxygen  takes  the 
electro-positive  substance,  and  the  combustible  the  electro-negative. 

2d.  In  the  combination  of  an  acid  with  a  base,  or  with  bodies  that  act  as  such, 
the  first  takes  the  positive  electricity,  and  the  second  the  negative  electricity. 

3d.  When  an  acid  acts  chemically  on  a  metal,  the  acid  is  electrified  positively, 
and  the  metal  negatively  :  this  is  a  consequence  of  the  second  law. 

4th.  In  decompositions,  the  electrical  effects  are  the  reverse  of  the  preceding. 

5th.  In  double  decompositions,  the  equilibrium  of  the  electrical  forces  is  not 
disturbed. 

The  quantity  of  electricity  required  to  produce  chemical 
action  is  enormous,  compared  with  the  amount  of  statical  electricity 
disturbed  by  the  common  frictional  machine.  Faraday  has,  in  his 
masterly  way,  demonstrated  this  fact  by  simple  experiment. 

He  has  shown  that  the  quantity  of  Voltaic  electricity  requisite  for  decomposing 
one  grain  of  water,  would  be  sufficient  to  maintain  at  a  red  heat  a  wire  of  plati- 
num about  one  one-hundredth  of  an  inch  (y^j)  in  diameter,  during  three  minutes 
forty-five  seconds,  the  time  requisite  to  effect  the  perfect  decomposition  of  the 
grain  of  water.  The  quantity  of  frictional  electricity  required  to  produce  the 
same  effect,  would  be  that  furnished  by  eight  hundred  thousand  discharges  of  a 
battery  of  Leyden  jars,  exposing  three  thousand  five  hundred  square  inches  of 
surface,  charged  with  thirty  turns  of  a  powerful  electrical  machine. 

Becquerel,  by  a  different  mode  of  experiment,  arrived  at  nearly   the  same 


ELECTRICITY.  599 

results.  Therefore,  to  decon  pose  a  grain  of  water,  requires  an  amount  of  elec- 
tricity equal  to  that  furnisted  by  the  discharge  of  an  electric  pane  having  a 
surface  of  thirty-two  acres.  "  Equal  to  a  very  powerful  flash  of  lightning." 
"  This  view  of  the  subject  gives  an  almost  overwhelming  idea  of  the  extraordi- 
nary quantity  of  electric  power  which  naturally  belongs  to  the  particles  of 
matter."  (Faraday  Expt.  Res.,  853-861.) 

899.  Polarization  and  transfer  of  the  elements  of  a  liquid. — 

The  electro-chemical  theory  has  been  much  expanded  by  the  researches 
of  De  la  Rive ;  he  explains  the  phenomena  of  polarization  and  the 
transfer  of  the  elements  of  a  liquid  in  the  following  manner : — 

His  theory  assumes  that  every  atom  has  two  poles,  contrary,  but  of  the  same 
force.  The  different  kinds  of  atoms  differ  from  each  other  in  that  some  have  a 
more  powerful  polarity  than  others.  When  two  insulated  atoms  are  brought 
near  each  other,  they  attract  each  other  by  their  opposite  poles  j  the  positive 
pole  of  that  which  has  the  strongest  polarity  unites  with  the  negative  pole  of 
that  which  has  the  feeblest  polarity.  A  compound  atom,  when  insulated,  has 
therefore  two  contrary  polarities  between  the  poles  of  a  pile ;  for  example,  the 
atom  is  so  arranged  that  its  -f-  pole  is  turned  to  the  platinum  (or  —  side)  of 
the  pile,  and  the  —  pole  is  turned  to  the  zinc  (or  -f-  side)  of  the  pile.  This 
same  action  occurs  with  other  atoms,  so  that  there  is  produced  a  chain  of  polar- 
ized particles  between  the  poles  of  the  pile. 

The  oxygen  of  the  particle  of  water  nearest  the  zinc  becomes  negative, 
because  of  its  affinity  for  the  zinc,  and  the  hydrogen  becomes  positive.  The 
other  particles  of  water  become  similarly  electrified  by  induction,  but  the 
platinum  has  become  negative  by  induction  from  the  zinc,  and  therefore  is  in  a 
condition  to  take  up  the  positive  electricity  from  the  zinc  of  the  contiguous 
hydrogen.  The  action  now  rises  high  enough  for  the  zinc  and  the  oxygen  to 
combine  chemically  with  each  other.  The  oxyd  of  zinc  thus  formed  dissolves 
in  the  liquid  (dilute  sulphuric  acid),  and  is  thus  removed.  But  the  partible  of 
hydrogen  nearest  the  zinc,  now  seizes  the  oppositely  electrified  oxygen  of  the 
adjacent  particle,  producing  a  fresh  atom  of  water.  The  particle  of  hydrogen 
which  terminates  the  flow  is  electrically  neutralized  by  the  platinum,  to  which  it 
imparts  its  excess  of  positive  electricity,  and  escapes  in  the  form  of  gas ;  and 
other  particles  of  water  are  continually  produced,  to  supply  the  place  of  those 
decomposed,  and  thus  continuous  action  is  maintained.  These  changes,  con- 
tinually taking  place,  furnish  an  uninterrupted  flow  of  electricity,  which  is 
conveniently  termed  a  Voltaic  current. 

Other  instances  of  electrolysis  are  explained  in  a  similar  way. 

900.  Chemical  affinity  and  molecular  attraction  distinguished. 
— According  to  De  la  Rive,  and  in  support  of  the  view  of  the  polarity 
of   atoms,   the  distinction   between    Chemical   affinity  and   molecular 
attraction  is  as  follows :  chemical  affinity  is  the  attraction  of  atoms, 
operating  by  their  contrary  electric  poles,  which  come  into  contact, 
while  physical  attraction  results  from  the  mutual  attractive  action  that 
the  atoms  exercise  over  each  other  in  virtue  of  their  masses.  .  This  last 
attraction  is  never  able  to  produce  contact,  because  of  the  repulsive  force 
of  the  ether  which  envelops  the  atom,  and  which  increases  in  proportion 
as  the  sphere  which  separates  the  attracted  atoms  diminishes  (146). 

901.  Peschell's  molecular  theory  of  the  pile.— Resting  upon  the 


600  PHYSICS   OF   IMPONDERABLE   AGENTS. 

opinion  long  held  by  many  chemists,  that  those  forces  which  lie  at  the 
basis  of  adhesion,  and  those  which  cause  chemical  affinity  are  not  essen- 
tially different,  Peschel  holds  that —  When  electricity  is  generated  in  any 
Voltaic  arrangement,  it  results  from  a  molecular  change,  brought  about 
in  the  touching  bodies  by  the  adhesive  force  which  subsists  between  them, 

This  theory  possesses  the  advantage,  that  no  new  power  need  be  assumed  to 
exist,  whereas  the  contact  theory  demands  the  existence  of  an  "electro-motive 
force,"  of  which  we  know  nothing.  It  also  accounts  for  the  production  of  elec- 
tricity, apart  from  any  chemical  action.  In  common  with  the  chemical  hypo- 
thesis, it  deduces  the  phenomena  of  the  single  battery  from  the  molecular  forces  ; 
it  considers  the  fluid  not  merely  as  a  conductor  of  electricity,  but  as  engaged  in 
its  production,  and  that  the  elements  of  the  battery,  by  the  physical  changes 
which  they  undergo,  are  the  actual  sources  of  electricity;  that  their  contact 
renders  this  change  possible,  and  it  is,  therefore,  the  occasion,  and  not  the  gene- 
rating cause,  by  which  the  electricity  is  produced.  By  this  view,  the  chemical 
hypothesis  is  only  a  special  case  of  the  molecular.  The  simultaneous  com- 
mencement of  chemical  action  with  the  development  of  electricity,  and  the 
circumstance  that  the  chemical  intensity  of  a  simple  Voltaic  arrangement 
increases  and  decreases  as  the  chemical  action  on  the  fluid  conductor,  and  on 
the  elements  of  the  battery  is  greater  or  less,  fully  accords  with  the  statements 
of  this  theory.  It  follows,  hence,  that  the  electrical  and  molecular  forces  are  one 
and  the  same,  and  that  the  latter  appears  as  electricity  whenever  it  passes  from 
one  mode  of  operation  into  the  other,  as,  e.  g.,  when  it  ceases  to  hold  the  elements 
of  the  water,  and  so  oxydizes  the  zinc. 

§  4.  Electro-Dynamics. 

I.     ELECTRO-MAGNETISM. 

902.  General  laws. — Electro-dynamics  is  that  department  of  physics 
devoted  to  the  mutual  action  of  Volta-electric  currents.  These  are 
distinct  from  the  phenomena  of  static  electricity.  The  phenomena  of 
electro-dynamics  may  all  be  arranged  under  the  following  general 
propositions. 

1.  Eoery  conductor,  conveying  a  current  of  electricity,  affects  a  free 
needle  as  a  magnet  would  do. 

2.  Electric  currents  affect  each  other  like  magnets. 

3.  A  magnet  acts  upon  an  electric  current  as  a  second  current  would 
have  done. 

4.  Electric  currents  in  conductors  excite  similar  currents  in  other  con- 
ductors within  their  influence. 

5.  Magnets  excite  electric  currents,  and  all  the  electrical  effects  depend- 
ing upon  them. 

Hence,  when  magnetism  is  excited  by  electric  currents,  it  is  called 
electro-magnetism :  and  inversely,  when  electrical  currents  result  from 
magnetism,  they  are  called  magneto-electrical  currents. 

It  is  impossible,  in  our  narrow  limits  of  space,  to  consider  each  of  these  pro- 
positions in  full  detail.  We  shall  endeavor,  however,  to  present  those  pheno- 
mena and  their  applications  which  are  of  most  general  interest. 


ELECTRICITY. 


601 


903.  CBrsted's  discovery.— In  1819-20,  Prof.  Hans  Christian  (Er- 
sted, of  Copenhagen,  in  a  course  of  researches  upon  the  relation  of  the 
Voltaic  apparatus  to  the  magnet,  made  the  discovery  of  the  fundamental 
fact  of  electro-magnetism,  stated  in  the  first  of  the  foregoing  proposi 
tions.  Many  physicists  had  before  sought  to  evolve  the  phenomena 
of  magnetism  from  the  battery ;  but  in  vain,  because  they  proceeded 
without  connecting  the  poles  by  a  conductor,  in  which  case,  of  course 
(as  we  now  clearly  see),  the  power  of  the  apparatus  is  dormant,  like 
stagnant  statical  electricity  in  an  unexcited  conductor.  (Ersted  closed 
the  battery  circuit  by  a  conductor  ;  and  therein  rests  his  discovery.  He 
found  when  such  a  conjunctive  wire  was  approached  to  a  free  needle, 
that  the  needle  was  influenced  by  it,  as  if  he  had  used  a  second  mag- 
net: in  other  words,  the  conducting  wire,  of  whatsoever  metal  it  might 
happen  to  be,  had  itself  become  a  magnet. 

If  positive  electricity  flows  from  south  to  north  over  a  horizontal 
conducting  wire,  placed  in  the  magnetic  meridian,  then  a  free  magnetic 
needle,  ba,  fig.  653,  would  have  its  north  end,  b,  deflected  to  the  west, 
653  654 


if  it  is  placed  below  the  conducting  wire,  and  to  the  east  if  it  is  placed 
above  the  wire.  If  the  needle  is  placed  on  the  east  side  of  such  a  con- 
ductor, its  north  end  is  depressed,  if  on  the  west  side  of  the  wire,  the 
north  end  of  the  needle  is  raised.  Reversing  the  direction  of  the  cur- 
rent, reverses  all  these  movements. 

The  rectangle,  fig.  65J,  surrounding  the  magnetic  needle,  has  three 
connections,  by  the  use  of  which  the  current  may,  at  pleasure,  be  sent 
above  or  below  the  needle. 

(Ersted  also  found  that  only  needles  of  steel  or  iron  were  thus  affected,  and 
not  those  of  brass,  lac,  and  other  non-magnetic  substances.  He  called  the  con- 
ductor a  "conjunctive  wire"  and  he  describes  the  effect  of  the  electric  current 
(or  the  "electric  conflict,"  as  he  calls  it),  as  resembling  a  helix ;  and  that  it  ia 
not  confined  to  the  wire,  but  radiates  an  influence  at  sorne  distance. 

The  effect  of  CErsted's  discovery  was  remarkable.     The  scientific  world  was   " 
ripe  for  it,  and  the  truth  he  thus  struck  out  was  instantly  seized  upon  by  Arago, 


602  PHYSICS    OF    IMPONDERABLE    AGENTS. 

Ampere,  Davy,  and  a  crowd  of  philosophers  in  all  countries.  The  activity  with 
which  this  new  field  of  research  has  been  cultivated,  has  never  relaxed,  even  to 
this  hour  ;  while  it  has  borne  fruit  in  a  multitude  of  important  theoretical  and 
practical  truths,  among  which  is  the  ELECTRO-MAGNETIC  TELEGRAPH,  one  of  the 
great  features  of  this  age. 

904.  The  electro-magnetic   current   moves   at  right   angles 
to   the    course    of  the    conjunctive   wire. — Let   a   current  flow 
over  a  conductor  in  the  direction  of  the  arrow,  fig.  655,  from  -f-  to  — ; 
a  small   bar  of   soft  iron,  or  a  steel  sewing-  g66 

needle,  held  vertically  before  this  wire,  be- 
comes  instantly  a  magnet,  with  its  N.  pole 
toward  the  earth — place  the  rod  of  iron  on  the 
opposite  side  of  the  conjunctive  wire,  and  its 

polarity  is  instantly  reversed,  as  in  the  figure.  Revolve  it  in  either  posi- 
tion in  a  vertical  plane  at  right  angles  to  the  conjunctive  wire,  and  the 
induced  poles  will  retain  their  relation  to  the  current  in  every  position  ; 
i.  e.,  the  end  marked  N.  in  the  figure,  will  remain  north  at  every  point 
of  the  revolution.  If  a  steel  needle  is  used,  it  retains  polarity  after 
the  current  ceases  to  act  on  it.  If  the  bar  or  needle  be  laid  parallel  to 
the  conjunctive  wire,  then  the  two  sides  of  the  needle  or  bar  have  oppo- 
site polarities. 

Hence,  it  follows,  that  a  free  magnetic  needle  tends  to  place  itself  at  right 
angles  to  the  path  of  an  electro-magnetic  current  traversing  a  conjunctive  wire, 
and  were  the  needle  free  from  the  directive  tendency  of  terrestrial  magnetism, 
it  would  so  place  itself.  The  electro-magnetic  current  is,  therefore,  a  tangential 
force,  and  acts  tangentially  upon  a  free  needle. 

Simple  as  is  the  relation  between  the  electric  current  on  a  wire,  and  the  order 
of  polarity  induced  by  it  in  a  needle,  its  correct  expression  is  always  difficult. 
To  aid  its  exact  statement  by  some  simple  formula,  Ampere  lays  down  the 
following  rule : — 

The  north  pole  of  a  magnet  is  invariably  deflected  to  the  left  of  the 
current  which  passes  between  the  needle  and  the  observer,  who  is  to  have 
his  face  towards  the  needle,  the  electric  current  being  supposed  to  enter 
from  his  feet  and  pass  out  of  his  head. 

A  verification  of  these  cardinal  principles  by  actual  experiment,  is 
the  only  way  in  which  the  student  «an  obtain  a  vivid  and  lasting  im- 
pression of  them. 

905.  Galvanometers  or  multipliers. — If  the  conjunctive  wire  is 
bent  into  a  rectangle,  fig.  656,  so  as  to  carry  656 

the  current  once,  or  many  times,  around  the 
needle,  then  the  effect  of  the  same  force  on  the 
needle  is  multiplied  in  proportion  to  the  num- 
ber of  convolutions.  Thus  Schweigger  con- 
trived his  multiplier,  fig.  656,  composed  of  a 
flat  spool  of  fine  insulated  copper  wire  within  which  the  needle  was 


ELECTRICITY. 


603 


658 


suspended.  By  this  means  a  very  feeble  current  became  quite  sensible. 
For  ordinary  purposes,  a  few  turns,  or,  it  may  be,  three  hundred  or 
four  hundred  convolutions  suffice ;  but,  for  particular  purposes,  and 
where  the  cur- 
rent is  very  fee- 
ble, many  thou- 
sand feet  of  very 
fine  wire  are 
used. 

In  Nobili's  dou- 
ble galvanometer, 
an  astatic  needle 
(787),  is  used,  in 

which  the  needles,  a  b,  b'  a',  fig.  657,  are  not 
quite  equal,  leaving  a  very  slight  directive 
force  only.  Fig.  658  shows  this  delicate  in- 
strument in  its  most  perfect  form,  as  used 
in  determining  the  laws  of  transmission  of 
heat,  as  well  as  for  other  purposes  demand- 
ing a  very  sensitive  instrument.  Only  the 
lower  and  stronger  needle  is  enclosed  in  the 
helix,  D,  while  the  system  is  suspended  by 
a  fibre  of  raw  silk,  beneath  a  glass  shade, 
leveled  by  three  screw  feet,  C.  The  ends 
of  the  spool  are  seen  at  R  K,  while  by  the 
head,  F,  the  whole  instrument  may  be  re- 
volved so  as  to  bring  the  wires  of  the  spool 
parallel  to  the  suspended  needle  at  rest, 
which  is  the  position  of  greatest  sensitive- 
ness. The  sensitiveness  of  such  an  arrange- 
ment is  very  great.  Suppose,  for  example, 
there  are  five  hundred  revolutions  in  the 
coil,  then  the  lower  needle  is  acted  on  one 
thousand  times,  and  the  upper  one  five  hundred  times  by  any  given  current ;  or 
the  original  force  of  the  current  is  multiplied  fifteen  hundred  times.  But  the 


directing  force  of  the  earth's  magnetism  on  a 
given  needle  is  proportional  to  the  squares  of  the 
vibrations  it  makes  (795).  Now,  assuming  that 
the  needles  alone  made  sixty  vibrations  in  a 
minute,  and  as  astatic  needles  only  ten,  then 
we  have  3600  :  100  as  the  numbers  representing 
the  effect  of  terrestrial  magnetism  in  the  two 
cases  j  or  it  is  thirty-six  times  less  in  the  astatic 
system  than  in  the  simple  needles,  and.  conse- 
quently, the  electric  current  will  affect  them 
thirty-six  times  more  than  if  they  were  not  asta- 
tic. The  deflecting  power  of  the  current  in 
question  will,  therefore,  be  increased  by  such  a 
galvanometer,  1500  X  36  —  54,000  times. 

A  less  expensive  form  of  galvanometer  is  seen  in  fig.  659. 


659 


604 


PHYSICS    OF    IMPONDERABLE    AGENTS 


906.  The   tangents    or   sine    compass    galvanometer. — Tins 
instrument,  invented  by  Pouillet,  is  designed  to  measure  currents  of 
greater  intensity  than  can  be  measured  by  the  common  galvanometer. 
Jt  depends  on  the  established  principle,  that  the  intensity  of  a  cur- 
rent is  proportional  to  the  sine  of  the  angular  deviation  of  the  needle. 
The   angle  of  deviation  being   known,  and 

consequently  its  sine,  the  intensity  of  the 
current  is  expressed  in  terms  of  the  sine. 

Fig.  660  shows  the  arrangement  of  this  instru- 
ment, in  which  the  current,  entering  by  the  conduc- 
tors, b  a,  through  the  ivory  piece,  E,  circulates  a 
few  times  only,  sometimes  only  once,  over  the  ver- 
tical circle,  M,  placed  in  the  magnetic  meridian. 
The  magnetic  needle,  m,  is  deflected  upon  the  hori- 
zontal circle,  N,  in  proportion  to  the  force  of  the 
current  in  M,  and  a  silver  index  needle,  n,  serves 
to  record  the  angular  deviation  of  m  from  its  neu- 
tral point.  When  the  needle  is  at  rest,  the  vertical 
circle,  M,  is  revolved  upon  the  standard,  0,  by  the 
button,  A,  until  its  plane  coincides  with  the  plane  ( 
of  deviation  of  m,  and  this  angular  distance  is' 
then  read  off  by  the  vernier,  C,  upon  the  lower 
graduated  circle,  H.  This  galvanometer,  or  a 
simpler  modification  of  it,  is  the  form  of  instrument  generally  used  in  electro- 
magnetic researches. 

907.  Rheostat. — This  simple  contrivance  of  Wheatstone's  serves  to 
introduce  a  longer  or  shorter  conducting  wire  into  any  circuit,  the  in- 
tensity of  which  it  is  proposed  to  measure  by  the  galvanometer. 

Since  the  intensity  of  the  current  is  inversely  as  the  length  of  the  circuit  (880), 
we  may,  by  increasing  or  diminishing  that 
length,  produce  from  any  current  a  deter- 
minate deviation  (say  30°),  on  the  galva- 
nometer. Fig.  661  shows  this  arrangement, 
composed  of  two  equal  and  parallel  cylin- 
ders, one  of  wood,  B,  and  the  other  of  brass, 
A,  supported  in  a  frame-work  and  revolving 
on  their  centres.  B  is  provided  with  a  spi- 
ral groove,  in  which  the  turns  of  a  copper 
conducting  wire  may  be  laid.  One  end  of 
this  wire  is  at  a,  in  connection  with  the  cur- 
rent pole,  o.  The  wire  may  all  be  wound 
on  B,  in  which  case  the  current  passes 
through  its  whole  length,  and  escapes  at  », 
through  the  metallic  connection  of  its  end, 
e,  with  A.  If  it  is  desired  to  shorten  the 
conductor,  the  handle,  d,  is  put  on  the  axis,  c,  and  A  is  revolved  from  left  to 
right,  until,  as  in  the  cut,  one-half,  for  example,  of  the  conductor,  is  wound  on 
A.  But  A,  being  a  metallic  conductor,  the  current  passes  to  n  by  the  shortest 
course,  and  the  only  part  of  the  wire  in  action  is  what  remains  wound  on  B, 


ELECTRICITY,  605 

and  this  quantity  is  read  off  by  an  index  and  graduation  engraved  on  the  farther 
ends  of  the  cylinders.     This  apparatus  is  indispensable  in  exact  observations. 

908.  Ampere's  electro-magnetic  discoveries  and  theory. — Im- 
mediately after  the  first  announcement  of  (Ersted's  discovery  of  the 
magnetic  powers  of  a  conjunctive  wire,  Ampere,  one  of  the  most  re- 
nowned of  the  French  physicists  (born  1755 — died  1836),  commenced  a 
series  of  experiments  (September,  1820)  to  determine  the  laws  con- 
cerned in  these  curious  phenomena.     Of  three  principal  hypothesis 
which  he  framed  to  this  end,  he  finally  accepted  and  demonstrated  the 
following,  viz. : — 

A  magnet  is  composed  of  independent  elements  or  molecules,  which 
ict  as  if  a  closed  electric  circuit  existed  within  each  of  them :  in  other 
words,  each  of  these  magnetic  molecules  may  be  replaced  by  a  conjunctive 
wire  bent  on  itself,  in  which  a  constant  current  of  electricity  is  maintained, 
as  from  a  Voltaic  circuit. 

This  hypothesis  he  maintained  by  singularly  ingenious  experiments,  many  of 
winch  were  the  direct  suggestion  of  the  hypothesis  itself,  and  he  brought  all, 
by  his  power  of  mathematical  analysis,  into  exact  conformity  with  his  theory. 
This  theory  recognises  only  such  forces  as  are  common  to  mechanical  physics, 
and  often  called  "push  and  pull"  forces.  These  forces  are  mutual,  and  belong 
to  all  electric  currents.  In  permanent  magnets,  the  minute  circular  and  parallel 
currents,  pertaining,  by  this  theory,  to  each  magnetic  molecule,  all  act  at  right 
angles  to  the  magnetic  axis  or  line  of  force.  Hence,  as  in  (Ersted's  experiment 
(903),  the  magnetic  needle  strives  to  place  itself  at  right  angles  to  the  path  of 
the  current  on  the  conjunctive  wire,  it  follows,  that  currents  in  the  magnet  seek 
a  parallelism  to  that  in  the  conjunctive  wire.  Granting  this  to  be  true,  it  fol- 
lows, as  a  corollary  from  the  premises, — 

1st.  That  two  free  conducting  wires  must  attract  or  repel  each  other,  according 
to  the  direction  of  the  currents  in  them. 

2d.    That  a  conjunctive  wire  may  be  made  in  all  respects  to  simulate  a  magnet. 

909.  Mutual  action  of  electric  currents. — Parallel  currents  attract 
each  other  when  they  flow  in  the  same  direction.   Thus,  in  fig.  662,  where 
the  arrows  and  the  signs  +  and  —  indicate  the  flow  of  the  currents  to 

662  663 


be  identical,  there  is  attraction,  while,  in  fig.  663,  the  same  signs  show 
the  currents  to  be  reversed,  in  conformity  to  the  law  that : — Parallel 
currents  repel  each  other  when  their  directions  are  opposite.  To  illustrate 
these  laws  experimentally,  one  of  the  conductors  should  be  fixed, 
and  the  other  movable.  The  following  simple  apparatus  also  illus- 
trates these  laws,  and  several  other  points  of  interest  presently  to  be 
noticed. 


606  PHYSICS    OF   IMPONDERABLE   AGENTS. 

De  La  Rive's  floating  current,  fig.  664,  is  a  little  battery  of  amalga- 
mated zinc,  z,  and  copper,  c,  or  zinc  and  platinum,  set  afloat  by  a  disc  of  cork, 
a  b,  whose  poles  -(-  and  —  are  connected  by  a  conjunctive  664 

wire,  s  t.  When  this  little  float  is  placed  in  a  vessel  of  acidu-  * 
iated  water  (water  with  one-twentieth  sulphuric  acdi),  an 
electric  current  flows  in  the  direction  of  the  arrow.  Then  >A 
join  the  poles  of  a  single  cell  of  Grove's  or  Smee's  battery 
by  a  conjunctive  wire  of  convenient  length,  and  stretching  c 
the  wire  between  the  two  hands,  approach  it  parallel  to  st; 
if  the  current  is  flowing  in  the  same  direction,  the  float  will  be  attracted  to  the 
wire  in  the  hands ;  if  otherwise,  repulsion  is  seen.  If  the  two  wires  are  not 
parallel  to  each  other,  then  the  movable  current  seeks  to  take  up  a  position  of 
parallelism,  or  one  in  which  the  two  currents  have  a  similar  direction.  A  little 
rectangular  frame  of  wood  3  X  6  in.,  may  be  wound  with  ten  or  twelve  turns  of 
fine  copper  wire,  covered  by  silk  in  the  manner  of  a  665 

galvanometer,  and  its  free  ends  connected  with  a  bat- 
tery will  give  a  stronger  current.  By  simply  turning 
the  frame  in  the  hand,  the  direction  of  the  current  is 
reversed. 

Roget's  oscillating  spiral,  fig.  665,  also  illus- 
trates the  law  of  attraction  of  parallel  conductors.  Here 
the  conductor  is  coiled  into  a  spiral,  which  is  suspended 
from  the  top  of  an  upright  metallic  standard  in  con- 
nection with  one  pole  of  a  battery,  while  the  other  end 
dips  into  mercury  in  the  glass,  in  connection  with  the 
other  pole,  K.  When  the  poles  are  joined,  each  turn  of 
the  spiral  attracts  the  next  turn,  shortening  the  spiral, 
and  breaking  the  mercurial  connection,  with  a  spark.  The  weight  of  the  spiral 
then  restores  the  connection,  and  thus  a  continuous  oscillating  movement  is 
kept  up. 

We  add  the  following  general  propositions  on  this  subject. 

1.  Two  currents  following  each  other  in  the  same  direction,  as  also 
different  parts  of  the  same  current,  repel  each  other. 

2.  Two  fixed  currents  of  equal  intensity,  flowing  near  and  parallel 
to  each  other  in  opposite  directions  (as  when  the  same  wire  returns  on 
itself  without  contact),  exert  no  influence  on  a  fixed  current  running 
near  them :   in  other  words,  they  exactly  neutralize  each  other,  and 
their  effect  is  null. 

The  rotation  of  electric  conductors  about  magnets,  and  the  reverse ; 
the  rotation  of  a  magnet  on  its  own  axis  by  an  electric  current,  and  the 
rotation  of  electrical  conductors  about  each  other,  are  all  points  most, 
curious  and  instructive  to  trace,  did  space  permit.  The  student  will 
find  these  principles  very  neatly  illustrated  by  appropriate  apparatus 
in  Davis' s  Manual  of  Magnetism.  The  researches  of  Henry,  Page,  and 
other  American  physicists,  have  made  very  important  additions  to  this 
department  of  physics. 

910.  Helix,  solenoid,  or  electro-dynamic  spiral. — By  winding 


ELECTRICITY. 


607 


668 


the  conjunctive  wire  into  a  helix,  as  in  fig.  666,  and  carrying  the  wire 
back  again  through  the  axis  of  this  666 

spiral,  CB,  the  effects  of  the  current  — »• 
from  A  to  B,  will  be  neutralized  by 
its  return  from  B  to  C,  and  there  will 
remain  only  the  effect  due  to  its  spiral  revolution  about  C  B.  Ampere 
called  this  form  of  the  wire  a  solenoid.  The  effect  of  the  helix  thus 
wound,  is  reduced  solely  to  the  influence  of  a  series  of  equal  and 
parallel  circular  currents.  By  winding  the  silk-covered  wire  in  the 
manner  shown  in  fig.  667,  the  two  ends  of  the  coil  are  returned  to  the 
centre  of  gravity,  and  being  pointed  667 

with  steel,  the  whole  system  can  be 
conveniently  suspended,  as  in  fig.  668, 
upon  what  is  called  an  Ampere's 
frame,  in  which  the  arrows  show  the 
course  of  the  current  from  the  battery  B 
to  the  helix  or  solenoid  thus  suspended. 
When  the  current  is  established,  the  axis  of  the  solenoid,  A  B,  swings 
into  the  magnetic  meridian,  while  its  several  spires  are  in  the  plane  of 
the  magnetic  equator.  This  position 
it  assumes  in  obedience  to  the  soli- 
citation of  terrestrial  magnetism ; 
consequently  it  simulates  in  all  re- 
spects the  character  of  a  magnetic 
needle,  although  possessing  not  a 
particle  of  iron  or  steel  in  its  struc- 
ture. If  a  second  helix,  b,  through 
which  also  a  current  passes,  is  now  ^g^Lj_?g 
presented  to  the  first,  as  in  fig.  668,  all  the  phenomena  of  attraction 
and  repulsion  will  be  seen,  the  action  of  the  two  helices  or  solenoids 
being  to  each  other  exactly  like  those  of  two  669 

magnets. 

De  La  Rive's  floating  current,  already  ex- 
plained in  |  909,  is  also  well  adapted  to  illustrate 
the  attractive  and  repulsive  influence  of  a  magnet 
on  a  free  conjunctive  wire,  as  well  also  as  its  obe- 
dience to  the  solicitations  of  terrestrial  magnet- 
ism. For  this  purpose  the  conjunctive  wire  is 
wound,  as  in  fig.  669,  into  a  helix.  Left  to  itself, 
this  apparatus  will  act  just  as  the  solenoid  on  the  frame,  fig.  668,  and 
will  obey  the  impulses  of  a  magnetic  bar,  or  of  another  solenoid. 


608  PHYSICS    OF    IMPONDERABLE    AGENTS. 

911.  Directive  action  of  the  earth. — These  effects  are  expressed 
in  the  following  law : — 

Terrestrial  magnetism  acts  upon  electric  currents  just  as  if  the  entire 
globe  was  encircled  with  electric  currents  from  E.  to  W.  in  lines  parallel 
to  the  magnetic  equator. 

The  direction  in  which  these  currents  are  supposed  to  move  is  the 
same  with  the  apparent  motion  of  the  sun,  and  the  one  in  which  the 
earth's  surface  receives  its  advancing  rays  ;  and  since  it  is  now  known 
that  electrical  currents  generated  by  heat  exert  precisely  the  same 
influence  on  the  magnetic  needle  as  Voltaic  currents  do,  therefore  it 
has  been  inferred  that  the  thermal  action  of  the  sun  is  the  generating 
and  maintaining  cause  of  the  currents  of  terrestrial  magnetism  (801). 

912.  Magnetizing  by  the  helix.— We  have  already  (805)  described 
a  mode  of  producing  magnets  from  an  electrical  current.     The  expla- 
nation of  this,  after  all  that  has  been  said,  is  easy.     As  each  volute  of 
the  helix,  carrying  an  electric  current,  is  itself  an  active  magnet,  it  is 
easy  to  conceive  that  under  the  united  influence  of  a  great  number  of 
such  circular  and  parallel  currents,  the  coercitive  force  of  a  steel  bar, 
or  bar  of  soft  iron,  should  be  decomposed,  and  active  magnetism  be 
thus  induced,  permanent  or  transient,  according  as  steel  or  iron  is  the 
subject  of  experiment.    Even  a  series  of  sparks  from  an  excited  elec- 
trical machine,  passed  through  a  helix,  will  magnetize  a  steel  needle. 

The  position  of  the  poles  in  a  bar  so  situated  will  depend  on  the  right-handed 
or  left-handed  twist  of  the  spire.  If  the  current  flows  from  -f-  to  — ,  and  the 
wire,  as  in  fig.  670,  turns  from  670 

left  to  right  (like  the  hands  of 
a  watch),  then  the  north  pole 
of  the  magnet  is  toward  the 
left ;  but  if  the  spire  turns,  as 
in  fig.  671,  from  right  to  left, 
or  opposite  to  the  hands  of  _,.  <-n- 
a  watch,  then  the  poles  are  A  U  \ 

reversed.     The  following  sim-          "    — -    •^s^>s^^s~ 
pie  formula,  by  Faraday,  will 

always  enable  the  student  to  "'•*• 

obtain  definite  notions  of  the  polarity  of  the  helix  : — "  Let  a  person,"  observes 
Faraday,  "  imagine  that  he  is  looking  down  upon  the  dipping  needle,  or  north 
magnetic  pole  of  the  earth,  and  then  let  him  think  upon  the  direction  of  the 
motion  of  the  hand  of  a  watch,  or  of  a  screw  moving  direct;  currents  in  that 
direction  would  create  such  a  magnet  as  the  dipping-needle." 

If  the  helix  is  wound  on  a  tube  of  glass,  paper,  or  wood,  these  substances 
offer  no  resistance  to  the  passage  of  the  power ;  but  if  a  tube  of  copper  or  other 
metal  were  employed,  the  magnetizing  power  of  the  current  on  the  enclosed  bar 
would  be  destroyed. 

If  the  same  helix  is  wound  in  two  opposite  directions,  as  in  fig.  672,  then,  accord- 
ing to  the  direction  of  the  current,  there  will  be  a  pair  of  north  poles  at  the 


ELECTRICITY.  609 

point  of  reversal  in  the  centre  (or  a  pair  of  south  ones),  and  the  two  ends  will 
have  the  same  name.  A  bar  of  steel  placed  in  such  a  helix 
will  remain  permanently  an  anomalous  magnet  (779).  Re- 
versing the  position  of  the  bar  in  the  helix,  or  reversing  the 
position  of  the  electrodes  in  the  binding  cups,  will  reverse 
its  polarity. 

Arago's  original  experiment. — If  a  short  conjunc- 
tive wire  of  copper,  or  any  non-conducting  metal,  is  strewn 
with  iron  filings,  they  will  arrange  themselves  as  seen  in 
fig.  673,  not  bristling  as  in  the  magnetic  phantom,  with 
opposite  polarities  (777),  but  in  close  concentric  rings,  disposed  over  the  whole 
length  of  the  conductor.  This  fact  was  observed  573 

by  Arago,  in  1824,  and  by  others,  before  the 
application  of  the  helix  to  the  induction  of 
magnetism  in  soft  iron. 

When  the  helix  is  closely  wound  with  many 
turns  of  insulated  wire,  and  excited  by  a  bat- 
tery of  considerable  quantity,  a  cylinder  of 
soft  iron,  as  a  b,  in  fig.  674,  will  be  drawn  into 
it  from  the  position  seen  in  the  figure,  with  great  power,  and,  after  several 
oscillations,  will  come  to  rest  in  the  middle  of  its  length,  in  „» . 

opposition  to  gravity,  realizing  the  fable  of  Mahomet's  coffin, 
suspended  in  mid  air  without  visible  support.  This  axial 
movement  is  availed  of  in  the  electro-magnetic  engine. 

913.  Electro-magnets. — Electro-magnets  are  masses 
of  soft  iron  wound  with  coils  of  closely  packed  and  insu- 
lated copper  wire,  varying  in  size  and  length,  according 
to  the  use  to  be  made  of  them.  Fig.  675  shows  the 
usual  form  of  those  designed  to  sustain  great  weights. 
The  spools,  A  and  B,  are  virtually  continuations  of  one  spool,  the  direc- 
tion of  the  whorl  being  apparently  reversed  by  the  bend  of  the  horse- 
shoe. If  a  lever  of  the  third  order  (113)  is  used  as  a  steelyard,  the 
lumber  of  heavy  weights  is  avoided  in  the  use  of  these  instruments, 
and  the  power  of  the  apparatus  is  easily  tested. 

Electro-magnets  develop  their  surprising  power  only  when  the  arma- 
ture is  in  contact  with  the  poles,  a  fact  due  to  induction  ;  without  their 
armatures,  they  sustain  not  a  tenth  part  of  their  maximum  load.  They 
are  capable  of  over-saturation  by  an  excess  of  battery  power,  and  after 
that  has  been  cut  off,  they  retain  a  remarkable  residual  force  so  long 
as  the  keeper  is  in  place,  but  as  soon  as  the  armature  is  detached,  the 
whole  of  this  residual  magnetism  is  lost.  Their  polarity  is  instanta- 
neously reversed  by  reversing  the  poles  of  the  battery.  This  complete 
and  immediate  paralysis  and  reversal  of  power,  renders  these  magnets 
of  inestimable  value  in  experimental  researches. 

Sturgeon,  of  England,  in  1825,  appears  to  have  been  the  first  to  produce  soft 
54 


610  PHYSICS   OP   IMPONDERABLE    AGENTS. 

iron  electro-magnets.  Prof.  Henry,  and  Dr.  Ten  Eyck,  in  1830,  produced  the 
first  electro-magnets  of  great  power,  by  a  new  mode  of  winding  the  inducing 
coil.  (Am.  Jour.  Sci.  [1]  XIX.  400.) 

Prof.  Henry,  on  a  soft  iron  bar  of  fifty-nine  Ibs.  weight^  used  twenty-six  coils 
of  wire,  thirteen  on  each  leg,  all  575 

joined  to  a  common  conductor  by 
their  opposite  ends,  and  having 
an  aggregate  length  of  seven  hun- 
dred and  twenty-eight  feet.  This 
apparatus,  with  a  battery  of  four 
and  seven-ninths  feet  of  surface, 
sustained  two  thousand  and  sixty- 
three  pounds  avoirdupois  :  with  a 
little  larger  battery  surface  it  sus- 
tained twenty-five  hundred  Ibs. 
This  electro-magnet  was  con- 
structed for  Yale  College  Labora- 
tory, in  1831,  and  is  still  among 
their  instruments. 


Mr.  J.  P.  Joule  (Annals  of 
Electricity,  V.  187),  in  1840, 
constructed  soft  iron  electro- 
magnets of  peculiar  form,  be- 
ing in  fact  tubes  with  very 
*hick  walls  cut  away  on  one 
tide  lengthwise,  and  wound  in 
\he  direction  of  the  length ; 
one  of  which,  weighing  15  Ibs., 
lield  2090  Ibs.,  equal  to  nearly 
140  times  its  own  weight.  It 
was  wound  with  4  covered  cop- 
per wires,  -fa  inch  diameter,  and  each  23  feet  long  only,  the  length  of  the 
soft  iron  being  8  inches,  and  its  outer  diameter  three  inches.  Another 
magnet  weighing  1057  grains  supported  twelve  pounds,  or  1286  times 
its  own  weight ;  and  a  very  minute  one,  which  weighed  only  63'3  grains, 
carried  on  one  occasion  1417  grains,  or  2834  times  its  own  weight.  The 
last  is  more  than  eleven  times  the  proportionate  load  of  the  celebrated 
magnet  of  Sir  Isaac  Newton,  g  806. 

914.  Page's  revolving  electro-magnet,  fig.  676,  affords  satisfactory 
evidence  of  the  great  rapidity  with  which  a  mass  of  soft  iron  may  receive  and 
part  with  magnetism,  having  its  polarity  reversed  also  by  a  change  of  position. 
In  this  instrument,  a  permanent  U-magnet  has  a  vertical  spindle  in  its  axis,  on 
the  upper  end  of  which  is  placed  a  mass  of  soft  iron,  destined  to  receive  induced 
magnetism  through  the  covered  wire  with  which  it  is  wound,  and  whose  ends  are 
represented  by  the  two  s?rew  cups,  one  on  each  side.  By  a  simple  contrivance, 


ELECTRICITY.  611 

called  an  interrupter,  or  break-piece  (formed  by  sawing  a  silver  ferrule  on  tha 
axis  into  two  parts  by  vertical  slits),  the  continuity  fl^., 

of  the  current  is  interrupted  twice  in  every  revolu- 
tion, when  the  position  of  the  armature  is  as  seen 
in  the  figure.  The  effect  of  this  arrangement  is  to 
paralyze  the  magnetic  force  at  the  right  instant  to 
permit  the  momentum  of  the  mass  to  carry  the 
armature  by  the  poles  of  the  fixed  magnet,  when 
the  battery  connection  is  again  completed,  new 
magnetism  induced,  and  the  motion  continued  as 
before.  Such  a  little  magnetic  engine  may  revolve 
with  a  velocity  of  2000  times  a  minute,  equal  to 
4000  reversals  of  polarity,- — each  reversal  being 
accompanied  by  a  passive  interval,  when  the  soft 
iron  is  no  magnet. 

915.    Power    of   electro-magnets. — The 

power  of  electro-magnets  depends,  1st,  on  the 
intensity  of  the  current;  2d,  on  the  number 
of  whorls  in  the  helix ;  3d,  on  the  kind  and 
shape  of  the  iron  bar ;  4th,  on  the  form  and  size  of  the  keeper  or  arma- 
ture. These  points  have  been  studied  by  Lenz  and  Jacobi,  and  many 
others,  of  whom  the  results  of  Dub  are  the  most  recent.  Dub  distin- 
guishes between  magnetism,  attraction,  and  sustaining  power,  in  electro- 
magnets, confining  the  term  magnetism  to  the  magnetic  excitation  due 
to  the  Voltaic  current.  Lenz  and  Jacobi  measured  this  by  means  of  the 
induced  current  excited  by  the  vanishing  of  the  magnetism  to  which  it 
is  proportional.  When  a  second  bar  of  soft  iron  is  caused  to  approach 
the  first,  this  also  becomes  magnetic  (by  induction),  and  by  n-fold  mag- 
netism, n2  times  the  attraction  is  produced ;  until  actual  contact  hap- 
pens, when  this  ratio  is  no  longer  maintained. 

Dub  gives  the  following  summary  of  his  results : — 

1.  The  attraction  of  U-shaped  electro-magnets,  with  an  equal  number 
of  windings,  is  proportional  to  the  squares  of  the  magnetizing  current 
force. 

2.  The  attraction  of  U  magnets  is,  with  equal  currents,  proportional 
to  the  square  of  the  number  of  windings  of  the  magnetizing  spirals. 

3.  The  attraction  of  U  magnets  is  proportional  to  the  square  of  the 
current  force  multiplied  by  the  square  of  the  number  of  windings. 
[This  is  true  alike  for  attraction  and  sustaining  force,  both  in  straight 
and  in  U  magnets.] 

4.  The  magnetism  of  massive  cylinders  of  iron  of  equal  length, 
magnetized  by  Voltaic  currents  of  equal  force,  and  by  spirals  of  an 
equal  number  of  windings,  closely  surrounding  the  core,  is  accurately 
proportional  to  the  square  roots  of  the  diameters  of  these  cylinders. 

5.  For  the  particular  case  in  which  the  surface  of  contact  does  not 


612  PHYSICS    OF    IMPONDERABLE    AGENTS. 

disturb  the  result,  the  attraction  and  sustaining  force  are,  with  equal 
magnetizing  forces,  proportional  to  the  diameters  of  the  bar  or  U- 
magnets. 

6.  The  attraction  of  bar  and  U-shaped  electro-magnets  with  equal 
magnetizing  forces,  increases  the  nearer  the  whole  of  the  windings  are 
to  the  poles. 

7.  The  attraction,  like  the  sustaining  force  of  U  electro-magnets — 
other  things  being  equal — remains  the  same,  whatever  be  the  distance 
of  the  branches  of  the  magnet. 

8.  The  length  of  the  branches  of  a  U-shaped  electro-magnet  has  no 
influence  on  its  attractive  or  sustaining  force,  if  the  windings  of  the 
spiral  surround  its  whole  length. 

In  addition  to  these  laws,  the  author  has  found  that  the  attraction 
which  a  helix  or  spiral  exerts  upon  a  soft  iron  bar  placed  in  its  axis, 
follows  the  same  law  as  an  electro-magnet;  hence  it  follows,  that: — 

9.  The  attraction  of  a  spiral  is  proportional  to  the  square  of  the  mag- 
netizing current,  multiplied  by  the  square  of  the  number  of  windings.* 

The  sustaining  power  of  an  electro-magnet  increases  with  the  mass 
of  the  armature  up  to  a  certain  point,  not  exceeding  the  mass  of  the 
electro-magnet  itself;  and,  moreover,  Liais  has  shown  that  an  arma- 
ture whose  face  of  contact  is  not  over  one-third  the  breadth  of  the 
poles  to  which  it  is  applied,  gives  a  maximum  effect. 

For  some  curious  results  with  circular  and  trifurcate  electro-magnets, 
and  the  applications  of  this  force  to  "  break  up"  railway  trains,  con- 
sult the  papers  of  Prof.  Nickles  (Am.  Jour.  Sci.  [2],  XV.,  104  and  380 ; 
and  XVI.,  110  and  337). 

916.  Vibrations  and  musical  tones  from  induced  magnetism. — 

Dr.  Page,  in  1837,  noticed  the  production  of  a  musical  sound  from  a  magnet, 
between  the  poles  of  which  a  flat  spiral  was  placed.  The  sound  was  heard 
whenever  contact  was  made  or  broken  between  the  coil  and  the  battery.  Two 
notes  were  distinguished,  one  the  proper  musical  tone  of  the  magnet,  and  the 
other  an  octave  higher.  De  la  Rive,  Delezenne,  and  others,  have  confirmed 
and  extended  these  curious  observations.  The  existence  of  molecular  disturb- 
ance in  receiving  and  parting  with  magnetic  induction,  has  been  farther  illus- 
trated by  the  same  ingenious  observer,  by  the  vibrations  imparted  to  Trevellyan's 
bars  by  the  current  from  two  or  three  cells  of  Grove's  battery.  (Am.  Jour.  Sci. 
[2],  IX.,  105.)  Trevellyan's  bars  are  prismatic  bars  of  brass,  hollow  on  one 
side,  so  as  to  rest  by  sharp  edges  on  blocks  of  lead.  When  these  are  gently 
warmed,  and  then  laid  upon  the  leaden  blocks,  the  unequal  expansion  and  con- 
traction of  the  two  metals  gives  the  brass  bars  a  slight  motion  of  vibration, 
due  to  molecular  disturbance  by  heat.  A  Voltaic  current,  according  to  Dr. 
Page's  observation,  produces  the  same  effect  as  heat,  but  more  remarkably. 

917.  Electro-magnetic  motions  and  mechanical  power. — The 

*  Am.  Jour.  Sci.  [2],  XVII.,  424. 


ELECTRCJITY. 


613 


facility  with  which  masses  of  soft  iron  may  be  endued  with  enormous- 
magnetic  power  by  currents  of  Voltaic  electricity,  and  again  discharged, 
or  reversed,  in  polarity,  has  led  to  numberless  contrivances  to  use  this 
power  as  a  mechanical  agent.  A  great  variety  of  pleasing  and  instruc- 
tive models  of  such  machines,  with  the  use  both  of  permanent  magnets 
and  of  electro-magnetic  armatures,  or  of  electro-magnets  only,  are 
described  in  Davis' s  Manual  of  Magnetism.  The  revolving  armature, 
fig.  676,  is  one  of  these. 

We  annex  a  figure  of  an  electro-magnetic  engine,  similar  to  one  by 
which  Dr.  Page  obtained  a  useful  effect  of  ten  horse-power,  in  driving 
machinery,  and  transporting  a  railway  train.  A  and  B,  fig.  677,  are 

677 


two  very  powerful  helices  of  insulated  copper  wire,  within  which  are 
two  heavy  cylinders  of  soft  iron,  CD,  counter-balanced  on  the  ends  of 
a  beam,  G  F  I,  like  the  working  beam  of  a  steam-engine.  By  the  move- 
ment of  an  eccentric,  L,  on  the  main  shaft  of  the  fly-wheel,  the  poles 
are  changed,  at  the  moment,  to  magnetize  and  de-magnetize,  alter- 
nately, the  two  helices,  drawing  into  them  the  two  soft  iron  cylinders, 
by  a  force  of  many  hundred  pounds.  Prof.  W.  R.  Johnson  tested  the 
force  of  an  engine  of  this  kind  built  by  Dr.  Page,  in  1850,  and  found 
it  to  give  about  six  and  a  half  horse-power.  (Am.  Jour.  Sci.  [2],  X., 
472.) 

M.  Jacobi,  of  St.  Petersburgh,  has  studied  this  subject  very  carefully,  and 
has  contrived  an  effective  form  of  rotating  machine,  very  similar  to  that  of 
Cook  and  Davenport,  so  well  known  in  the  United  States  in  1837.  Froment, 
of  Paris,  has  also  constructed  a  powerful  apparatus  of  this  sort,  in  which  arma- 
tures of  soft  iron  on  the  periphery  of  a  wheel  are  drawn  towards  electro-magnets 
placed  radially. 

In  all  these  machines,  it  is  heat  developed  by  chemical  action  that  is  trans- 
formed, in  the  form  of  magnetic  attraction,  into  mechanical  work  (761).  As 
the  result  of  a  great  many  experiments,  Mr.  Joule  has  shown  that  the  best  theo- 
retical result  fro'rn  the  heat,  equivalent  to  the  solution  of  a  grain  of  zinc  in  a 
64* 


614 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


battery,  is  eighty  Ibs.  raised  one  foot  high.  But  a  grain  of  coal  burned  in  a 
Cornish  boiler,  raises  one  hundred  and  forty-three  Ibs.  one  foot,  and  the  price  of 
the  coal  is  to  that  of  the  zinc  as  9d.  per  cwt.  to  216ti.  per  cwt.  Therefore,  under 
the  best  conditions  (which  are  never  reached  in  practice),  the  magnetic  force  is 
25  times  dearer  than  that  of  steam.  Until,  therefore,  zinc  is  cheaper  than  coal, 
in  the  proportion  of  80  to  143,  coal  will  probably  be  burned  in  atmospheric  air, 
preferably  to  the  combustion  of  zinc  in  sulphuric  acid,  to  produce  mechanical 
work. 

918.  Conversion  of  magnetism  into  heat. — Foucault  has  shown  that 
the  magnetism  induced  in  a  disc  of  copper  revolving  between  the  poles  of  an  elec- 
tro-magnet, is  con  verted  into  heat.  678 

For  this  purpose,  a  powerful  elec- 
tro-magnet is  supported  upon  a 
basement,  fig.  678 ;  two  pieces  of 
soft  iron  are  attached  to  the  poles 
of  the  magnet,  so  that  they  con- 
centrate, upon  the  two  faces  of  a 
metallic  disc,  their  magnetism  of 
induction.  This  disc  of  copper 
receives,  by  means  of  pulleys,  a 
rapid  revolution,  which  will  con- 
tinue for  a  long  time,  if  no  cur- 
rent exists  in  the  electro-magnet ; 
but  if  a  current  from  a  battery 
of  two  or  three  cells  is  passed 
through  the  wire,  the  disc  is 
almost  immediately  stopped  ;  if,  however,  against  this  resistance  the  disc  is  forced 
to  revolve,  the  expense  of  force  is  converted  into  heat,  and  the  temperature  of 
the  disc  is  rapidly  raised. 

II.     DIAMAGNETISM. 

919.  Action  of  magnetism  on  light. — Fig.  679  shows  the  appa- 

679 

M 


ratus  designed  by  Ruhmkorff,  in  illustration  of  Faraday's  magnetic 


ELECTRICITY. 


615 


rotatory  polarization  of  light  already  spoken  of  under  Optics  (560). 
Two  powerful  inducing  coils,  N  and  M,  surround  two  hollow  cylinders 
of  soft  iron,  S  and  Q.  The  current  enters  the  bobbins  by  A,  and  fol- 
lowing the  direction  of  the  arrows,  returns  by  B.  The  two  coils  slide 
in  the  groove  in  the  base,  K,  on  the  two  supports,  00,  so  that  they 
may  be  approached  or  withdrawn  at  pleasure  by  turning  the  screws, 
m  m.  A  commutator,  or  interrupter  of  the  current,  is  arranged  at  H  n, 
At  a  and  b  are  two  Nicol's  prisms  (553),  of  which  a  has  a  vernier  or 
index,  reading  the  degrees  on  the  graduated  circle,  P.  To  make  the 
experiment,  a  piece  of  heavy  glass,  or  silicious-borate  of  lead,  c,  is 
placed  on  a  support  between  the  poles  S  and  Q.  A  ray  of  light  from 
the  candle,  polarized  by  the  prism,  b,  is  transmitted  through  the  glass 
in  the  axis  of  the  poles.  When  the  current  is  applied,  the  ray  of  light 
appears  to  be  revolved,  similarly  to  the  effect  produced  on  polarized  light 
by  quartz,  or  oil  of  turpentine  (556).  A  great  number  of  other  solids  and 
liquids  are  found  to  act  in  a  like  manner,  but  to  a  less  degree,  than  in 
the  case  of  "  heavy  glass."  As  no  rotation  of  the  ray  takes  place  unless 
there  is  some  medium  on  which  the  magnetism  may  act,  it  has  been 
argued  with  some  force  by  Becquerel  and  others,  that  the  action  is 
wholly  due  to  a  molecular  change  in  the  solid  under  experiment.  A 
reversal,  however,  of  the  direction  in  which  the  ray  travels,  reverses 
the  direction  of  rotation  in  the  polarized  ray,  a  circumstance  not  found 
in  bodies  in  the  natural  state.  This  apparatus  also  serves  to  illustrate 
the  phenomena  of  diamagnetism. 

920.  Diamagnetism. — We  have  already  (799)  alluded  to  the  action 
of  magnetism  upon  all  bodies,  discovered  by  Dr.  Faraday,  in  1846,  a 
discovery  which  alone  would  place  its  author  in  the  highest  rank  of 
modern  philosophers.  By  the  use  of  the  apparatus,  fig.  680,  he  proved 
that  every  substance  which  he  tried,  solid,  680 

fluid,  or  gaseous,  was  sub- 
ject to  magnetic  influence, 
assuming  either  the  equa- 
torial or  axial  position, 
according  to  its  nature. 

For  solids,  and  some  flu- 
ids, fig.  681  shows  the  ar- 
rangement. Two  bluntly 
rounded  polar  pieces  of  soft 
iron  are  fitted  into  the  open- 
ings of  the  spools,  S  and  Q,  while  between  them  are  suspended  on  a  silk  fibre 
cubes,  TH,  or  short  bars  of  the  various  magnetic  metals,  bismuth,  antimony,  cop- 
per, lead,  tin,  &c.  If  the  cube  is  spinning  about  when  the  current  passes,  the 
induced  magnetism  arrests  its  motion  in  whatever  position  it  may  be ;  and  if 


616  PHYSICS    OF    IMPONDERABLE   AGENTS. 

the  metal  has  the  form  of  a  little  bar,  it  rests  athwart  the  axis  like  a  cross.  If 
non-magnetic  liquids,  alcohol,  water,  and  most  saline  solutions,  are  confined  in 
little  narrow  bottles  (like  homoeopathic  vials),  hung  like  m,  fig.  681,  these  are 
similarly  affected.  If  they  are  filled,  however,  with  magnetic  solutions,  the  salts 
of  iron,  nickel,  or  cobalt,  they  then  arrange  themselves  axially. 

Plticker  has  shown  that  if  these  magnetic  solutions  are  placed  in  watch- 
glasses  upon  the  poles,  S  Q,  as  in  fig.  680,  according  as  the  poles  are  nearer  or 
farther  asunder,  these  liquids  are  heaped  up  in  one  or  two  elevations,  as  iu  A 
and  B. 

The  flame  of  a  candle  placed  between  the  poles,  S  Q,  fig.  682,  is  strongly  re- 
pelled, a  fact  first  observed  by  Father  Bancalari,  of  Genoa,  532 
and  the  flames  of  combustible  gas  from  various  sources 
are  differently  affected,  both  by  the  nature  of  the  com- 
bustible and  by  the  nearness  of  the  poles.  The  flame 
from  turpentine  is  most  curiously  affected,  being  thrown 
into  the  form  of  a  parabola,  whose  two  arms  stretch  upward 
a  great  distance,  and  are  each  crowned  by  a  spiral  of 
smoke.  Oxygen,  which,  in  the  air,  is  powerfully  magnetic 
(799),  becomes,  when  heated,  diamagnetic.  A  coil  of  pla- 
tinum wire,  heated  by  a  current  of  Voltaic  electricity,  and 
placed  beneath  the  poles  of  Faraday's  apparatus,  occasions  a  powerful  up- 
ward current  of  air,  but,  when  magnetism  is  induced,  the  ascending  current 
divides,  and  a  descending  current  flows  down  between  the  upward  currents. 
The  following  list  expresses  the  order  of  some  of  the  most  common  paramag- 
netic substances,  viz.  :  iron,  nickel,  cobalt,  manganese,  palladium,  crown-glass, 
platinum,  osmium.  The  zero  is  vacuum.  The  diamagnetics  are  arranged  in  the 
inverse  order,  commencing  with  the  most  neutral :  arsenic,  ether,  alcohol,  gold, 
water,  mercury,  flint-glass,  tin,  "  heavy  glass,"  antimony,  phosphorus,  bismuth. 

Pliicker  has  further  demonstrated  the  important  fact,  that  the  optic  axis  of 
Iceland  spar  is  repelled  by  the  magnet — a  fact  probably  true  of  many  crystals — 
in  some  of  which  the  magnetic  axis  is  parallel  to  the  longer  axis  of  crystalliza- 
tion. Thus,  a  piece  of  kyanite  will,  under  the  influence  even  of  the  earth's 
magnetism,  arrange  itself  like  a  magnetic  needle. 

III.     ELECTRIC  TELEGRAPH. 

921.  Historical. — The  thought  of  making  telegraphic  communica- 
tions by  electricity  appears  to  have  suggested  itself  as  soon  as  it  was 
known  that  an  electrical  current  passed  over  a  conducting  wire  with- 
out sensible  loss  of  time.  The  following  brief  summary  of  well-known 
historical  facts,  will  serve  at  once  to  show  how  impossible  it  is  justly  to 
bestow  the  exclusive  merit  of  the  electric  telegraph  upon  any  inventor, 
while  at  the  same  time  it  strikingly  illustrates  what  is  true  of  every 
important  invention,  that  final  success  rescues  from  oblivion  ma'ny 
schemes  that  had  hardly  vitality  enough  in  their  day  to  find  a  place 
in  the  records  of  history. 

In  1747,  Dr.  J.  WATSON  erected  a  telegraph  from  the  rooms  of  the  Royal 
Society,  in  London,  for  two  miles  or  more,  over  the  chimney  tops,  using  fric- 
tional  electricity  on  a  single  wire,  with  the  earth  for  a  return  circuit.  In  1748, 
Dr.  FRANKLIN  set  fire  to  spirits  of  wine  by  a  current  of  electricity  sent  across 


ELECTRICITY.  617      X 

the  Schuylkill  on  a  wire,  and  returning  by  the  river  and  the  earth.  In  1774, 
LE  SAGE,  a  Frenchman,  established  at  Geneva  an  electric  telegraph,  in  which 
he  used  twenty-four  wires  insulated  in  glass  tubes  buried  in  the  earth,  each 
wire  communicating  with  an  electroscope,  and  corresponding  to  a  letter  of  the 
alphabet,  and  excited  by  an  electrical  machine.  (MoGNio  Traite,  59.)  In  1787, 
BETANCOURT,  in  Spain,  made  an  effort  to  employ  electricity  for  telegraphing  by 
passing  signals  from  a  Leyden  vial  over  wires  connecting  Madrid  with  Aran- 
juez,  a  distance  of  twenty-six  miles.  SALVA,  in  1796,  also  presented  to  the 
Academy  of  Madrid,  a  plan  of  an  electric  telegraph  of  his  own  invention,  which 
received  the  patronage  of  the  Prince  of  Peace.  In  1800,  the  public  announce- 
ment of  VOLTA'S  discovery  of  the  pile  supplied  a  new  means  for  telegraphing, 
far  more  certain  than  frictional  electricity,  and  accordingly  we  find,  that  in 
1811,  Prof.  SOEMMERING,  of  Munich,  proposed  to  the  Academy  in  that  city  a 
complete  plan,  with  details,  for  an  electro-chemical  telegraph,  in  which  he  used 
thirty-five  wires  (twenty-five  for  the  German  alphabet,  and  ten  for  the  numerals), 
tipped  with  gold  and  covered  by  the  same  number  of  glass  tubes  filled  with  water, 
to  be  decomposed  whenever  the  corresponding  letter  or  numeral  was  touched  by 
the  battery  wire  on  a  key-board  at  the  other  end.  This  is  the  type  of  all  electro- 
chemical telegraphs.  Dr.  J.  REDMAN  COXE,  of  Philadelphia,  in  1816,  in  Thomp- 
son's Annals  of  Philosophy,  apparently  without  knowledge  of  Soemmering's  plan, 
proposes  a  similar  one  by  the  use  of  Voltaic  electricity.  In  1819-20,  OERSTED'S 
discovery  of  electro-magnetism,  and  AMPERE'S  development  of  the  subject,  opened 
the  way  to  electro-magnetic  telegraphy.  (Ersted  first,  and  then  Ampere,  proposed 
the  plan  of  a  telegraph,  using  the  deflections  of  a  magnetic  needle  for  signals  ;  the 
type  of  Wheatstone's  needle  telegraph  ;  but  their  suggestions  were  never  put  in 
practice.  In  1823,  Dr.  F.  RONALDS,  of  England,  published  a  volume  detailing 
the  plan  upon  which  he  had  previously  constructed  eight  miles  of  electric  tele- 
graph, and  in  which  he  used  a  movable  disc,  carrying  the  letters,  the  type  of  all 
dial  telegraphs.  In  1825,  WILLIAM  STURGEON,  of  Woolwich,  England,  made  the 
first  electro-magnet  of  soft  iron,  without  which,  further  progress  in  the  electro- 
magnetic telegraph  was  impossible.  Prof.  JOSEPH  HENRY,  in  1830,  described  a 
mode  of  giving  greater  power  to  electro-magnets,  and  the  same  philosopher,  in 
1831,  devised  the  first  reciprocating  electro-magnet  and  vibrating  armature, 
including  also  the  principle  of  the  relay  magnet,  so  indispensable  an  auxiliary  in 
the  Morse  system.  (Am.  Jour.  Sci.  [1]  XX.  840.)  In  1834,  Messrs.  WEBBER 
and  GAUSS  established  an  electro-magnetic  telegraph  at  Gb'ttingen,  between  the 
Observatory  and  the  Physical  Cabinet  of  the  University,  and  used  it  for  all  the 
purposes  of  scientific  communication. 

In  1836,  Prof.  J.  F.  DANIELL  invented  the  constant  battery  (874),  without 
whicn  any  mode  of  electric  telegraph  would  have  been  futile. 

In  1837 — a  year  ever  memorable  in  telegraphic  history  for  the  first  general  and 
successful  introduction  of  the  electro-magnetic  telegraph — and  almost  at  the  same 
time  appeared  MORSE,  in  the  U.  S.  j  STEINHEIL,  at  Munich;  and  A^HEATSTONE 
and  COOKE,  in  England;  as  distinct  and  independent  claimants  for  the  honor  of 
this  discovery.  Prof.  J.  D.  Forbes,  the  able  historian  of  the  Physical  Sciences, 
in  the  eighth  edition  of  the  Encyclopedia  Brit.  America,  speaking  of  these 
inventions,  says:  "the  telegrajh  of  the  two  last  (Steinheil  and  Wheatstone) 
resembles  in  principle  (Ersted's  and  Gauss's  :  that  of  the  first  (MoRSE)  is  entirely 
original,  and  consists  in  making  a  ribbon  of  paper  move  by  clock-work,  whilst 
interrupted  marks  are  impressed  upon  it  by  a  pen,"  <fcc.  *  *  "  The  telegraphs 
of  Morse  have  the  inestimable  advantage,  that  they  preserve  a  permanent  record 


618 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


of  the  despatches  which  they  convey."     This  advantage,  it  is  but  just  to  say, 
they  share  with  Bain's  electro-chemical  telegraph. 

922.  The  earth  circuit.— Although  Drs.  Watson  and  Franklin 
(1747-8)  used  the  earth  as  the  return  circuit  in  their  telegraphic  experi- 
ments, it  was  considered  essential  in  the  use  of  Voltaic  electricity  to  em- 
ploy at  least  two  wires,  until  Steinheil,  in  1837,  in  the  construction  of  his 
telegraph  at  Munich,  dispensed  with  the  whole  resistance  of  the  return 
wire  by  burying  a  large  plate  of  copper  at  each  station,  with  which  the 
circuit  wire  communicated.  This  certainly  must  be  esteemed  one  of  the 
most  important  discoveries  in  connection  with  the  telegraph ;  but  from 
some  cause  or  other  it  obtained  for  some  years  but  little  publicity, 
although  described  at  length  in  the  Comptes-Rendus,  of  Sept.  10,  1838. 
Bain  re-discovered  the  same  fact  some  years  later,  and  Matteucci,  of 
Pisa,  in  1843,  made  experiments  which  convinced  the  most  incredulous 
of  the  truth  of  this  important  fact. 

Fig.  683  illustrates  the  mode  of  using  the  earth  circuit,  now  universal  in  all 
telegraphs.  S  and  S'  are  two  distant  stations,  with  their  batteries,  b  b',  and  mag- 
nets mm'.  A  wire  passing  over  insulating  posts,  through  the  air,  connects  S  and 
S'.  One  pole  of  each  battery  is  connected  with  the  earth  through  the  magnets, 

683 


ending  in  plates  of  copper,  P  P'.  Neither  battery  will,  however,  act,  unless  one 
of  the  breaks,  or  finger-keys,  S  or  S',  is  depressed.  If  the  finger-key,  S,  is 
depressed,  the  circuit  consequently  is  completed  through  the  earth,  for  the  bat- 
tery, 6,  while  that  of  b'  remains  open.  The  arrows  show  the  course  of  the 
current,  and  this  will  be  reversed  when  the  circuit  at  S  is  closed.  The  explana- 
tion of  this  curious  fact  appears  to  be,  not  that  the  electricity  is  conducted  back 
by  the  earth  to  its  origin  at  the  battery,  but  that  the  molecular  disturbance  in 
which  the  polarity  of  the  circuit  consists,  is  effectually  relieved  by  communica- 
tion with  the  common  reservoir  of  neutral  electricity  (815),  and  so  conduction 
proceeds  without  interruption.  Any  number  of  parallel  currents  may  thus  co- 
exist without  interference.  This  simple  device  saves  not  only  half  the  expense 


ELECTRICITY.  619 

of  constructing  lines,  but  it  more  than  doubles  their  power  of  electrical  trans- 
mission.    For  the  rapidity  of  the  current,  refer  to  g  818. 

923.  Varieties  of  electro-telegraphic  communication. — There 
are  essentially  but  two  modes  of  electro-telegraphic  communication, 
viz. :  the  electro- mechanical  and  the  electro-chemical.   Various  and  seem- 
ingly unlike  as  are  the  numerous  ingenious  contrivances  for  this  purpose, 
they  all  fall  under  one  of  these  two  divisions. 

The  electro-mechanical  form  of  telegraphic  apparatus,  embraces 
the  needle  telegraph,  the  dial  telegraphs,  and  the  electro-magnetic,  or 
recording  telegraphs :  both  those  which,  like  Morse's,  use  a  cipher,  and 
those,  like  House's,  which  print  in  legible  characters. 

The  electro-chemical  telegraphs  (having  their  type  in  Soemmer- 
ing's  original  contrivance)  depend  on  the  production  of  a  visible  and 
permanent  effect,  as  the  result  of  some  chemical  decomposition  at  the 
remote  station  ;  of  these,  Bain's  is  the  best  known. 

This  is  not  the  place,  had  we  time,  to  give  all  the  details  of  the  well- 
known  machines  in  use  for  telegraphic  purposes.  A  few  words,  stating 
the  principles  on  which  they  all  depend,  with  a  notice  of  two  or  three 
of  those  most  used  in  the  United  States,  must  suffice. 

As  the  needle  telegraph  of  Messrs.  Wheatstone  and  Cooke  (depend- 
ing on  the  deflection  of  a  needle  by  a  galvanometer  coil)  has  never  been 
used  in  this  country,  and  cannot  compete  with  either  of  the  systems 
adopted  here,  it  is  needless  to  describe  it.  It  requires  one  operator  to 
read  the  movements  of  the  needle,  and  another  to  record  the  message, 
and  its  average  capacity  is  not  over  ten  or  twelve  words  per  minute. 
The  dial  telegraph  of  Froment,  and  others,  is  open  to  the  same  objec- 
tions. 

924.  Morse's  recording  telegraph. — Every  electro-telegraphic  ap- 
paratus implies  the  use  of  at  least  two  instruments,  one  for  recording, 
and  one  for  transmitting  the  message.     Besides  these,  in  most  cases 
there  is  need  of  a  relay  magnet,  which  receives  the  circuit  current  and 
acts  to  bring  into  use  the  power  of  a  local  battery,  by  which  the  work 
of  recording  is  performed.    This  is  requisite  because  the  circuit  current 
is  usually  too  feeble  to  do  more  than  establish  a  communication  with 
the  local  battery.     Every  recording  instrument  has  a  clock-work,  or 
some  similar  mechanical  movement,  to  carry  forward  the  paper  fillet  on 
which  the  record  is  impressed,  at  a  regular  rate  of  motion.     Fig.  684 
shows  the  Morse  recording  instrument. 

It  consists,  essentially,  of  a  simple  lever,  A,  with  a  soft  iron  armature,  D, 
over  the  electro-magnets,  E  F,  by  which  the  electrical  impulses  are  propagated 
to  the  pen  or  stylus,  o.  A  weight,  P,  gives  motion  to  a  train  of  wheels,  K  C,  by 
which  the  fillet  of  paper,  pp,  s  carried  over  the  rollers,  G  H,  in  the  direction  of 


620  PHYSICS    OF    IMPONDERABLE    AGENTS. 

the  arrows.     A  feeble  spring,  r,  withdraws  the  point,  o,  and  armature,  D,  when 
the  electricity  ceases,  and  the  motion  of  the  pen-lever  is  farther  adjusted  by  two 

684 


regulating  screws,  m  m,  that  can  be  set  at  pleasure.     The  battery  current  enters 
the  apparatus  at  the  binding  screws,  a  b. 

The  message  is  recorded  by  a  cipher  of  dots  and  dashes,  made  on  the  moving 
fillet  by  the  point  of  the  pen-lever.  The  lever  moves  in  obedience  to  the  impulses 
of  the  operator  at  the  transmitting  station,  who  presses  the  "finger-  key,"  for  a 
longer  or  shorter  instant,  according  to  what  he  would  transmit.  Every  motion 
of  the  pen-lever  gives  a  sound,  corresponding  to  the  letter  communicated ;  and 
to  a  practiced  operator,  this  sound  becomes  a  definite  language,  which  his  ear 
interprets  with  unfailing  certainty, 
so  that  he  literally  hears  the  mes- 
sage and  translates  it  without  the 
necessity  of  looking  at  the  record. 
Fig.  685  shows  the  spring  finger -key, 
by  which  messages  are  transmitted. 
The  Morse  instrument  has  the  ad- 
vantage  of  great  mechanical  simpli- 
city, so  that  it  requires  but  little 
skill  to  manage  it,  and  its  record 
being  permanent  and  sufficiently 
rapid  for  all  ordinary  purposes,  it 
has  come  into  more  general  use  in 
the  United  States  than  any  other,  and  over  the  continent  of  Europe  has  also  been 
very  generally  adopted.  Mr.  Morse  conceived  this  plan  of  telegraphic  trans- 
mission in  1833,  but  it  was  only  in  1837  he  applied  for  his  first  patent,  and  in 
1844  the  first  line  was  built  in  the  United  States,  from  Washington  to  Baltimore. 

925.  House's  electro-printing  telegraph. — This  most  ingenious 
instrument  records  its  message  in  plain  printed  characters,  and,  as  a 
mechanism,  must  be  regarded  as  one  of  the  most  wonderful  results  of 


ELECTRICITY. 


621 


inventive  genius.     A  drawing  of  its  chief  parts,  some  of  the  details 
being  omitted,  is  seen  in  fig.  686. 

Its  chief  parts  are  a  key -board,  marked  with  the  letters  of  the  alphabet ;  a 


type-wheel,  o,  on  which  the  letters  of  the  alphabet  are  engraved ;  a  helical  coil 
of  fine  wire  in  the  cylinder,  A,  in  connection  with  the  circuit,  and  which  oper- 
ates to  open  a  valve  for  the  emission  of  a  blast  of  air,  compressed  by  a  pump 
under  the  table  into  a  reservoir,  B.  The  purpose  of  this  blast  is  to  work  the 
escapement  regulating  the  motions  of  the  type-wheel,  o.  This  is  the  only 
function  of  the  electricity  in  the  recording  machine;  every  other  motion  is  a 
mechanical  one.  The  electricity,  by  opening  and  closing  the  air-valve,  regulates 
the  motion  of  the  type-wheel,  arresting  it  at  the  pleasure  of  the  operator  at  the 
distant  station,  who,  by  touching  on  his  key-board  the  letter  he  would  trans- 
mit, arrests  the  type-wheel  of  the  recording  instrument  at  that  letter ;  a  simple 
mechanism  then  presses  the  fillet  of  paper  on  the  face  of  the  type,  and  moves 
it  forward  to  receive  the  next  impression.  Its  actions  are  quicker  than 
thought,  and,  owing  to  the  exact  duality  of  the  two  machines  in  every  part,  and 
the  perfect  equality  of  their  motion,  the  operator  transmitting  is  as  conscious  as 
him  receiving,  if  there  is  any  error,  aided  as  he  is  by  a  tell-tale  above  the  type- 
wheel,  showing,  in  our  design,  the  letter  A.  It  is  impossible,  without  many 
pages  of  detail,  and  minute  drawings  of  the  parts,  to  render  this  marvel  of 
mechanical  art  perfectly  intelligible.  But  the  general  thought  of  the  inventor 
is  clear  enough,  to  place  the  recording  apparatus  at  the  control  of  the  trans- 
mitting operator,  through  the  agency  of  compressed  air,  controlled  by  the  electric 
current,  and  controlling,  in  its  turn,  the  escapements  of  the  recording  apparatus. 
It  prints  about  one  hundred  letters  per  minute,  on  a  circuit  of  one  hundred  and 
fifty  miles. 

926.  The  electro-chemical  telegraph  depends  on  the  decompose 
tion,  by  the  electrical  current,  of  a  salt  of  iron  with  which  the  papei 
fillet  is  saturated,  and  the  production  of  a  blue  or  red  stain  upon  it. 
The  same  clock-work  movement  used  by  Morse,  carries  forward  the 
paper  over  a  metallic  cylinder,  which  is  one  pole  of  the  circuit,  while 
55 


622  PHYSICS    OF    IMPONDERABLE    AGENTS. 

a  steel  pen  (if  a  blue  mark  is  intended,  or  copper,  if  red  is  intended), 
in  connection  with  the  other  pole,  bears  steadily  upon  the  paper ;  the 
least  transit  of  electric  force  decomposes  the  prussiate  of  potassa  with 
which  the  paper  is  charged,  producing  a  stain.  To  insure  the  damp- 
ness in  the  fillet  requisite  for  electrical  conduction,  Maison-Neuve  has 
proposed  to  charge  it  with  a  solution  of  nitrate  of  ammonia,  a  salt 
(  whose  attraction  for  moisture  is  such  that  the  paper  remains  always 
damp.  To  avoid  errors,  as  well  as  to  insure  greater  rapidity,  Bain, 
who  was  the  author  of  this  system,  proposed  to  prepare  the  messages, 
on  fillets  of  paper,  punched  with  holes  by  a  machine  called  a  compositor 
or  multiplier.  Humaston  has  lately  so  improved  the  mechanism  of  this 
compositor,  that  it  is  possible,  by  combining  this  apparatus  with  the 
Bain  system  of  reading,  to  transmit  not  less  than  three  thousand  signals 
per  minute,  equal  to  six  hundred  letters,  or  one  hundred  and  twenty- 
five  words  of  five  letters  each.  The  punched  fillets  take  the  place  of 
the  finger-key  as  a  circuit  breaker  for  the  transmission  of  the  message. 

Autograph  telegraphic  messages  can  be  transmitted  by  the  elec- 
tro-chemical method,  by  writing  upon  the  transmitting  cylinder,  with 
solution  of  hardened  wax,  and  then  causing  a  tracing  point  to  traverse 
the  cylinder  with  a  close  spiral  from  end  to  end.  The  result  is,  the 
interruption  of  the  current  where  the  wax  is,  and  a  corresponding 
blank  space  left  on  the  paper  at  the  receiving  station.  The  union  of 
these  white  spaces  gives  what  was  written  in  wax,  as  a  white  character 
on  a  dark  ground. 

927.  Submarine  telegraphs— the  Atlantic  cable.— The  first  sub- 
marine telegraphic  cable  was  successfully  sunk  in  August,  1851,  con- 
necting Dover,  in  England,  with  France,  at  Cape  Griz  Nez.  Since  that 
time,  numerous  other  submarine  cables  have  been  laid,  of  which  that 
through  the  Black  Sea  was  the  longest,  until  the  placing  of  the  Atlantic 
cable  was  accomplished,  on  the  5th  of  August,  1858.  The  failure  of 
this  great  enterprise  is  now  believed  to  be  attributable  to  injuries  received 
by  the  cable  before  submergence.  Its  failure  was  gradual, — over  400 
messages  being  transmitted  before  it  became  totally  inactive. 

Fig.  687  shows  the  size  and  mode  of  construction  of  this  cable.  The  con- 
ducting wire  is  formed  of  seven  strands  of  No.  687 
32  copper,  twisted  into  a  cord,  and  buried  in 
refined  gutta  percha,  laid  on  by  machinery  in 
three  coatings,  over  which  are  placed  several 
strands  of  tarred  cord.  The  whole  is  encased 
in  seventeen  strands  of  iron  wire,  each  strand 
formed  of  seven  No.  30  iron  wires.  It  weighs 
about  two  thousand  Ibs.  to  the  nautical  mile,  and  about  two  thousand  miles  of 
it  lie  submerged  between  Valentia  Bay,  Ireland,  and  Trinity  Bay,  Newfound- 
land. The  shore  end  is  formed  of  ten  miles  of  much  stronger  cable,  enclosing, 
however,  the  same  conductor. 


ELECTRICITY.  623 

The  problem  of  scientific  as  well  as  practical  interest  in  long  cables,  is  the 
possibility  of  transmitting  signals  through  them  -with  sufficient  rapidity  for 
useful  purposes.  Faraday  has  shown  (Ept.  Res.  vol.  3d,  p.  507 — 523  and  575), 
that  a  gutta-percha  covered  wire  is,  when  submerged  in  water,  in  very  different 
electrical  conditions  from  what  it  is  in  air.  In  the  water  it  simulates  the  charac- 
ter of  the  electrical  condenser,  or  Leyden  vial,  and  when  thus  charged  by  induc- 
tion, must  be  discharged  before  a  second  wave  can  be  transmitted  through  it; 
and  when  the  electric  pulses  are  frequent,  as  in  telegraphic  communications,  the 
effect  of  the  electric  conflict,  as  (Ersted  originally  termed  it,  is  to  produce  a 
tremor  in  place  of  sharp  and  decided  beats.  Those  who  would  know  the  history 
of  the  telegraph  more  in  detail,  will  consult  Schaffner's  Telegraphic  Manual, 
and  Prescott's  History  and  Practice  of  the  Electric  Telegraph,  Boston,  1860. 

928.  Electrical  clocks  and  astronomical  records. — If  a  clock 
pendulum  is,  by  any  mechanical  device,  made  to  open  and  close  the 
circuit  in  a  telegraphic  arrangement,  it  is  obvious,  that  if  the  clock 
beats  seconds,  these  will  appear  recorded  as  dots  at  equal  intervals 
upon  the  paper  fillet.     An  astronomer,  watching  the  transit  of  a  star 
across  the  wires  of  his  telescope,  with  his  hand  upon  the  finger-key  of 
the  same  circuit,  closes  it  at  the  exact  instant  of  time,  and  the  record 
of  the  passage  of  the  star  is  fixed  with  unerring  certainty  between  the 
beats  of  the  clock  and  upon  the  same  fillet  which  bears  record  of  the 
time  in  seconds  and  their  subdivisions.    This  beautiful  system  is  wholly 
and  peculiarly  American,  as  the  clear  records  of  science  show,  and 
offers  incomparably  the  best  possible  mode  of  determining  longitude 
differences.     The  names  of  Bache,  Bond,  Gould,  Locke,  Mitchel,  Sax- 
ton,  Walker,  Wilkes,  and  others,  are  inseparably  connected  with  the 
history  of  this  important  application  of  the  telegraph,  for  the  details 
of  which  the  student  is  referred  to  the  American  Journal  of  Science, 
the  proceedings  of  the  American  Association  for  the  advancement  of 
Science,  and  the  reports  of  the  United  States  Coast  Survey. 

Bain,  it  is  believed,  constructed  the  first  electrical  clock  (in  1842),  which  was 
moved  by  a  current  from  a  large  copper  and  zinc  plate  buried  in  the  earth,  or, 
better,  to  a  zinc  plate  buried  in  charcoal.  By  any  simple  mechanical  arrange- 
ment, the  motion  of  the  pendulum  reverses  or  breaks  the  current  at  every  beat, 
and  by  the  aid  of  a  stationary  magnet,  the  vibratory  movement  due  to  the  elec- 
tric current  is  strengthened  and  perpetuated.  It  is  possible  to  transmit  the 
same  electric  current  to  any  number  of  clocks,  in  the  same  place,  or  in  different 
places,  and  thus  secure  exact  equality  of  time. 

Fire-alarm. — Boston,  Philadelphia,  and  some  other  cities  are  provided 
with  a  telegraphic  system  due  to  Dr.  Channing  and  Mr.  Farmer,  by  which  a 
fire-alarm  is  sounded  simultaneously  in  every  district:  a  detailed  description  of 
which  will  be  found  in  Am.  Jour.  Sci.  [2],  XIII.,  58. 

§  5.   Electro-dynamic  Induction. 

I.     INDUCED  CURRENTS. 

929.  Currents  induced  from  other  currents. — Volta-electric 


624          PHYSICS  OF  IMPONDERABLE  AGENTS. 

induction. — The  phenomena  of  electro-magnetism  seem  to  point,  as 
an  almost  necessary  consequence,  to  the  discovery  made  by  Faraday,  in 
1831-2,  of  induced  currents,  as  well  as  of  magneto-electricity.  Faraday 
argued  thus : — 

1st.  That  as  a  wire  carrying  a  current  acts  like  a  magnet,  therefore  it 
ought,  by  induction,  to  excite  a  current  in  another  wire  near  it. 

2d.  That,  as  magnetism  is  induced  by  electric  currents,  so  magnets 
ought  also,  under  proper  conditions,  to  excite  electric  currents. 

The  first  of  these  theses  Faraday  sustained  thus :  Let  a  double  helix, 
or  bobbin,  be  wound  of  two  parallel  silk-covered  wires,  about  a  cylin- 
der of  wood  (which  being  withdrawn  afterwards,  leaves  the  helix  hol- 
low), in  close  contact,  but  perfectly  insulated,  so  that  the  two  wires 
run  side  by  side  through  their  whole  course.  Let  the  ends,  a  b,  fig.  688, 
of  one  wire  be  connected  with  a 
galvanometer,  or  magnetizing  spi- 
ral, while  a  battery  current  enters 
the  other  wire  by  c,  and  passes 
out  by  d.  When  contact  is  made 
between  c  and  the  battery,  the 
galvanometer  needle  is  deflected 
by  a  current  moving  in  the  same 
direction  with  the  battery  or  pri- 
mary current.  This  deflection,  however,  is  only  for  a  brief  instant. 
After  a  few  vibrations,  the  needle  comes  to  rest,  although  the  battery 
current  still  flows.  Break  now  the  contact  between  the  wire,  c,  and 
the  battery,  and  the  galvanometer  needle  is  again  deflected  by  a  second- 
ary or  induced  current ;  but  this  time  it  moves  in  the  opposite  direction 
to  the  first.  These  are  called  secondary  or  induced  currents.  They  are 
momentary,  but  are  renewed  with  every  interruption  of  the  battery 
circuit,  and  their  strength  is  always  proportional  to  the  strength  of  the 
primary  or  inducing  current.  If  a  mass  of  soft  iron  (or,  better,  a 
bundle  of  soft  iron  wires)  is  placed  in  the  core  of  the  helix,  the  force 
of  the  induced  currents  is  greatly  increased.  This  action  of  a  current 
from  a  Voltaic  battery,  Faraday  called  Volta-electric  induction. 

The  phenomena  of  influence  (828)  in  electricity  present  a  strong 
analogy  to  these  facts,  and  support  the  probability  that  the  secondary 
currents  in  the  case  of  Voltaic  induction,  are  also  due  to  decomposi- 
tion of  the  natural  electricity  of  the  second  wire,  by  the  current  on 
the  first.  In  fact,  a  current  of  statical  electricity  may  be  substituted 
for  the  Voltaic  current  with  similar  results,  as  was  shown  by  Henry, 
in  1838  (Trans.  Am.  Phil.  &AJ.,  vol.  6,  N.  S.,  and  Am.  Jour.  Sci.  [1], 


ELECTRICITY. 


625 


689 


XXXVIII.,  209).  Fig.  689  is  a  convenient  form  of  apparatus  designed 
by  Matteucci,  for  this  experiment.  Two  coils  of  insulated  wire,  A  B, 
are  sustained  on  movable  feet,  ad- 
mitting of  near  approach.  When 
the  charge  of  a  Leyden  jar,  D,  is 
passed  through  the  coil  cd  on  A,  a 
person  whose  hands  grasp  the  con- 
ductors, ih,  of  the  coil,  B,  will  re- 
ceive a  shock,  the  violence  of  which 
increases  with  the  closer  approach 
of  A  and  B.  The  direction  of  the  current  in  B,  is  the  reverse  of  that 
in  A.  If  a  galvanometer  is  inserted  in  the  circuit  ih,  its  needle  is 
deflected,  or,  if  a  magnetizing  spiral  is  used,  needles  may  be  magnetized 
by  it. 

930.  Induced  currents  of  different  orders. — By  using  a  series  of 
flat  spirals  of  copper  ribbon  alternating  with  helices  of  fine  insulated 
copper  wire,  arranged  as  in  fig.  690,  Prof.  Henry  (in  1838)  demonstrated 


that  secondary  or  induced  currents  produced  other  induced  currents  of 
the  second,  third,  fourth,  and  so  on,  as  far  as  the  ninth  order.  Thus,  the 
flat  spiral,  A,  receiving  the  battery  current,  induces,  at  every  rupture 
of  that  current,  a  secondary  intense  current  of  opposite  name  in  B, 
while  the  second  flat  spiral,  C,  receives  from  B  a  quantity  current, 
inducing  a  tertiary  intense  current  in  the  second  fine  wire  spiral,  W, 
and  so  on.  The  signs  -f  and  —  alternate  after  the  first  remove  from 
the  battery  current,  as  is  easily  demonstrated  by  inserting  magnetizing 
spirals  in  the  conducting  wires,  and  using  steel  sewing-needles  as  tests. 
A  screen  or  disc  of  metal  introduced  between  any  two  of  691 

these  coils,  cuts  off  the  inductive  influence.     But  if  the 
screen  has  a  slit,  a  6,  cut  from  the  centre  to  the  circum- 
ference, as  in  fig.  691,  the  induction  is  the  same  as  if  no 
screen  were  present.     Discs  or  screens  of  wood,  glass,  paper,  or  other 
non-conductors,  offer  no  impediment  to  this  induction. 
65  * 


626 


PHYSICS    OP    IMPONDERABLE    AGEN'ib. 


930.  Extra-current,  or  the  induction  of  a  current  on  itself. — 

The  effect  of  a  long  and  stout  conductor  in  giving  a  vivid  spark  and 
shocks  from  a  single  cell  (which  alone,  or  with  a  short  conductor,  gives 
neither  sparks  nor  shocks),  was  first  noticed  in  1832  by  Prof.  Henry. 
(Am.  Jour.  Sci.  [1],  XXII.,  404.)  This  fact  was  afterwards  the  subject 
of  investigation  by  Faraday,  in  December,  1834,  and  also  by  Henry, 
in  January,  1835.  The  arrangement  used  by  Prof.  Henry  is  seen  in 
tig.  692.  A  small  battery,  L,  is  connected  with  the  flat  spiral  of  cop- 

692 


per  ribbon,  A,  by  wires  from  the  battery  cups,  Z  and  C ;  when  this 
communication  is  broken  by  drawing  the  end  of  one  of  the  battery 
wires,  Z,  over  the  rasp,  a  brilliant  spark  is  seen  at  the  instant  of  break- 
ing contact.  No  spark  is  drawn  on  making  contact.  Moreover,  if  a 
fine  wire  coil,  W,  is  placed  in  the  relation  to  A  shown  in  the  figure, 
there  is  only  a  feeble  spark  seen  on  breaking  the  battery  contact,— 
while  the  powerful  secondary  current  already  named  is  set  up  in  W, 
violently  convulsing  the  hands  which  grasp  its  terminals.  The  strong 
spark  from  the  large  flat  coil  or  single  wire  in  the  first  case,  is  then  the 
equivalent  of  the  current  which  would  be  produced  in  the  second  case, 
if  such  current  were  permitted.  This  reflux  current  induced  on  a  con- 
ductor, and  the  outflow  or  recoil  of  which  produces  vivid  sparks,  is 
what  Faraday  calls  the  extra  current.  In  powerful  coils,  this  extra 
current  produces  sparks,  the  report  of  which  resembles  the  explosion 
of  a  pistol,  especially  under  the  inductive  influence  of  a  powerful  elec- 
tro-magnet, as  in  the  engine  of  Dr.  Page,  already  noticed.  The  heavy 
coils  of  this  apparatus  produced  sparks  from  the  extra  current  from 
two  to  six  inches  in  length,  and  having  the  same  rotative  action  as  the 
conductor  itself.  (Am.  Jour.  Sci.  [2],  XI.,  191.)  Many  forms  of  elec- 
tro-magnetic apparatu^  in  which  two  coils  are  combined,  show  the 
extra  current  in  a  striking  manner,  as  in : — 

931.  Page's  vibrating  armature  and  electrotome. — In  this  appa- 
ratus, fig.  693,  the  flow  of  the  battery  current  is  interrupted  by  the 
movements  of  the  bent  wire,  P  W  C.  At  M  is  a  bundle  of  soft  iron 


ELECTRICITY. 


62' 


wires,  forming  the  core  of  the  inducing  coil.    Becoming  magnetic,  these 

attract  a  small  mass  of  iron  on  the  end  of  P  to  M.     This  movement 

raises  the  other  end  out  of  the  mercury  in  the  cup,  C,  with  a  brilliant 

spark,  due  to  the  flow  of  the 

extra  current,  the  magnetism 

having    disappeared    by  the 

break    of   the    battery  flow. 

Gravity  then  restores  the  wire 

to   its  original  position,  thus 

renewing  the  battery  current 

and  the  magnetism,  and  with 

it  the  spark  in  C.    A  fine  wire 

induction  coil  of  two  thousand 

or  three  thousand  feet,  wound  about  the  inducing  coil,  develops  the 

secondary  currents  already  noticed,  with  powerful  physiological  and 

other  inductive  effects,  resembling  statical  electricity. 

932.  Induced  currents  from  the  earth's  magnetism. — The  earth's 
magnetism  also  induces  electrical  currents  in  metallic  bodies  in  move- 
ment ;  another  of  the  discoveries  of  Faraday.    For  this  purpose,  a  helix 
in  the  form  of  a  ring  is  made  to  revolve  with  its  axis  at  right  angles  to 
the  magnetic  meridian,  and,  consequently,  each  point  of  the  ring  de- 
scribes circles  parallel  to  the  plane  of  this  meridian.     A  pole  changer 
on  the  axis  is  so  arranged  as  to  keep  the  induced  current  moving  always 
in  the  same  direction  ;  -when  so  arranged,  and  its  terminal  wires  are  con- 
nected with  a  galvanometer,  a  deviation  of  the  needle  indicates  the  flow 
of  a  current  to  the  east  or  the  west,  according  to  the  direction  of  the 
rotation. 

933.  Conversion  of  dynamic  into  static  electricity. — The  in- 
duction coil. — By  careful  insulation  of  the  secondary  coil  of  fine  wire 
— as  well  in  itself  as  from  the  primary  or  magnetizing  wire — electricity 
of  high  tension  is  produced,  surpassing,  in  energy  and  abundance,  that 
from  machines  of  the  greatest  power.     Masson,  in  1842,  first  succeeded 
in  obtaining  these  results,  but  in  a  very  feeble  manner  compared  with 
those  we  now  know.     Ruhmkorff,  of  Paris,  in  1851,  constructed  the 
coils  which  bear  his  name.     By  careful  insulation  of  the  fine  wire 
coil,  he  succeeded  in  producing  sparks  of  about  two  inches  in  length 
between  the  electrodes,  charging  and  discharging  a  Leyden  jar  with 
astonishing  rapidity.     No  electrical  instrument  has,  in  modern  times, 
been  more  celebrated. 

Ritchie,  of  Boston,  has  so  vastly  improved  this  apparatus,  as  to  de- 
serve the  highest  praise  from  all  interested  in  physical  research. 
Ritchie's  form  of  the  induction  coil  is  shown  in  fig.  694.  The  cause 


628 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


of  the  superiority  in  the  American  apparatus  is  due  chiefly  to  the 
mode  of  winding  the  fine  wire  coil,  by  which  it  is  possible  to  use  with 
success  a  wire  of  eighty  thousand  feet  in  length,  while  the  limit  in  the 
instruments  made  by  Ruhmkorff  was  about  ten  thousand  feet.  The 
extreme  length  of  spark  obtained  by  the  European  instruments,  was, 
for  the  French,  about  two  inches  (Jean's);  and  for  the  English,  four 
inches  (Hoarder's)  ;  the  American  instruments  have  projected  a  torrent 
of  sparks  over  sixteen  inches  in  free  «fr ;  while  the  one  shown  in  fig.  694, 
is  limited  to  about  nine  inches. 

The  chief  parts  of  this  apparatus  are  the  two  coils,  an  interrupter  to  the  pri- 
mary circuit,  and  the  condenser. 
In  the  instrument  here  figured, 
over  sixty-eight  thousand  feet 
of  silk-covered  copper  wire, 
the  softest  and  purest  possible, 
twelve  thousandths  of  an  inch 
in  diameter  (No.  32  of  the  wire 
gauge),  is  wound  upon  the  ex- 
terior bobbin,  C.  About  two 
hundred  feet  of  wire,  one- 
seventh  of  an  inch  in  diameter 
(No.  9),  forms  the  inducing 
wire,  whose  ends  -j-  and  —  are 
visible  in  the  binding  screws 
on  the  base.  A  heavy  glass 
bell,  «,  insulates  the  coils  from 
each  other,  and  its  foot  is 
turned  outwards  by  a  flange  us 
wide  as  the  thickness  of  the 
coil.  The  induction  coil,  for 
more  perfect  insulation,  is  also 
encased  in  thick  gutta  percha.  The  ends  of  this  coil  are  carried  by  gutta-per- 
cha covered  conductors,  to  two  glass  insulating  stands  (only  one  of  which  is 
visible  in  our  figure),  where  they  end  in  sliding  rods  pointed  with  platinum  at 
one  end,  and  having  balls  of  brass  at  the  other.  The  interrupter  devised  by 
Mr.  Ritchie,  is  the  toothed  wheel,  b,  which  raises  a  spring  hammer,  the  blows 
of  which  fall  upon  the  anvil,  o,  breaking  contact  between  two  stout  pieces  of 
platinum.  The  European  machines  are  provided  with  a  self-acting  break- 
piece;  but  experience  has  shown,  by  comparative  trials,  that  there  is  an 
advantage  in  varying  the  rapidity  of  the  interruptions,  according  to  the  class 
of  effects  to  be  produced,  and  that  a  certain  time  is  requisite  for  the  complete 
charge  and  discharge  of  the  soft  iron  wires  (which  form  the  core  of  the  battery 
circuit),  longer  than  the  automatic  break-piece  allows. 

The  object  of  the  condenser  (which  is  due  to  Mr.  Fizeau)  is  to  destroy,  by 
induction,  the  greater  part  of  the  force  of  the  extra  current,  which,  owing  to  the 
very  powerful  magnetism  developed  in  the  core  of  soft  iron  within  the  battery 
coil,  would  otherwise  greatly  impair  the  power  of  the  apparatus,  as  it  moves  in 
i  direction  opposite  to  the  primary  current  (931).  The  condenser  consists,  in 
che  instrument  figured,  of  one  hundred  and  forty  square  feet  of  tin-foil,  divided 


ELECTRICITY.  629 

into  three  sections  (two  of  50,  and  one  of  40  feet),  whose  termini  are  at  e.  The 
tin-foil  of  the  condenser  is  carefully  insulated  by  triple  folds  of  oiled  silk,  and 
laid  away  in  the  base  of  the  instrument,  in  a  cell  prepared  for  it,  quite  out  of 
view. 

The  battery  force  needed  to  excite  this  apparatus,  is  only  two  or  three  large- 
sized  cells  of  Bunsen's  battery. 

934.  Effects  of  the  induction  coil. — The  physiological  effects  are 
so  distressing  and  even  dangerous,  that  too  great  care  cannot  be  taken 
to  avoid  them.  M.  Quet  was  confined  to  his  bed  for  some  time,  after 
having  accidentally  received  the  shock.  Small  animals  are  instantly 
killed  by  its  discharge. 

The  luminous  effects. — When  a  series  of  sparks  passes  between 
the  points  of  platinum,  or  between  the  balls,  they  are  of  a  zigzag  form, 
and  accompanied  by  a  loud  noise  and  a  strong  odor  of  ozone.  Their 
color  is  violet  and  yellowish,  or  greenish  yellow.  If  the  points  are 
within  an  inch  or  two,  the  stream  of  sparks  appears  to  be  continuous, 
a  fourth  of  an  inch  broad,  surrounded  by  a  violet  areola,  and  crossed 
by  numerous  lines  at  right  angles  to  its  path.  If  it  is  blown  by  the 
breath,  or  by  a  bellows,  it  is  deflected  into  a  curve,  and  a  bright  flame 
is  seen  projected  for  some  distance  beyond  the  purple  or  violet  stream 
of  electric  light.  The  color  of  the  flame  varies  with  the  nature  of  the 
electrodes  (885).  If  one  of  the  electrodes  is  covered  by  a  small  glass 
flask,  the  power  of  the  induction  is  such  that  a  stream  of  violet  elec- 
tricity is  seen,  as  it  were,  to  pass  directly  through  the  glass,  while  the 
ball  of  the  flask  is  covered  with  a  magnificent  net-work  of  violet  light, 
spread  out  like  the  blood-vessels  upon  the  eye-ball. 

If  an  ^Epinus  condenser,  or  a  Leyden  jar,  is  put  in  the  path  of 
the  current,  the  length  of  the  spark  is  much  diminished,  but  its 
intensity  and  splendor  are  increased  twenty-fold.  The  electric  light 
then  becomes  intensely  white,  and  the  sound  of  the  explosion  of  the 
successive  sparks,  when  these  are  drawn  by  a  slow  movement  of  the 
break-piece,  is  like  the  snap  of  fulminating  mercury,  or  the  sound  of  a 
pistol,  while  the  electric  stream  appears  continuous.  If  a  Newton's 
chromatic  disc  is  caused  to  revolve  before  it,  each  spark  causes  the 
colors  of  the  revolving  disc  to  appear  stationary,  although  without  this 
evidence  of  an  intermittent  character,  the  stream  of  electricity  would 
appear  to  be  unbroken. 

Splendid  phenomena  of  fluorescence  with  canary-colored  glass — chemical 
decompositions,  deflagrations  of  the  leaf  metals,  discharges  of  flashes  of  light- 
ning over  the  surface  of  a  metallic  mirror,  a  gilded  board,  or  wet  table,  and 
numerous  other  most  beautiful  and  instructive  experiments,  are  made  with  this 
apparatus.  Indeed,  nearly  all  the  phenomena  of  static  electricity  are  shown  by 
it,  and  some  of  them  with  a  power  which  no  frictional  apparatus  can  approach. 
It  Is  curious  to  observe,  that  the  sparks  of  this  kind  of  electricity  pass  freely 


680 


PHYSICS    OF    IMPONDERABLE    AGENTS. 


from  pointed  wires  (826).  If  two  fine  iron  wires  are  used  as  the  electrodes,  the 
negative  wire  alone  reddens  and  burns,  unless  the  current  is  very  energetic.  All 
the  apparatus  used  for  showing  the  luminous  effects  of  machine  electricity, 
$  852,  may  be  employed  with  this  apparatus  with  vastly  greater  brilliancy. 

The  chemical  effects  of  the  induction  coil  are  shown  in  the  decom- 
position of  water,  &c.,  while  a  stream  of  sparks  from  it,  passed  through 
a  tube  containing  air,  soon  causes  the  production  of  reddish  vapors  due 
to  the  formation  of  hyponitric  acid  from  the  union  of  the  elements  of 
the  air.  Mr.  Gassiot  has  lately  shown  (Phil.  Mag.  Aug.  I860)  that  the 
intensity  of  the  coil  is  such  as  to  transmit  electrolytic  effects  across 
glass,  or  apparently  through  the  walls  of  a  Florence  llask. 

935.  Light  of  these  currents  in  a  vacuum. — The  difference  be- 
tween the  light  from  the  positive  and  the  negative  electrodes  has 
already  been  noticed.  Owing  to  the  absence  of  intense  effects  of  heat 
in  the  currents  from  the  induction  coil,  they  695 

are  particularly  adapted  to  illustrate  this  dif- 
ference, especially  in  vacuo. 

In  a  vacuum  tube,  or  the  electrical  egg  well 
exhausted,  a  torrent  of  rosy  or  violet  fire  falls, 
from  the  positive  electrode  above,  toward  the 
negative,  which  is  surrounded  with  a  blue  and 
white  light,  extending  down  the  stem,  with 
splendid  fluorescence  (533).  If  the  vacuum  is 
made  upon  vapor  of  turpentine,  or  of  phosphorus 
in  the  egg,  or  in  an  auroral  tube,  a  most  wonder- 
ful phenomena  shows  itself;  the  stratification 
of  the  electrical  light  in  alternate  bands  of  light 
and  darkness,  surrounding  and  depending  from 
the  positive  pole,  as  indicated  in  fig.  695.  This 
curious  phenomenon  was  first  observed  by  M-r. 
Grove.  Vapor  of  alcohol,  wood-naptha,  biclorid 
of  tin,  or  bisulphid  of  carbon,  may  be  used,  each 
with  a  different  effect. 

Mr.  Gassiot  has  studied  with  great  care  the 
character  of  the  spark  in  vacuums  formed  on 
various  gases  and  vapors,  and  has  established 
the  curious  fact,  that  in  a  perfect  Torricellian 
vacuum,  the  spark  will  not  pass,  showing  that 
an  extremely  tenuous  vapor  is  essential  to  its  passage.  These  facts 
bear  in  an  important  manner  on  the  phenomena  of  the  Aurora  Borealis. 

Gassiot's  cascade  in  vacuo. — If  we  place  in  a  vacuum  a  goblet 
coated  with  tin-foil  in  the  manner  of  a  Leyden  jar,  and  carry  the  indue- 


ELECTRICITY. 


631 


tion  current  to  its  bottom  by  means  of  a  wire  passing  through  the  cap 
of  the  air-bell,  as  in  fig.  696,  the  other  electrode  being  in  communication 
with  the  air-pump  plate  on  which  the  whole  appa- 
ratus stands,  we  are  delighted  to  see,  when  the  cur- 
rent is  established  from  the  induction  coil,  the  vase 
overflow  like  a  fountain  with  a  gentle  cascade  of 
light,  wavy  and  gauze-like,  falling  like  an  auroral 
vapor  on  the  metallic  base.  This  experiment  re- 
quires a  very  good  vacuum,  and  is  certainly  one 
of  the  most  beautiful  exhibitions  in  luminous  elec- 
tricity. 

936.  Rotation   of   the   electric   light  about 
a   magnet. — We   here   recall    the    early   observa- 
tion of  Davy,  §  883,  on  the  influence  of  a  magnet  I 

on  the  Voltaic  arc.  If  an  electro-magnet  is  enclosed  in  the  elec- 
trical egg,  and  a  very  perfect  vacuum  is  made  within  it,  when  the 
induction  current  is  caused  to  flow,  the  electrical 
stream  is  seen  to  revolve  in  a  steady  and  easy  man- 
ner about  the  magnet,  the  direction  of  its  motion 
corresponding  to  the  polarity  of  the  magnet.  In 
fig.  697  is  shown  such  an  apparatus.  The  magnet 
here  is  a  bundle  of  soft  iron  wires  enclosed  in  a 
glass  tube,  and  passing  through  the  foot,  so  that 
when  the  instrument  is  placed  on  one  pole  of  an 
electro-magnet,  the  mass  of  wires  may  be  magnetized 
inductively.  Two  platinum  wires  -f-  and  —  pass  in 
glass  tubes  hermetically  through  the  walls  of  the 
vessel,  into  the  vacuum  and  form  the  points  of  attach- 
ment for  the  electrodes. 

937.  Applications  have  been  made  of  the  induc- 
tion current  for  firing  blasts  and  sub-aqueous  maga- 
zines, and  also  for  lighting  simultaneously  all  the  gas  burners  in  a  large 
audience  room  or  theatre. 

Electrical  blasting  by  Ruhmkorff's  coil  is  easily  accomplished  by  tb* 
use  of  Stateham's  fuse,  fig.  698 

698,  which  is  only  a  gutta-per- 
cha covered  conductor,  A  B, 
in  which  the  discharge  is  in- 
terrupted at  points,  a  b,  buried 
in  the  gunpowder,  producing 
its  eombu  tion,  even  at  a  dis- 
tance of  many  miles,  and  in  many  distinct  mines,  or  blast  holes,  SM« 


632  PHYSICS    OF    IMPONDERABLE   AGENTS. 

cessively,  but  almost  at  the  same  instant.  Dr.  Hare  first  employed  his 
calorimotors  for  electrical  blasting  in  1831.  *  (Am.  Jour.  Sci.  [1]  XXI. 
139.)  But  the  use  of  an  extended  battery,  and  all  uncertainty,  is 
avoided  by  using  the  induction  coil.  Ruhmkorff,  in  experiments  made 
at  Villette,  inflamed  gunpowder  with  this  coil  through  about  sixteen 
miles.  In  excavating  the  Napoleon  docks  at  Cherbourg,  lately,  over 
65,000  cubic  yards  of  rock  were  thrown  out  by  one  series  of  blasts  fired 
in  this  way. 

II.     MAGNETO-ELECTRICITY. 

938.  Currents  induced  by  magnets. — If  the  helix  in  fig.  699  is 
connected  with  a  galvanometer,  and  a  bar  magnet  is  quickly  thrust 
into,  and  suddenly  withdrawn  from  it,  699 

the  needle  of  the  galvanometer  indi- 
cates the  movement  of  a  current  of 
electricity  opposite  in  the  two  cases, 
and  whose  direction  in  each  case  is 
opposite  to  that  of  a  current  which,  on 
Ampere's  theory,  would  produce  a 
magnet  like  the  one  employed.  It  is 
hardly  needful  to  say  that  reversing 
the  ends  of  the  bar  magnet,  reverses  the  movements  of  the  galvano- 
meter. This  is  a  case  of  magnetic  electric  induction. 

This  fact  is  also  illustrated  in  other  modes,  viz.  :— 

a.  By  revolving  a  circular  plate  of  copper  between  the  poles  of  a 
horse-shoe  magnet  (arranged  in  general  like  fig.  678),  the  axis  of  the 

700 


copper  being  in  connection  with  one  pole,  and  the  edge  with  the  other, 
a  series  of  sparks  may  be  obtained,  as  in  Faraday's  original  experiment, 
some  device  being  inserted  to  interrupt  the  current  during  the  revolu- 
tion. 


ELECTRICITY. 


633 


b.  By  a  helix  on  tlie  armature  of  a  magnet,  the  ends  of  the  helix  being 
connected  with  the  poles  respectively,  on  suddenly  sliding  the  armature 
from  the  poles  of  the  magnet,  a  spark  is  seen,  and  if  the  fingers  grasp  the 
wires  at  the  same  time,  a  shock  follows.  This  fact  was  first  announced 
in  December,  1831,  by  Srs.  Nobili  and  Antinori.  Saxton  constructed 
the  first  magneto-electric  machine  in  which  the  armature,  wound  with 
a  helix,  was  made  to  revolve  in  front  of  the  poles  of  a  magnet,  and  so  to 
reproduce  all  the  phenomena  of  static  and  voltaic  electricity  from  per- 
manent magnets.  Fig.  700  shows  an  improved  form  of  Saxton's  appa- 
ratus, where  the  double  inducing  coil  revolves  by  means  of  a  motor 
wheel  and  band  between  the  poles  of  two  powerful  magnetic  batteries. 
The  magnetic-electric-induction  is  interrupted  by  the  little  crown-wheel 
seen  on  the  upper  end  of  the  axis  of  the  revolving  coils. 

Clarke's  magneto  electric  apparatus. — This  apparatus  is  a  modi- 
fication of  Saxton's,  and  consists  of  a 
powerful  magnetic  battery,  A,  fig.  701, 
clamped  on  the  upright  board,  R,  by  the 
clamp  C.  The  wheel,  F,  puts  in  motion 
two  helices,  H  G-,  wound  upon  a  rotating 
armature  of  soft  iron.  The  electrical  cur- 
rent induced  in  the  coils  is  interrupted  by 
the  spring,  or  hook,  Q,  which  rubs  on  the 
interrupted  back  piece,  H,  while  the  circuit 
is  completed  by  the  hook,  0,  passing  upon 
the  continuous  part  of  the  spindle,  R.  A 
stout  wire,  T,  movable  at  pleasure,  con- 
nects the  two  sides,  M  and  N,  otherwise 
insulated  by  the  piece  of  dry  wood,  L. 
When  the  coils  are  rapidly  rotated  before 
the  poles  of  the  magnet,  the  current  is  in- 
terrupted twice  .in  every  revolution  by  the 
hook,  Q,  with  the  production  of  a  brilliant 
spark.  If  the  coils  are  composed  of  a  long 
and  fine  wire,  then  powerful  shocks  will  be 
experienced  by  one  holding  the  handles  R 
and  S,  but  capable  of  a  great  graduation,  by  changing  the  position  of  the  break 
piece,  H,  with  reference  to  the  point  of  the  revolution  when  it  leaves  Q.  These 
shocks  may  be  made  quite  intolera-  702 

ble. 

If  the  conducting  wires  of  the 
intensity  coil  terminate  in  a  decom- 
posing apparatus,  fig.  702,  trains 
of  minute  gas  bubbles  are  seen  to 
rise  from  the  platinum  points  under 
the  tubes,  showing  the  production 
cf  dynamic  from  magnetic  electri- 
city. Other  effects  of  the  intense 
class,  as  the  decomposition  of  iodid 
of  potassium,  may  also  be  produced  with  it.  Substituting  a  coil  of  large  wire 
56 


634          PHYSICS  OP  IMPONDERABLE  AGENTS. 

not  over  two  hundred  feet  long,  for  the  small  long  wire,  the  quantity  armature  is 

produced,  from  which  brilliant  sparks,  the  deflagration  of  mercury,  and  setting 

fire  to  ether,  as  in  fig.  703,  may  be  produced ;  mercury,  in  a  copper  spoon,  B,  is 

touched  by  the  revolving  points,  A,  on  the  end  703 

of  the   axis,   d,  and   with   every   disruption    of 

the   circuit,  the   extra   current   discharges  with 

splendid  effect.     A  platinum  wire   may  also   be 

ignited,    and    electro-magnets    charged    by   the 

same  armatures.     Thus  we  see  all  the  effects  of 

electricity,  physical   and   physiological,  coming 

from  a  magnet. 


939.  Identity     of     electricity     from 
whatever    source. — It  follows  from    all 
that  has  been  said,  that  the  phenomena  of 
magnetic,  static,  and   dynamic   electricity, 
are  all  capable  of  being  produced  each  by 
the  other ;  and  the  conclusion  seems  war- 
ranted tha-t  electricity,  from  whatever  source,  is  one  and  the  same 
power. 

Numerous  and  instructive  forms  of  apparatus  have  been  devised  to  demon- 
strate this  point,  as  well  also  as  to  illustrate  in  detail,  the  principles  we  have, 
for  want  of  space,  been  compelled  to  state  in  terms  too  concise.  The  student 
and  teacher  will  find  it  useful  to  consult  the  figures  of  Davis's  Manual  of  Mag- 
netism for  various  forms  of  apparatus,  due  to  the  ingenuity  of  Faraday,  Dr.  Page, 
and  many  others.  For  works  of  standard  authority,  he  is  referred  to  Faraday's 
experimental  researches,  and  De  La  Hive's  treatise  on  electricity,  each  in  three 
volumes. 

§  6.    Other  Sources  of  Electrical  Excitement. 

940.  Universality  of  electrical  excitement. — Every  change  in 
the  physical  or  chemical  condition  of  matter,  seems  to  be  attended 
with    electrical    excitement.     This   is    evident  from    the    phenomena 
attending  the  cleavage,  or  pulverizing,  of  many  minerals  and  crys- 
tallized substances,  as  sugar,  mica,  zinc-blende,  and  numerous  other 
substances  which  evolve  light  when  suddenly  cleaved.     If  precautions 
are  taken  to  insulate  these,  as  with  mica  it  is  easy  to  do,  by  sealing 
wax,  they  also  show  the  effects  of  electrical  excitement  by  the  con- 
denser.    The  production  of  crystals  is  often  also  accompanied  by  elec- 
trical light. 

Combustion,  evaporation,  the  escape  of  gas  attending  chemical  trans- 
formations, chenjical  decompositions  and  combinations,  have  all  been 
known  to  evolve  electricity  when  properly  observed  ;  but  in  most  such 
cases,  the  phenomena  are  too  complicated  to  render  it  clear  to  which, 
if  indeed  to  any  single  action  of  those  enumerated,  the  excitement  is 
due. 


ELECTRICITY.  635 

The  electrical  currents  set  up  by  heat  (thermo-electricity),  and  those 
arising  from  the  phenomena  of  life  (animal  electricity),  are  the  most 
important  of  all  sources  of  electricity  not  before  dwelt  on,  and  to  them 
we  will  now  briefly  advert. 

I.     THERMO-ELECTRICITY. 

941.  Thermo-electricity. — The  discovery  of  this  source  of  elec- 
trical currents  is  due  to  Seebeck,  of  Berlin,  in  1821.  He  found  that 
if  two  metals  of  unlike  crystalline  texture  and  conducting  power  are 
united  by  solder,  and  the  point  of  junction  is  either  heated  or  cooled, 
an  electrical  current  is  excited,  which  in  general  flows  from  the  point 
of  junction  to  that  metal  which  is  the  poorer  conductor.  Fig.  705 
shows  such  an  arrangement  of  two  little  bars  of  bismuth  and  anti- 
mony. When  the  junction,  e,  704 
is  heated,  a  current  of  positive 
electricity  flows  from  the  bis- 
muth, 6,  to  the  antimony,  a.  If 
the  form  of  a  rectangle  is  given 
to  this  arrangement,  as  in  fig. 
704,  an  instrument  resembling 
Schweigger's  multiplier  is  form- 
ed (905),  by  which  the  magnetic  needle  is  deflected.  A  twisted  wire 
also  produces  a  thermo-electric  current  when  the  twisted  portion  is 
gently  heated,  and,  besides  metals,  other  solids,  and  even  fluids,  give 
rise  to  this  species  of  electricity.  The  order  in  which  the  metals  stand 
in  reference  to  this  power  is  wholly  unlike  the  Voltaic  series,  and 
appears  related  to  no  other  known  property  of  these  elements.  The 
rank  of  the  principal  metals  in  the  thermo-electric  series  is  as  follows, 
as  determined  by  Becquerel: — The  numbers  prefixed  give  the  order  of 
each  metal  in  the  table  of  specific  heats  as  determined  by  Regnault. 
Those  having  the  highest  specific  heat,  as  a  general  rule,  being  first  in 
positive  power  (+)  in  the  thermo-electric  magnet :  6  antimony  ;  1  iron  ; 
2  zinc ;  4  silver ;  7  gold ;  3  copper ;  5  tin ;  9  lead ;  8  platinum  ;  10 
silver. 

When  the  junction  of  any  pair  of  these  is  heated,  the  current  passes 
from  that  which  is  highest,  to  that  which  is  lowest  in  the  list,  the  ex- 
tremes affording  the  most  powerful  combination. 

Becquerel  has  found  the  intensity  of  the  current  in  a  thermo-electric 
combination  to  be  proportional  to  the  difference  of  temperature  in  the 
solderings  up  to  100°  or  120°  F.,  one  of  the  points  being  at  32°.  Above 
this  limit,  the  increase  of  intensity  is  less  and  less,  with  an  increase  ot 


636  PHYSICS    OF    IMPONDERABLE    AGENTS. 

heat.    In  a  couple  of  copper  and  iron,  the  increase  of  current  was  in- 
sensible near  570°  F. 

In  a  compound  thermo-electric  series,  intense  effects,  analogous  to 
those  of  the  Voltaic  pile,  are  obtained  only  when  half  705 

the    solderings    are    heated,    the    alternates    being 
cooled. 

Thermo-electric  motions. — If  a  compound  ring 
of  brass  and  German-silver  is  suspended  within  the 
poles  of  a  magnet,  as  in  fig.  706,  when  the  soldering 
of  the  ring  is  heated,  a  revolution  is  set  up,  through 
the  influence  of  the  magnet  on  the  electric  current, 
quite  analogous  to  similar  electro-magnetic  motions. 

Cold  produced  by  electrical  currents. — If  we 
pass  a  feeble  current  of  electricity  through  a  pair  of 
antimony  and  bismuth,  the  temperature  of  the  system 
rises,  if  the  current  passes  from  the  former  to  the 
latter ;  but  if  from  the  bismuth  to  the  antimony,  cold  is  produced  in 
the  compound  bar.  If  the  reduction  of  temperature  is  slightly  aided 
artificially,  water  contained  in  a  cavity  in  one  of  the  bars  may  be  frozen. 
Thus  we  see  that,  as  a  change  of  temperature  disturbs  the  electrical 
equilibrium,  so,  conversely,  the  disturbance  of  the  latter  produces  the 
former. 

942.  Melloni's  thermo-multiplier. — We  have  already  alluded  to 
this  delicate  metallic  thermometer,  §  588,  and  have  shown  its  applica- 
tion in  the  phenomena  of  dia-  708  707 
thermancy  (642).     This  instru- 
ment  consists   of   a   series    of 

small  bars  of  antimony  and  bis- 
muth, a  and  b,  fig.  707,  soldered 
together  at  their  alternate  ends. 
Two  wires  connect  the  opposite 
members,  n  and  m,  fig.  708,  of 
this  battery,  with  a  galvanoma- 
ter.  The  needle  of  the  galva- 
nometer is  suspended  over  a  graduated  circle,  and  moves  in  exact 
accordance  with  a  thermo-electric  current  produced  by  the  battery. 
The  least  difference  in  temperature  between  the  opposite  faces  of  this 
battery,  produces  a  thermo-electric  current,  deflecting  the  needle  of 
the  galvanometer,  fig.  658,  as  already  explained  in  §  642. 

II.     ANIMAL  ELECTRICITY. 

943.  The  galvanic  current.— We  have  already  spoken  of  the  di* 


ELECTRICITY. 


637 


covery  by  Galvani  of  electrical  currents  in  animals,  living,  or  recently 
dead,  flowing  from  the  outer  or  cutaneous,  to  the  inner  or  709 
mucous  surface.  Thus,  when  contact  is  made  between  the 
muscles  of  the  thigh  and  the  lumbar  nerves,  by  bending 
the  legs  of  a  vigorous  frog,  fig.  709,  contractions  imme- 
diately follow.  Aldini,  who  was  a  zealous  advocate  of 
Galvani's  views,  during  the  controversy  between  the  fol- 
lowers of  Galvani  and  Volta,  demonstrated  the  existence 
of  such  a  current  in  other  animals  by  the  legs  of  a  frog  used 
as  a  galvanoscope.  For  this  purpose,  he  brought  the 
lumbar  nerve  of  a  frog,  held  as  in  fig.  710,  in  contact  with 
the  tongue  of  an  ox  lately  killed,  while  the  hand  of  the  operator,  wet 
with  salt  water,  grasped  an  ear  of  the  ani*  710 

mal  to  complete  the  circuit.  The  legs  were 
then  convulsed  as  often  as  the  nerves  touch 
the  mucous  surface  of  the  tongue.  The  same 
delicate  electroscope  also  shows  similar  ex- 
citement when  its  pendulous  ischiatic  nerves 
touch  the  human  tongue, — the  toe  of  the 
frog  being  held  between  the  moistened 
thumb  and  finger  of  the  experimenter. 

Matteucci,  of  Pisa,  in  1837  (forty  years 
after  Galvani's  result  was  obtained),  has  the 
merit  of  reviving  Galvani's  original  and  cor- 
rect opinion  as  to  the  vital  source  of  this 
electricity.  He  demonstrated,  that  a  current  of  positive  electricity  is 
always  circulating  from  the  interior  to  the  exterior  of  a  muscle,  and  that, 
although  the  quantity  is  exceedingly  small,  yet,  by  arranging  a  series  of 
muscles,  having  their  exterior  and  interior  surfaces  alternately  con- 
nected, he  produced  suffi  711 
cient  electricity  to  cause 
decided  effects.  By  a  series 


decomposed  the  iodid  of 

potassium,  deflected  a  galvanometer  needle  to  90°,  and,  by 
a  condenser,  caused  the  gold  leaves  of  an  electroscope  to 
diverge.  The  irritable  muscles  of  the  frog's  legs  form  an 
electroscope  fifty-six  thousand  times  more  delicate  than  the 
most  delicate  gold-leaf  electrometer.  When  the  pendulous 
nerve  of  a  single  leg,  arranged  in  a  glass  tube,  as  in  fig.  712, 
is  touched  in  the  places  where  electrical  excitement  is  suspected,  the 
66* 


638  PHYSICS    OF    IMPONDERABLE    AGENTS. 

muscles  in  the  tube  are  instantly  convulsed.  Du  Bois  Raymond,  of 
Vienna,  has  demonstrated  the  existence  of  these  currents,  in  his  own 
person,  by  the  use  of  the  galvanometer,  for  which  purpose  the  muscles 
of  the  hands  and  arms  are  alternately  contracted  on  a  metallic  bar  in 
connection  with  a  galvanometer. 

944.  Electrical   animals. — In  some  marine  and  fresh-water  suii- 
mals,  a  special  apparatus  exists,  adapted  to  produce,  at  pleasure,  pow- 
erful currents  of  statical  electricity,  either  as  a  means  of  defence,  or  of 
capturing  their  prey.     Of  these,  the  electrical  eel,  of  Surinam,  first 
described  by  Humboldt,  and  the  cramp-jish,  or  torpedo,  a  flat  fish  found 
on  our  own  coast,  are  the  most  remarkable.     They  have  an  alternate 
arrangement  of  cellular  tissue  and  nervous  matter  in  thin  ulates  of  a 
polygonal  form,  constituting  a  perpetually  charged  electrical  battery, 
arranged  in  the  manner  of  a  pile.    By  touching  their  opposite  surfaces, 
a  very  violent  shock  is  received,  such  as  to  disable  a  very  nowerful 
man,  or  even  a  horse.     Prof.  Matteucci  has  shown  us  how  to  charge  a 
Leyden  jar,  by  placing  the  torpedo  between  two  plates,  arranged  like 
the  plates  of  a  condenser ;  and  Faraday  has  published  an  interesting 
account  of  his  experiments  with  the  eels  of  Surinam,  from  which  he 
not  only  obtained  shocks,  but  made  magnets,  deflected  the  galvanome- 
ter,  produced   chemical  decompositions,  evolved   heat  and  electrical 
sparks.    (Expt.  Res.  1749-1795.)    The  student  is  also  referred  to  Prof. 
Matteucci's  interesting  "  Lectures  on  Living  Beings,"  for  further  details 
on  this  very  interesting  subject,  and  to  a  memoir,  on  the  American 
Torpedo  (Dr.  D.  H.  Storer,  Am.  Jour.  Sci.  [1],  XLV.,  164). 

945.  Electricity  of   plants. — Pouillet,   in  his   researches  on  the 
origin  of  atmospheric  electricity,  made  the  interesting  discovery  of  the 
disengagement  of  negative,  electricity  during  the  germination  of  seeds, 
and  the  growth  of  plants.     This  observer  estimates  that  a  surface  of 
100  square  yards  covered  with  vegetation  disengages,  in  a  day,  more 
electricity  than  is  required  to  charge  the  most  powerful  Leyden  battery. 

Currents  of  electricity  have  also  been  detected  in  fruits,  and  in  the 
bark,  roots,  and  leaves  of  growing  plants ;  the  roots,  and  all  internal 
parts  of  plants  filled  with  juice,  being,  according  to  Buff,  negative  with 
relation  to  the  exterior  or  less  humid  parts. 

I  For  Probkms  on  Electricity,  see  end  of  Meteorology.} 


APPENDIX. 

CHAPTER  I. 

METEOROLOGY. 

946.  Meteorology  is  that  branch  of  natural  philosophy  which  treats 
af  the  atmosphere  and  its  phenomena.     The  subject  may  properly  be 
divided  into — 1st,  Climatology ;  2d,  Aerial  phenomena,  comprehending 
winds,  hurricanes,  and  water-spouts ;  3d,  Aqueous  phenomena,  includ- 
ing fogs,  clouds,  rains,  dew,  snow,  and  hail ;  4th,  Luminous  and  elec- 
trical phenomena,  as  lightning,  rainbows,  and  aurora  borealis. 

Our  narrow  lin\its  of  space  restrict  our  remarks  on  this  interesting 
subject  to  a  very  inadequate  rehearsal  of  its  principles.  The  student 
will  refer  to  the  works  of  Espy  and  Blodget,  and  the  papers  of  Coffin, 
Henry,  Loomis,  Redfield  and  others,  in  the  transactions  of  the  Ameri- 
can Philosophical  Society,  publications  of  the  Smithsonian  Institution, 
the  United  States  Patent  Office,  and  the  American  Journal  of  Science, 
for  an  exhibition  of  the  American  results  in  this  science, 
g  1.  Climatology. 

947.  Climates,  seasons. — By  climate  is  meant  the  condition  of  a 
place  in  relation  to  the  various  phenomena  of  the  atmosphere,  as  tem- 
perature, moisture,  &c.     Thus,  we  speak  of  a  warm  climate,  a  dry 
climate,  &c. 

A  season  is  one  of  the  four  divisions  of  the  year,  spring,  summer, 
autumn,  and  winter.  Astronomical  seasons  are  regulated  according  to 
the  march  of  the  sun.  In  meteorology  it  is  sought  to  divide  them 
according  to  the  march  of  temperature.  Winter  being  the  most  rigor- 
ous of  seasons,  it  is  so  arranged  that  its  coldest  days  (about  January 
15th)  fall  in  the  middle  of  the  season.  Hence,  winter  consists  of  De- 
cember, January,  and  February ;  spring  of  March,  April,  and  May, 
&c.  Few  meteorologists  have  regard  to  the  astronomical  divisions, 
which  make  winter  begin  December  21st. 

948.  Influence  of  the  sun. — The  sun  is  the  principal  cause  that 
regulates  variations  in  temperature.     In  proportion  as  this  luminary 
rises  above  the  horizon,  the  heat  increases ;  it  diminishes  as  soon  as  it 
sets.     The  temperature,  also,  depends  on  the  time  it  remains  above  the 
horizon.     The  sun,  in  winter,  sends  its  rays  obliquely  upon  the  earth, 
and  at  this  season,  therefore,  less  heat  is  received  than  in  summer, 
when  its  rays  are  more  nearly  perpendicular.     Mathematicians  have 

(639) 


b40  APPENDIX. 

in  vain  endeavored  to  deduce  the  temperature  of  days  and  seasons 
from  the  height  of  the  sun  above  the  horizon.  This  failure  is  owing 
to  many  accidental  and  local  causes,  which  modify  the  result, — as  ele- 
vation above  the  ocean,  inclination  of  the  surface,  vicinity  of  seas,  lakes, 
or  mountains,  prevalent  winds,  &c. 

949.  Meteorological  observations,   to  be  compared  with  each 
other,  especially  when  made  in  different  locations,  should  be  made  at 
certain  fixed  hours  of  the  day.     The  hours  regarded  as  most  suitable 
for  this  purpose,  are  6  A.  M.,  2  F.  M.,  and  10  P.  M.     To  these  hours  are 
sometimes  added  9  A.  M.,  and  6  p.  M. 

950.  Mean  temperature. — The  mean  or  average  daily  tempera- 
ture is  commonly  obtained  by  observing  the  standard  thermometer  at 
stated  times  during  the  day,  and  then  dividing  the  sum  of  these  tem- 
peratures, respectively,  by  the  number  of  observations.     It  has  been 
ascertained,  that   the  mean   temperature  deduced  from  observations 
taken  at  6  A.  M.,  2  p.  M.,  and  10  p.  M.,  corresponds  almost  exactly  with 
the  mean  obtained  from  observations   taken   every  hour  in  the  24 ; 
hence  the  three   hours  named  are   considered    the   proper  hours  for 
taking  observations.    The  lowest  temperature  of  the  day  occurs  shortly 
before  sunrise ;  the  highest  a  few  hours  after  noon.     The  mean  daily 
temperature,  at  Philadelphia,  is  found  to  be  one  degree  above  the  tem- 
perature at  9  A.  M. 

By  taking  the  average  of  all  the  mean  daily  temperatures  throughout 
the  year,  the  mean  annual  temperature  is  obtained. 

951.  Monthly  variations  in  temperature. — In  the  successive  months 
of  the  year,  there  is  a  regular  variation  in  temperature.     From  the 
middle  of  January,  the  temperature  rises,  at  first  slowly,  in  April  and 
May  rapidly,  then  less  rapidly  to  the  end  of  July,  when  it  attains  its 
maximum.     It  falls  first  slowly  in  August,  rapidly  in  September  and 
October,  and  reaches  the  minimum  about  the  middle  of  January. 

In  the  United  States,  the  monthly  variations  of  temperature  are  nearly  as 
follows.  (The  figures  attached  to  the  signs  -\-  and  —  by  the  side  of  each  month, 
signify  the  number  of  degrees  colder  or  warmer  it  is  than  the  one  immediately 
preceding.) 

January,  the  coldest;  February,  +2°  to  4°;  March,  8°  to  10°;  April,  10°; 
May,  9°  to  12°;  June,  7°  to  9°;  July,  4°  to  6°;  August,  —1°  to  3°;  September, 
—5°  to  8°;  October,  —8°  to  10°;  November,  —10°  to  14°;  December,  —10°  to 
15°.  The  coldest  days  are  generally  about  the  15th  of  January;  the  warmest, 
near  the  25th  of  July.  The  means  of  the  months  of  April  and  October,  are 
very  near  the  annual  mean. 

952.  The  range  of  temperature  during  the  year,  is  due  to  variations 
in  the  length  of  days  and  nights,  and  the  height  of  the  sun  above  the 
horizon  at  noon. 

In  January,  when  the  days  begin  to  increase  in  length,  the  sun  acts  with  more 
force,  because  its  angular  height  is  greater,  and  because  it  remains  longer  above 


METEOROLOGY. 


641 


the  horizon.  This  change  is  slow  at  first,  and  it  is  only  towards  the  vernal 
equinox  that  the  increase  in  temperature  is  considerable.  The  days  being  then 
longer  than  the  nights,  the  earth  receives  more  heat  than  it  loses  by  radiation. 
The  temperature  increases  more  slowly  as  the  summer  solstice  is  approached, 
because  the  changes  in  the  height  of  the  sun  and  length  of  the  day,  are  small. 
After  the  solstice,  the  temperature  continues  to  increase,  until  about  July  25th ; 
the  heat  received  through  the  day  being  still  greater  than  the  quantity  lost 
during  the  night.  As  the  days  decrease  in  length,  and  the  sun  approaches  the 
equator,  the  temperature  falls,  and  attains  its  minimum  near  the  middle  of 
January.  For  the  extremes  of  natural  temperature,  compare  section  744. 

953.  Variations  of  temperature  in  latitude. — The  mean  tem- 
perature of  different  places  on  the  same  latitude,  varies  according  to 
the  height  of  the  sun  at  mid-day  above  the  horizon  at  these  points. 
The  highest  temperature  is,  therefore,  found  at  the  equator ;  it  dimin- 
ishes either  way  to  the  poles. 

The  mean  summer  temperature  of  regions  midway  between  the  poles  and  the 
equator,  may  be  as  high  as  at  the  equator,  because  the  sun  is  above  the  horizon 
a  greater  number  of  hours.  At  the  poles,  however,  where  the  sun  is  above  the 
horizon  during  six  months  of  the  year,  the  rays  are  directed  so  obliquely  that 
their  calorific  action  is  very  feeble. 

The  temperature  is  not  the  same  for  places  in  the  same  latitude  in 
the  two  hemispheres,  as  is  seen  in  the  following  table : — 


Places. 

Latitude. 

Temp. 

Places. 

Latitude.       Temp. 

Falkland  Isles,     . 
Buenos  Ayres, 
Rio  Janeiro,     .     . 

51°  S. 
34°  36'  S. 

22°  56'  S. 

47°'23 
62°-6 
73°-96 

London,.     ... 
Savannah,  .     .     . 
Calcutta,     .     .     . 

51°31'N. 
32°05'N. 
22°35'N. 

50°-72 
64°-58 
78°-44 

This  variation  is  owing  to  a  variety  of  local  causes,  such  as  the  ele- 
vation and  form  of  the  land,  proximity  to  large  bodies  of  water,  the 
general  direction  of  winds,  &c. 

954.  Variations  of  temperature  in  altitude. — The  average  diminu- 
tion in  temperature  in  ascending  from  the  sea  level  is  1°  F.  for  every  300  feet. 
Supposing  the  average  temperature  of  the  air  at  the  level  of  the  sea,  near  the 
equator,  to  be  80°,  and  toward  the  poles  0°,  the  figures  in  the  second  and  third 
column  of  the  following  table  will  express  approximately  the  temperature  at  dif- 
ferent elevations.  (From  Daniell.) 

DECREASE  OP  TEMPERATURE  IN  THE  ATMOSPHERE  PROM  ELEVATION. 


Altitude  in  feet. 

Equatorial  tempera- 
ture. 

Arctic  temperature. 

0- 

80° 

0° 

5,000- 

64°-4 

-  18°-5 

10,000- 

48°-4 

—  37°-8 

15,000- 

31°-4 

—  58°-8 

20,000- 

12°-8 

-  82°-l 

25,000- 

—  7°-6 

—  109°-1 

30,000- 

—  30°-7 

—  140°-3 

642 


APPENDIX. 


955.  Limit  of  perpetual  snow. — It  follows  from  what  has  just 
been  stated,  that  in  every  latitude,  at  a  certain  elevation,  there  must 
be  a  point  where  moisture  once  frozen  must  ever  remain  congealed. 
The  lowest  point  at  which  this  is  attained  is  called  the  limit  of  per- 
petual snow,  or  the  snow-line.  This  point  is  generally  highest  near  the 
equator,  and  sinks  towards  either  pole.  There  are,  however,  numerous 
exceptions  to  this  rule. 

LIMIT    OF    PERPETUAL    SNOW    AT    DIFFERENT    PLACES. 


Places. 

Latitude. 

Snow-lines. 

Straits  of  Magellan,    
Chili,     
Quito,    ...          

54°  S. 
41°  S. 
00° 

3760  feet 
•  6009     < 
15,807     ' 

Himalaya,  North  side,     .     ,     .     . 
Alps,      

30°  15'  N. 

42°  N. 

16,719     < 

8220     « 

W   Cordilleras,  

14°  30'  S. 

18,631     ' 

19°  N. 

14,763     ' 

_$3tna,    .          

37°  30'  N. 

9531     l 

Kamtschatka       .                               . 

56°  40'  N 

5248     < 

It  has  been  observed  that  the  different  heights  of  perpetual  frost  decrease 
rery  slowly  as  we  recede  from  the  equator  until  we  reach  the  limit  of  the  torrid 
tone,  when  they  decrease  more  rapidly.  The  average  difference  for  every  5°  of 
latitude  in  the  temperate  zone  is  1318  feet,  while  from  the  equator  to  30°  the 
average  is  only  664  feet,  and  from  60°  to  80°  of  latitude  it  is  only  891  feet.  The 
limit  of  perpetual  snow  presents  remarkable  and  inexplicable  phenomena  at 
different  points :  thus  it  is  much  higher  in  the  Himalayas,  latitude  14°  15'  N., 
than  at  the  equator.  Humboldt  remarks  that  the  limit  is  not  due  alone  to 
geographical  latitude,  that  it  is  owing  to  a  combination  of  many  causes,  such  as 
differences  in  the  temperature  of  each  season,  the  direction  of  the  winds,  the 
habitual  dryness  or  humidity  of  the  atmosphere,  the  form  of  the  mountain,  its 
vicinity  to  other  peaks,  <fec. 

956.  Isothermal  lines. — If  all  the  points  whose  mean  temperature 
is  the  same  are  connected  by  lines,  a  series  of  curves  are  obtained, 
which  Humboldt  was  the  first  to  trace  on  charts,  and  which  he  has 
named  isothermes,  or  isothermal  lines  (from  Iffoq,  equal,  and  OZpiJ.r^ 
heat).  The  latitude  and  longitude  are  the  principal  conditions  which 
determine  the  temperature  of  any  point  upon  the  earth's  surface,  but  the 
influence  of  these  conditions  is  greatly  modified  by  numerous  accidental 
and  local  influences:  hence,  the  isothermal  lines  present  numerous 
sinuosities  instead  of  passing  around  the  earth  parallel  to  any  degree 
of  latitude.  The  introduction  of  isothermes  formed  an  important  epoch 
in  meteorological  science,  for  by  it  have  been  established  the  great  laws 
of  the  distribution  of  heat  over  the  surface  of  the  earth  for  the  four 


METEOROLOGY.  643 

seasons.     The  chart  of  isoclinal  lines,  fig.  543,  serves  also  to  illustrate 
th&  general  direction,  and  place  of  isothermal  lines. 

|  2.    Aerial  Phenomena. 

957.  General  consideration  of  winds. — Wind  is  air  in  motion. 
Winds  are  generally  caused  by  variations  in  the  temperature  of  the 
earth,  produced  in  part  by  the  alternation  of  day  and  night,  and  the 
change  of  the  seasons.     The  air  in  contact  with  the  hotter  portion  of 
the  earth  becomes  heated,  and  being  lighter  than  before,  rises,  while 
the  surrounding  air  rushes  in  below  to  supply  rls  place.    The  revolution 
of  the  earth  on  its  axis,  also  comes  in  as  an  important  modifying  cause 
of  the  thermal  conditions.     Winds  are  also,  sometimes,  caused  by  the 
sudden  displacement  of  large  volumes  of  air,  as  in  the  fall  of  an  ava- 
lanche.    Winds  are  named  from  the  points  of  the  horizon  from  which 
they  blow. 

958.  Propagation  of  winds. — Whether  a  wind  is  first  felt  in  the 
country  from  which  it  comes,  or  in  that  to  which  it  is  directed,  is  still 
an  unsettled  question.    It  would  seem,  however,  that  often  at  least  it  is 
first  felt  in  the  region  to  which  it  is  directed. 

It  has  already  been  said  that  winds  are  caused  by  inequalities  in  the  tempera- 
ture of  the  air.  If  the  air  above  a  certain  region,  as  in  the  tropics,  becomes 
heated,  it  rises,  and  the  air  in  the  vicinity  rushes  into  the  space  abandoned  by  the 
ascending  column.  This  air  becomes  rarefied,  and  this  rarefaction  is  communi- 
cated from  point  to  point,  just  as  the  waves  of  sound  expand.  The  wind  is  thus 
propagated  in  a  direction  opposite  to  that  in  which  it  blows.  Such  winds  are 
called  winds  of  aspiration.  Winds  which  are  propagated  in  the  same  direction 
from  which  they  blow  are  called  winds  of  insufflation.  Franklin  made  some 
interesting  observations  on  winds  of  aspiration.  He  noticed  that  a  violent  north- 
east wind,  which  arose  about  7  o'clock,  p.  M.,  in  Philadelphia,  was  not  felt  at 
Boston  until  11  o'clock  in  the  evening.  Again,  a  violent  south-west  wind  blew 
first  at  Albany,  and  afterwards  at  New  York.  But  the  existence  of  winds  of 
insufflation  is  not  less  well  proven.  The  terrible  hurricane  from  the  south-west, 
on  the  29th  of  November,  1836,  arrived  at  London  at  10  o'clock  in  the  morn- 
ing, at  the  Hague  at  1  o'clock  in  the  afternoon,  at  Amsterdam  at  1£,  at  Hamburg 
at  6,  at  Lubeck  at  7,  and  at  Stettin  at  half-past  9  o'clock  in  the  evening. 

959.  Anemoscopes. — The  direction  of  currents  of  air  blowing  at 
great  heights  may  often  be  determined  by  the  direction  in  which  the 
clouds  move.   The  direction  in  which  surface  winds  move  is  determined 
by  means  of  anemoscopes  (from  avspoq,  wind,  and  0x0x6$,  one  who 
watches). 

The  ordinary  vane  is  the  simplest  anemoscope.  From  its  position  on  the  top 
of  an  edifice,  observations  of  it  are  extremely  inconvenient,  and  as  ordinarily 
constructed,  it  is  not  sufficiently  delicate  to  move  with  slight  agitations  of  the 
air.  Anemoscopes,  suitable  for  accurate  observation,  are  variously  constructed. 
They  may  consist  of  two  or  more  fan-wheels,  whose  axis  supported  horizontally 
is  in  connection  with  a  vertical  bar.  The  lower  end  of  this  bar  is  delicately 


644 


APPENDIX. 


supported,  and  has  a  needle  attached  to  it  at  right  angles,  moving  over  a  com- 
pass dial-plate.     The  needle  points  upon  the  dial  the  direction  of  the  wind. 

960.  Anemometers  (from  avspioq,  wind,  and  p.irpov,  measure)  are 
instruments  designed  to  measure  the  velocity  of  winds. 

The  velocity  of  winds  is  indicated  by  the  force  with  which  they  move,  i.  e., 
the  pressure  they  exert.  Some  anemometers  are  constructed  so  as  to  exhibit  the 
amount  of  pressure  excited  by  a  wind  upon  a  plate  placed  perpendicular  to  its 
own  direction.  This  plate  may  be  supported  on  a  spiral  spring,  the  extent  of 
its  compression  indicating  the  force  of  the  wind.  Fig.  713  represents  a  simple 
form  of  this  class  of  instruments.  Other 
anemometers  indicate  the  velocity  of  the 
wind  by  the  number  of  revolutions  given 
to  a  fan-wheel  in  a  given  time.  Such  an 
one  is  Woltmann's  anemometer.  It  con- 
sists essentially  of  a  small  wind-mill,  to 
which  is  attached  an  index  marking  the 
number  of  revolutions  per  minute.  The 
stronger  the  wind,  the  greater  the  number  of  revolutions  made.  The  necessary 
data  for  ascertaining  correctly  with  this  instrument  the  velocities  of  winds  are 
easily  obtained  as  follows : — Nothing  more  is  necessary,  than  on  a  calm  day,  to 
travel  with  the  apparatus  on  a  carriage  or  rail  car,  observing  the  number  of  re- 
volutions made  in  going  any  known  distance  in  a  given  time.  The  effect  will 
be  the  same  as  if  the  air  was  in  motion.  A  table  is  then  constructed,  indicating 
the  velocity  of  a  wind  which  turns  the  sails  forty,  fifty,  sixty,  or  more  times  per 
minute. 

Anemometers  of  very  various  forms  have  been  designed.     No  one  yet  con- 
structed indicates  the  velocity  of  winds  with  absolute  precision. 

961.  The  velocity  of  winds  varies  from  that  which  scarcely  moves 
a  leaf  to  that  which  overthrows  the  staunchest  oak. 

VELOCITY  AND  POWER  OP  WINDS  (Smeaton). 


Velocity  of  the  wind. 
Miles  per  hour. 

Perpendicular  force  on  one 
sq.  ft.  iu  Ibs.  avoirdupois. 

Common  appellation  of  such 
winds. 

1 

•005 

Hardly  perceptible. 

4 
5 

•079 
•123 

.  Gentle  wind. 

n 

15 

•492 
1-107 

Pleasant  brisk  gale. 

20 
25 

1-968 
3-075 

Very  brisk. 

30 
35 

4-429 
6-027 

. 

High  wind. 

40 

7-873 

Very  high. 

50 

12-300 

Storm. 

60 

17-715 

Great  storm. 

80 

31-490 

Hurricane. 

100 

49-200 

Violent  hurricane. 

Formulae. — The  following  formulae  for  determining  the  velocity  of 


METEOROLOGY.  645 

winds  from  the  observed  pressures,  have  been  deduced  from  Smeaton's 
table  given  above : — 

If  F  represents  the  velocity  per  hour  in  miles,  and  P  represents  the  pressure 
sn  a  square  foot  of  surface  at  right  angles  to  the  direction  of  the  wind : — 

p 

or   F  =  14-257-i/P. 

0-00492 

The  pressure  in  pounds  avoirdupois,  on  a  square  foot  of  surface,  when  the  wind 
moves  one  mile  an  hour,  being  =  0-00492  Ibs. 

To  obtain  the  velocity  per  second  in  feet,  we  multiply  by  5280  (the  number  offset 
in  a  mile),  and  divide  by  3600,  the  number  of  seconds  in  an  hour,  and  we  have 

5280         5280  ^ 
^  3600  ~~"  3600  ' 

Winds  are  divided  into  three  classes,  viz.,  regular,  periodical  and 
variable. 

962.  Regular  winds  are  those  which  blow  continuously  in  a  nearly 
constant  direction,  as  the  trade  winds. 

Trade  winds  occur  in  the  equatorial  regions,  on  both  sides  of  the 
equator  to  about  30°  of  latitude.  Those  in  the  northern  hemisphere 
blow  from  the  north-east  to  the  south-west ;  those  in  the  southern  hemis- 
phere from  the  south-east  to  the  north-west. 

These  winds  are  produced  by  the  unequal  distribution  of  heat  upon  the  surface 
of  the  earth,  and  by  the  rotation  of  the  earth  on  its  axis.  From  the  vertical 
position  of  the  sun,  the  equatorial  regions  are  intensely  heated,  the  temperature 
gradually  diminishing  towards  the  poles.  The  heated  air,  above  the  equator, 
rises  and  blows  off  in  the  upper  regions  of  the  atmosphere  towards  either  pole. 
At  the  same  time,  currents  are  established  on  the  surface  of  the  earth  to  supply 
to  the  equatorial  regions  the  air  which  the  upper  currents  have  carried  off.  If 
the  earth  were  at  rest,  these  winds  would  blow  due  north  and  south.  But  the 
earth  is  revolving  on  its  axis,  from  west  to  east,  at  the  equator ;  therefore,  the 
eastern  velocity  is  greatest,  but  it  gradually  diminishes  towards  the  poles.  In 
consequence  of  this,  the  wind  blowing  from  the  north  pole,  towards  the  equatoj:, 
acquires  a  westerly  direction,  and  seems  to  come  from  the  north-east,  and  for 
the  same  reason,  the  wind  blowing  from  the  south  pole  towards  the  equator,  also 
acquires  a  westerly  direction,  and  seems  to  come  from  the  south-east. 

These  trade  winds  are  not  stationary,  moving  to  the  north  in  the  summer  of 
the  northern  hemisphere,  and  south  as  the  sun  withdraws  to  the  southern  tropic. 

The  general  direction  of  these  trade  winds  is  no  more  altered  by  the  form  of 
continents,  their  elevation  and  headlands,  than  is  the  general  course  of  the 
waters  in  a  river  by  rocks  in  its  bed,  though  abrading  surfaces  and  irregulari- 
ties may  produce  a  thousand  eddies  in  the  main  stream. 

963.  Periodical  winds  are  those  which  blow  regularly  in  the  same 
direction,  at  the  same  seasons  of  the  year,  or  hours  of  the  day.     The 
most  interesting  winds  of  this  class  are  the  monsoons,  and  the  land  and 
the  sea  breezes. 

The  monsoons  occur  within,  or  near  the  tropics;  they  blow  from  a  certain 
quarter  about  one-half  of  the  year,  and  from  an  opposite  point  during  the  other 
half.  The  cause  of  the  monsoons  is  found  in  the  effect  produced  by  the  sun  in 

67 


646 


APPENDIX. 


his  annual  progress  from  one  tropic  to  another,  successively  heating  the  land  on 
either  side  of  the  equator.  The  simoon  is  a  periodical  wind  which  blows  over 
the  deserts  of  Asia  and  Africa;  it  is  noted  for  its  high  temperature,  and  the 
sand  which  it  raises  in  the  atmosphere,  and  carries  along  with  it.  This  wind 
from  the  Great  Sahara  desert  blows  over  Algeria  and  Italy,  and  reaches  even 
the  north  shores  of  the  Mediterranean,  where  it  receives  the  name  of  sirocco. 

On  the  coasts  and  islands  within  the  tropics,  and  to  some  extent  in  temperate 
regions,  a  sea  breeze  daily  occurs  flowing  from  the  sea  to  the  land  during  the 
day;  as  it  gradually  subsides,  it  is  succeeded  by  a  land  breeze,  flowing  from  the 
land  to  the  sea.  In  some  places  these  breezes  are  scarcely  perceptible  beyond 
the  shore ;  in  others,  they  extend  inland  for  miles. 

The  causes  of  the  land  and  sea  breezes  are  very  apparent.  During  the  day, 
while  the  sun  shines,  the  land  acquires  a  higher  temperature  than  the  water  of  the 
surrounding  ocean.  The  air,  above  the  land,  becomes  heated,  and  rises.  To 
supply  the  place  of  that  which  has  risen,  air  flows  in  from  the  sea,  constituting 
the  sea  breeze.  But  when  the  sun  descends,  the  land  rapidly  loses  its  heat,  by 
radiation,  while  the  temperature  of  the  ocean  is  scarcely  changed.  In  conse- 
quence of  this,  the  air  above  the  land  becomes  cooled,  and  therefore  more  dense, 
and  flows  towards  the  water,  constituting  the  land  breeze.  At  the  same  time,  in 
the  higher  regions  of  the  atmosphere,  air  flows  in  from  the  sea  to  the  land. 

964.  Variable  winds  are  those  which  blow  sometimes  in  one  direc- 
tion, sometimes  in  another.     The  direction  of  winds  is  influenced  by 
numerous  causes,  as  the  nature  and  form  of  the  surface  of  the  earth, 
the  proximity  of  large  bodies  of  water,  &c.     In  these  latitudes,  the  di- 
rection of  the  prevailing  winds  is  from  the  north-west  to  the  south-east. 

965.  General  direction  of  winds  in  the  higher  latitudes. — In 
the   table   given   below,  the  relative  frequency  of  different  winds  is 
given.     The  total  number  of  winds  in  each  country  is  represented  ly 
1000  ;  the  figures  in  the  table  represent  their  relative  frequency. 

FREQUENCY    OF    DIFFERENT    WINDS. 


Countries. 

N. 

N.  E. 

E. 

S.  E. 

S. 

S.  W. 

W. 

N.W. 

England,   .  .  . 

82 

Ill 

99 

81 

Ill 

225 

171 

120 

France,    .  .  . 

126 

140 

84 

76 

117 

192 

155 

110 

Germany,  . 

84 

98 

119 

87 

97 

185 

198 

132 

Denmark,  .  .  . 

65 

98 

100 

129 

92 

198 

161 

156 

Sweden,  .... 

102 

104 

80 

110 

128 

210 

159 

106 

Russia,  .... 

99 

191 

81 

130 

98 

143 

166 

192 

North  America,  . 

96 

116 

49 

108 

123 

197 

101 

210 

In  these  countries  there  is  a  predominance  of  south-west  winds,  with  the 
exception  of  Russia,  where  the  greater  proportion  are  from  the  north-west.  In 
all  the  northern  hemisphere  there  is  a  predominance  of  westerly  winds.  This  is 
shown  by  the  fact  that  the  average  length  of  the  voyage  from  New  York  to 
Liverpool  by  packet  is  but  23  days,  while  that  of  the  return  voyage  is  40.  In 
the  high  southern  latitudes  the  same  thing  is  observed.  Lieut.  Maury  remarks 
that  at  Cape  Horn  there  are  three  times  as  many  westerly  as  easterly  winds. 


METEOROLOGY.  647 

96G.  Physical  properties  of  winds. — Winds  are  hot,  cold,  dry, 
or  moist,  according  to  the  direction  from  which  they 'come,  and  the 
kind  of  surface  over  which  they  pass. 

If  they  come  over  the  sea,  from  lower  latitudes,  they  are  warm  and 
moist ;  if  across  the  land,  and  from  the  north,  they  are  cold  and  dry. 
Our  north-east  winds  are  cold  and  moist,  because  they  come  from  the 
north,  over  the  Atlantic  Ocean.  South  winds  are  here  warm  and 
humid  ;  north  winds  cold  and  dry. 

967.  Hot  winds, — Over  the  deserts  of  Asia  and  Africa,  an  intensely 
hot  wind  occasionally  prevails.     In  Arabia,  it  is  called  simoon,  signi- 
fying poisonous :  in  Egypt,  khamsin,  because  it  blows  forty  days.     In 
the  western  part  of  the  Great  Desert,  and  in  Guinea,  it  bears  the  name 
of  harrnattan. 

The  soil  of  these  countries  is  uniformly  covered  with  a  fine  reddish  sand, 
which  becomes  prodigiously  heated  by  the  sun's  rays.  As  the  wind  passes  ovei 
this  surface,  it  becomes  intensely  heated ;  the  fine  particles  of  sand  are  raised  in 
the  air,  giving  a  reddish  or  purplish  tinge  to  the  atmosphere ;  the  sky  becomes 
obscured,  the  sun  loses  its  brilliancy,  as  the  winds  blow  from  the  desert.  The 
barometer  falls  very  low,  plants  dry  up,  and  evaporation  takes  place  with  great 
rapidity  from  the  surface  of  the  skin,  giving  rise  to  the  greatest  suffering. 
Whole  caravans  have  been  known  to  perish,  the  prey  of  a  consuming  thirst. 

968.  Hurricanes,  or  cyclones,  are  terrific  storms,  often  attended 
by  thunder  and  lightning ;  they  are  distinguished  from  every  other 
tempest  by  their  extent,  their  power,  and  the  sudden  changes  in  their 
direction.     From  numerous  observations,  "it  appears  that  hurricanes 
are  storms  of  wind,  which  revolve  around  an  axis,  upright  or  inclined 
to  the  horizon,  while,  at  the  same  time,  the  body  of  the  storm  has  a 
progressive  motion  over  the  surface  of  the  earth."     This  law  has  been 
established  by  Iledfield  and  Reid.     Their  progressive  velocity  varies 
from  ten  to  thirty  or  forty  miles-  per  hour;  the  rotatory  velocity  is 
sometimes  as  much  as  a  hundred  miles  per  hour.     The  diameter  of  a 
hurricane  is  from  a  hundred  to  five  hundred  miles,  though  sometimes, 
as  in  the  Cuban  hurricanes,  it  is  much  more. 

Fig.  714  shows  the  origin,  rotation,  and  general  course  of  hurricanes  in  both 
the  northern  and  southern  hemispheres.  These  terrible  storms  have  never  been 
known  to  sweep  across  the  equator,  although,  in  one  case,  similar  hurricanes  were 
raging  at  the  same  time,  on  both  sides  of  the  equator. 

A  northern  hurricane  commences  with  a  violent  rotary  motion,  as  shown  by 
the  arrows  at  a,  in  latitude  10°  or  15°  north  of  the  equator,  corresponding  very 
nearly  with  the  sun's  northern  declination,  and  extending  over  an  area  of  from 
50  to  200  or  300  miles,  the  rotary  motion  of  the  storm  tending  inwards  towards 
its  centre.  At  the  same  time  the  general  progress  of  the  storm  is  obliquely 
west  and  northward  until  it  reaches  the  limit  of  tbo  north-east  trade  winds,  where 
it  sweeps  around,  taking  a  north-easterly  direction,  the  vortex  enlarging  as  it 
progresses,  spreading  over  an  area  ot"  000  or  1000  miles,  until  at  last  it  moves 


648 


APPENDIX. 


JAN. TO  APR 


8.L. 


in  a  nearly  easterly  direction,  and  exhausts  its  force  by  its  excessive  enlarge- 
ment, in  latitude  40°  or  50°  N.  714 

Southern  hurricanes  pursue  a  similar  course  in 
the  southern  hemisphere,  as  shown  in  the  lower 
part  of  the  figure.  The  circular  arrows  show  the 
rotation  of  the  air  in  the  area  of  the  cyclone,  and 
the  arrows  in  the  parabolic  curve,  a  b  c,  show  the 
general  course  of  the  moving  storm. 

The  arrow,  NET,  shows  the  region  of  the 
north-east  trade  winds,  and  the  parallel  of  lati- 
tude, L  N  E  T,  shows  their  northern  limit.  The 
arrow,  SET,  and  line,  L  S  E  T,  also  show  the 
region  and  limit  of  the  south-east  trades. 

Between  the  northern  and  southern  hurricane 
regions,  is  the  zone  of  variable  winds,  which  the 
hurricanes  are  not  known  to  pass.  On  either  side 
of  the  zone  of  variable  winds  lie  the  zones  of 
expansion,  in  which  hurricanes  originate.  The 
letters,  D  D,  indicate  the  most  dangerous  portion 
of  the  hurricane  track. 

It  is  now  well  ascertained  that,  in  both 
hemispheres,  the  air  in  a  cyclone  or  hurri- 
cane rotates  in  a  direction  contrary  to  that 
of  the  course  of  the  sun.  Thus,  in  the 
northern  hemisphere,  the  course  of  the  sun  is  from  the  east  around  to 
the  south,  then  to  the  west  and  north,  and  the  moyement  of  the  air  in 
the  hurricane  is  in  the  opposite  direction ;  i.  e.,  from  the  north,  by  the 
west,  south,  and  east,  or  in  a  direction  contrary  to  the  motion  of  the 
hands  of  a  watch,  lying  with  the  face  upward.  In  the  southern  hemi- 
sphere, the  course  of  the  sun  is  from  the  east,  by  north,  west,  and  south, 
and  that  of  the  cyclone  is  from  the  north,  by  east,  south,  and  west,  or 
in  the  direction  of  the  hands  of  a  watch.  East  winds  are,  in  both 
hemispheres,  characteristic  of  a  commencing  hurricane  (i.  e.,  an  east 
wind  is  always  found  on  the  front  of  the  advancing  storm,  as  shown  in 
the  figure) ;  while,  in  general,  west  winds  occur  only  in  the  latter  part 
of  the  storm,  as  decreasing  winds ;  hence,  in  the  northern  hemisphere, 
the  most  dangerous  part  of  a  hurricane  is  in  the  advancing  border  of 
the  right  hand  semicircle,  or  about  the  line  D  D ;  while,  in  the  south- 
ern hemisphere,  the  dangerous  limit,  D  D,  is  the  advancing  quadrant 
of  the  left  hand  semicircle. 

The  effect  of  the  rotary  movement  of  the  hurricane  is  to  accumulate 
the  air  around  its  outer  margin,  with  a  pressure  increasing  as  it  recedes 
from  the  centre ;  consequently,  the  barometer  is  lowest  at  the  middle 
of  a  storm,  and  highest  at  its  extremity.  The  barometer  oscillates 
before  and  during  a  hurricane,  rising  and  falling  rapidly,  owing  to  the 


METEOROLOGY. 


649 


inequality  of  the  pressure  which  causes  the  storm;    so  that: — Great 
barometric  oscillations  generally  announce  the  approach  of  a  tempest. 

By  careful  observation  of  the  barometer,  the  mariner  anticipates  the 
approach  of  a  hurricane,  or  other  dangerous  storm.  So,  also,  by  care- 
ful attention  to  the  course  of  the  winds,  and  the  sailing  directions, 
based  on  the  researches  of  Redfield,  Reid,  and  Maury,  he  knows  how 
t  >  sail  out  of  the  track  of  a  hurricane  after  it  has  commenced. 

969.  Tornadoes  or  whirlwinds  are  distinguished  from  hurricanes, 
chiefly  in  their  extent  and  continuance.     They  are  rarely  more  than  a 
few  hundred  rods  in  breadth,  and  their  whole  track  is  seldom  more 
than  twenty -five  miles  in  length.     The  continuance  of  tornadoes  is  but 
a  few  seconds  at  any  one  place.     They  are  oftentimes  of  great  energy, 
uprooting  trees,  overturning  buildings,  and  destroying  crops. 

970.  Water-spouts  .differ  from  whirlwinds  in  no  other  respect  than 
that  water,  or  vapor  of  water,  is  subjected  to  their  action,  instead  of 
bodies  upon  the  surface  of  the  land. 

Water-spouts  first  appear  as  an  inverted  cone,  extending  downward  from  a 
dark  cloud.  As  the  cone  approaches  the  water,  the  latter  becomes  agitated,  the 
spray  rises  higher  and  higher,  and  finally,  buth  uniting,  there  is  formed  a  con- 
tinuous column  from  the  cloud  to  the  water,  usually  bent  as  in  fig.  715,  but  some- 


lunes  erect.  After  a  little  time,  the  column  breaks,  and  the  phenomena  disap- 
pear. As  to  the  origin  of  water-spouts,  philosophers  are  divided.  Kaemtz,  a 
distinguished  German  meteorologist,  assumes  that  they  are  due  principally  to 
two  opposite  winds,  which  pass  side  by  side,  or  when  a  very  brisk  wind  prevails 
in  the  higher  regions  of  the  atmosphere,  while  it  is  clear  below.  Peltier,  and 
other  physicists,  ascribe  water-spouts  to  an  electrical  cause. 

Water-spouts  are,  in  great  part,  formed  of  atmospheric  water,  as  is  shown  by 
the  fact,  that  the  water  escaping  from  them  is  not  salt,  even  in  the  op6n  s<a*. 
57* 


650  APPENDIX. 

If  the  atmosphere  is  not  moi&t,  there  is  no  condensation  of  vapor,  and  the  only 
noticeable  phenomenon  is  the  violence  of  the  wind  and  its  rotatory  motion. 

971.  General  laws  of  storms. — Great  storms,  in  temperate  climates, 
are  governed  by  general  laws,  presenting  more  or  less  analogy  to  the 
movements  of  hurricanes.  As  a  general  thing,  the  great  storms  which 
pass  over  North  America  have  no  connection  with  the  storms  of  Europe  ; 
and  the  storms  of  both  continents  are  modified  in  their  course  and 
general  phenomena  by  the  configuration  and  elevation  of  the  land. 

Great  storms  of  rain  and  snow,  and  also  lesser  storms,  which  prevail 
in  the  United  States  from  November  to  March,  are  governed  by  the 
following  general  laws,  which  have  been  condensed  from  the  researches 
of  Professors  Espy  (Reports  to  United  States  Senate),  and  Loomis 
(Smithsonian  Contributions,  1860). 

1.  Storms  travel  from  the  region  of  the  Mississippi  eastward  as  far 
as  the  Gulf  of  St.  Lawrence,  and  disappear  in  the  Atlantic  Ocean. 

2.  They  are  accompanied  with  a  depression  of  the  barometer,  often 
amounting  to  an  inch  or  more  below  the  mean  height,  along  a  line  of 
great  extent  from  north  to  south,  the  line  being  curved  with  its  convexity 
eastward.     In  the  front  and  rear  of  the  storm,  there  is  a  rise  of  the 
barometer,  which,  in  some  places,  is  more  than  an  inch  above  the  mean. 

3.  Great  storms  travel  from  the  Mississippi  to  the  Connecticut  River 
in  twenty-four  hours ;  and  from  the  Connecticut  to  Newfoundland  in 
nearly  the  same  time,  or  about  thirty-six  miles  an  hour  ;  though  some- 
times they  appear  to  remain  nearly  stationary  for  four  or  five  days. 

4.  The  area  covered  by  a  storm  is  nearly  circular,  often  of  great 
extent ;  frequently  1000  miles  from  east  to  west,  and  2000  or  3000 
miles  from  north  to  south. 

5.  For  several  hundred  miles,  on  each  side  of  the  centre  of  a  violent 
storm,  the  wind  inclines  inwards  towards  the  area  of  least  pressure, 
and,  at  the  same  time,  it  circulates  around  the  centre  in  a  direction 
contrary  to  the  motion  of  the  hands  of  a  watch.     Compare  |  968. 

6.  On  the  borders  of  the  storm,  near  the  line  of  maximum  pressure, 
the  wind  has  but  little  force,  and  tends  outwards  from  the  line  of  great- 
est pressure. 

7.  The  wind  uniformly  tends  from  an  area  of  high  barometer  towards 
an  area  of  low  barometer. 

8.  In  the  northern  parts  of  the  United  States,  the  wind  generally,  in 
great  storms,  sets  in  from  the  north  of  east,  and  terminates  from  the 
north  of  west ;  and  in  the  southern  states,  the  wind  generally  sets  in 
from  the  south  of  east,  and  terminates  from  the  south  of  west. 

9.  During  the  passage  of  storms,  the  wind  generally  veers  from  the 
".vstward  around  by  the  south,  and  then  towards  the  west. 


METEOROLOGY.  65 1 

10.  In  a  great  storm,  the  area  of  high  thermometer  frequently  does 
not  coincide  with  the  area  of  low  barometer,  or  with  the  centre  of  rain 
and  snow.    But  in  the  United  States,  on  the  north-east  side  of  a  storm, 
at  a  distance  of  500  miles  from  the  area  of  rain  and  snow,  the  ther- 
mometer sometimes  rises  as  much  as  twenty  degrees  above  its  mean 
height. 

11.  In  Europe,  storms  are  often  modified  and  controlled  by  the  Alps 
of  Switzerland,  which  appear,  for  days  together,  to  serve  as  the  centre 
of  great  storms. 

For  the  connection  of  barometric  changes  with  changes  of  weather,  see  sec- 
tion 271 ;  and  for  fuller  discussions  of  the  theory  and  laws  of  storms,  see  the 
works  already  referred  to  above,  and  also  £$  946,  968. 

§  3.   Aqueous  Phenomena. 

972.  Humidity  of  the  air. — Vapor  of  water  is  always  contained  in 
the  air.  This  may  be  demonstrated  by  placing  a  vessel  filled  with  ice 
or  a  freezing  mixture  in  the  atmosphere ;  in  a  little  time  the  vapor 
from  the  air  will  be  condensed  on  the  walls  of  the  vessel,  in  the  form 
of  minute  drops  of  water. 

Air  is  said  to  be  saturated  with  moisture,  when  it  contains  as  much  of  the 
vapor  of  water  as  it  is  capable  of  holding  up  at  a  given  temperature.  That  the 
capacity  for  moisture  is  greater  as  the  temperature  increases,  is  shown  in  the 
following  table : — 

A  body  of  air  can  absorb 

At    32°  F.,  the  160th  part  of  its  own  weight  of  watery  vapor. 
«     59°  "      «      80th  «  "  «  « 

"     86°  "      "      40th  "  "  "  " 

"   113°  "      "      20th  "  "  "  " 

It  will  be  noticed  that  for  every  27°  of  temperature  above  32°,  the  capacity 
of  air  for  moisture  is  doubled.  From  this  it  follows,  that,  while  the  tempera- 
ture of  the  air  advances  in  an  arithmetical  series,  its  capacity  for  moisture  is 
accelerated  in  a  geometrical  series. 

Table  XXI.,  Appendix,  shows  the  weight  of  aqueous  vapor  in  a  cubic 
foot  of  saturated  air,  at  temperatures  from  0°  to  100°  F. 

Absolute   humidity, — relative   humidity. — The   term  absolute 
humidity  of  the  air  has  reference  to  the  quantity  of  moisture  contained^ 
in  a  given  volume.     Relative  humidity  refers  to  the  dampness,  or  its 
proximity  to  saturation  with  aqueous  vapor. 

The  absolute  humidity  is  greatest  in  the  equinoctial  regions,  and  diminishes 
towards  either  pole ;  it  diminishes,  also,  with  the  altitude,  but  the  true  ratio  is 
not  fully  known.  The  absolute  humidity  is  also  greater  on  coasts  than  inland, 
in  summer  than  in  winter,  and  less  in  the  morning  than  about  midday. 

Relative  tumidity  is  dependent  upon  the  mutual  influence  of  absolute  humidity 
and  temperature.  The  atmosphere  is  considered  dry  when  water  rapidly  evapo- 
rates, or  a  wet  substance  quickly  dries.  The  expressions  wet  and  dry  convey 
simply  an  idea  of  the  relative  humidity  of  the  atmosphere,  and  have  no  refer- 


652  APPENDIX. 

ence  to  the  absolute  quantity  of  moisture  present;  for  a  damp  air  is  rendered  dry 
by  raising  its  temperature,  and  a  dry  air  damp  by  cooling  it. 

Near  great  bodies  of  water,  the  atmosphere  generally  contains  a  greater 
amount  of  moisture,  both  absolute  and  relative,  than  at  inland  places,  or  over 
arid  plains  and  deserts. 

973.  Hygrometers  are  instruments  by  which  the  humidity  of  the 
atmosphere  is  determined.  They  are  of  various  kinds,  and  may  be 
classified  as  follows : — chemical  hygrometers,  absorption  hygrometers, 
condensation  hygrometers,  and  psychrometers. 

All  hygroscopic  substances  (viz.,  those  which  have  an  affinity  for  water)  are 
chemical  hygrometers.  The  amount  of  moisture  in  the  air  is  determined  with 
these  substances,  by  filling  a  tube  with  chlorid  of  calcium,  for  example,  and 
passing  a  known  volume  of  air  through  it;  the  increase  in  weight  of  the  tube, 
after  the  experiment,  indicates  the  weight  of  moisture  present  in  the  air.  This 
method  yields  the  best  results,  but  is  difficult  of  execution. 

Saussure's  hygrometer  depends  upon  the  elongation  and  contrac- 
tion of  a  hair  by  increase  or  diminution  of  relative  humidity  ;  but  such 
instruments  afford  no  means  of  accurate  comparison. 

Daniell's  hygrometer  depends  upon  the  condensation  of  moisture 
by  means  of  artificial  cold. 

It  consists  of  a  glass  tube,  bent  twice  at  right  angles,  having  a  bulb  at  either 
extremity.  The  bulb,  A,  fig.  716,  is  partly  filled  with  ether,  into  which  is  inserted 
the  ball  of  a  delicate  thermometer,  enclosed  in  the 
stem  of  the  instrument.  The  tube  is  filled  with  the 
vapor  of  ether,  the  air  having  been  driven  out.  The 
bulb,  B,  is  covered  with  fine  muslin.  Upon  the  sup- 
porting pillar,  a  second  thermometer  is  placed.  In 
order  to  determine  the  dew  point,  or  hygrometric 
state  of  the  atmosphere,  by  this  instrument,  a  few 
drops  of  ether  are  allowed  to  fall  upon  the  muslin- 
covered  bulb,  evaporation  of  the  ether  takes  place, 
the  bulb  is  cooled,  and  condenses  the  ethereal  vapor 
within.  In  consequence  of  this  effect,  the  ether  in 
A  evaporates,  causing  a  reduction  of  temperature, 
indicated  by  the  internal  thermometer.  At  a  certain  "^^  /  --" 

point,  the  atmospheric  moisture  begins  to  form  in  a  ring  of  dew  upon  the  bulb 
A.     The  difference  at  this  moment  between   the  degrees  indicated  by  the  two 
^|:hermometers,  denotes  the  relative  humidity  of  the  atmosphere ;  the  dryer  the 
air,  the  greater  is  this  difference. 

August's  psychrometer  or  hygrometer  of  evaporation  depends 
for  its  action  upon  the  rapidity  of  evaporation  in  the  open  air.  It  con- 
sists of  two  similar  thermometers,  it',  placed  side  by  side,  tig.  717, 
supported  on  a  frame.  The  bulb  of  t'  is  covered  with  fine  muslin,  the 
lower  end  of  which  dips  into  a  small  vessel,  v,  like  a  bird-glass,  con- 
taining water ;  by  this  arrangement,  the  bulb  is  kept  continually  moist. 
Evaporation  takes  place  from  the  moistened  bulb,  with  a  rapidity  vary- 
ing with  the  humidity  of  the  atmosphere,  and  a  corresponding  depression 


METEOROLOGY. 


653 


in  the  temperature  of  the  thermometer  is  produced.  The  hygrometrio 
state  of  the  atmosphere  is  determined  from  the  observed  difference  in  the 
two  thermometers  by  the  use  of  tables  prepared  for  the  purpose.  (Meteo- 
rological and  Physical  Tables,  Smithsonian  Collection.)  717 

This  is  a  very  convenient  instrument  to  determine  the 
condition  of  the  air  in  dwellings  heated  by  different 
methods.  Observations  with  this  instrument  show  how 
much  our  comfort  and  health  depend  upon  preserving 
the  proper  state  of  humidity  or  dryness  in  our  dwellings, 
or  in  the  sick-room. 

974.  Fogs,  or  mists,  are  visible  vapors  that  float  in 
the  atmosphere,  near  the  surface  of  the  earth.     Fogs  are 
produced  by  the  union  of  a  body  of  cool  air  with  one  that 
is  warmer  and  humid.     Many  philosophers,  as  Saussure 
and  Kratzenstein,  consider  that  the  globules  or  vesicles  of 
which  a  fog  is  composed,  are  hollow,  the  water  serving  only 
as  an  envelope  ;  it  is  probable  this  is  true,  in  some  cases : 
there  are  probably  also  mixed  with  the  vesicles  many  mi- 
nute drops  containing  no  free  air.    According  to  Kaemtz, 
the  average   diameter  of  fog  globules  does  not   exceed 
TsVff  °f  an  inch-     Maille,  of  Paris,  has  computed  that  it 
would  require  200,000,000  fog  globules  to  make  a  drop 
of  rain  ^  of  an  inch  in  diameter. 

975.  Dew  is  the  moisture  of  the  air  condensed  by 

coming  in  contact  with  bodies  cooler  than  itself.  The  temperature 
at  which  this  deposition  of  moisture  commences,  is  called  the  dew 
point  (674).  The  dew  point  varies  according  to  the  hygrometric  state 
of  the  atmosphere  ;  being  nearer  the  temperature  of  the  air,  the  more 
completely  the  air  is  saturated  with  moisture.  In  this  climate,  in  sum- 
mer, the  dew  point  is  often  30°  or  more  below  the  temperature  of  the 
atmosphere.  In  India,  it  has  been  known  to  be  as  much  as  61°. 

Cause  of  dew. — Dr.  Wells,  of  London  (born  in  South  Carolina), 
determined,  by  his  researches,  the  cause  of  dew.  It  may  be  given 
briefly  as  follows : — During  the  day,  the  surface  of  the  earth  becomes 
heated  by  the  sun,  and  the  air  is  warmed  by  it.  When  the  sun  goea 
down,  the  earth  continues  to  radiate  heat  without  receiving  any  in 
return,  and  thus  its  temperature  diminishes.  The  air  loses  its  heat 
more  slowly,  and  is  cooled  only  when  it  comes  in  contact  with  the 
cooler  earth.  If  this  cooling  reaches  the  dew  point  of  the  air,  moisture 
is  condensed  in  the  form  of  small  drops  upon  cold  objects  (good  radia- 
tors), as  the  soil  or  vegetation. 

Circumstances    influencing    the    production    of    dew. — The 


654 


APPENDIX. 


amount  of  iew  deposited  in  a  given  time  depends  upon  the  humidity, 
tranquility,  and  serenity  oi  the  air.  Since  dew  is  the  moisture  of  the 
atmosphere  condensed,  it  is  evident  it  must  be  affected  by  the  amount 
the  air  contains.  On  a  windy  night,  the  air  in  contact  with  cold  objects 
is  so  quickly  changed,  that  it  is  not  cooled  down  to  the  dew  point ,  but 
gentle  agitation  of  the  air  favors  the  production  of  dew,  bringing  more 
moist  air  to  furnish  dew  to  cold  objects.  The  most  copious  deposits  of 
dew  take  place  on  cool,  clear  nights.  For,  when  there  are  clouds,  these 
radiate  back  the  heat  which  has  escaped  from  the  earth,  and  thus  pre- 
vent its  cooling,  and  therefore  no  dew  is  deposited.  If  the  clouds  sepa- 
rate only  for  a  short  time,  dew  is  rapidly  deposited. 

Straw,  mats,  boards,  &c.,  used  by  gardeners  to  protect  delicate  plant? 
from  freezing,  act  in  the  same  manner  as  clouds,  to  prevent  the  deposit 
of  dew  or  frost.  See  Fig.  718. 

976.  Substances  upon  which  dew  falls. — Dew  does  not  fall  upon 
all  substances  alike ;  in   consequence  of  differences  in  radiating  ana 
conducting  power,  certain  substances  cool  quicker  and  more  perfectly 
than  others.     The  dusty  road,  the  rocks,  and  barren  soil,  cool  slowly, 
receiving  heat  from  the  earth  by  conduction,  and  therefore  on  them  but 
little  dew  falls.     Trees,  shrubs,  grasses,  and  vegetation  of  every  kind, 
radiate   heat  easily,  and,  on  account  of  their  peculiar  structure,  they 
receive  but  little  heat  from  the  earth,  or  other  objects,  by  conduction  ; 
hence  they  become  rapidly  cooled,  and  abundance  of  dew  is  deposited 
upon  them. 

977.  Frost  is  frozen  dew.    When  the  temperature  of  the  earth  sinks 
in  the  night  to  the  freezing  point,  the  aqueous  vapor  then  deposited 
congeals  in  the  form  of  sparkling  crystals,  known  as  hoarfrost.     Fig. 
718,  from  Stoeckhardt,  in  which  the  arrows  indicate  the  movements  of 

718 


beat,  and  the  numerals  the  temperature  of  the  air,  will  render  the  phe- 
nomena of  dew  and  frost  more  intelligible. 

The  sun's  rays  in  winter,  may,  in  the  day,  warm  the  soil  to  53°,  as 
in  the  figure,  while  the  air  above  the  ground  is  50°.     At  night,  the  ra- 


METEOROLOGY.  655 

diation  into  a  cloudless  sky,  will  reduce  the  temperature  of  the  ground 
to  43°,  or  even  33°,  while  the  air  above  the  same  points  is  46°  or  39°. 
But  a  cloud  resting  above  the  earth  prevents  radiation,  and  reflects  the 
heat  back  to  the  earth.  So  dew  or  frost  will  be  deposited  on  the  upper 
surface  of  a  platform  when  radiation  takes  place  freely,  while  boards, 
like  the  cloud,  reflect  back  the  heat  coming  from  the  ground. 

978.  Clouds  are  masses  of  vapor  that  float  in  the  upper  regions  of 
the  atmosphere.     They  are  distinguished  from  fogs  only  by  their  alti- 
tude ;  they  always  result  from  the  partial  condensation  of  the  vapors 
that  rise  from  the  earth.     As  clouds  often  float  in  regions  whose  tem- 
perature is  many  degrees  below  the  freezing  point,  they  are  sometimes, 
no  doubt,  composed  of  frozen  particles. 

Clouds  being  condensed  moisture,  are  heavier  than  the  air,  and  have  a  ten- 
dency to  fall  to  the  earth.  They  are  kept  suspended  in  the  air,  1.  By  ascending 
currents  during  the  day,  the  warmer  air  dissolving  the  cloud  as  fast  as  it  falls 
into  it.  Such  clouds  are  more  elevated  at  midday  than  in  the  morning,  and 
they  descend  towards  the  earth  at  evening. 

2.  Horizontal  currents  also  oppose  the  fall  of  clouds.     The  minute  vesicles  or 
globules,  whichever  they  may  be,  are  carried  forward  and  dissolved  by  the  drier 
air  on  the  advancing  side  of  the  cloud,  while  on  the  windward  side  of  the  cloud, 
vapor  is  constantly  precipitated. 

3.  The  resistance  of  the  air  opposes  the  rapid  descent  of  clouds.     This  resist- 
ance is  in  the  inverse  proportion   to  the  dimensions  of  the  particles.     For  this 
reason,  considerable  time  would  be  required  for  vapor  to  descend  even  a  few 
hundred  feet.     If,  as  many  writers  suppose,  the  water  of  clouds  exists  in  the 
form  of  minute  vesicles  containing  air,  the  expansion  of  the  enclosed  air  by 
heat  would  at  once  account  for  the  buoyancy  of  clouds  j  for  they  would  float  like 
balloons  in  air  of  their  own  aggregate  density,  and  every  increase  of  heat  would 
increase  their  buoyancy. 

979.  Classification  of  clouds. — Clouds  are  generally  divided  into 
four  great  classes,  viz. :  the  nimbus,  the  cumulus,  the  stratus,  and  the 
cirrus,  as  shown  in  the  diagram,  fig.  719. 

Intermediate  forms  of  clouds  are  distinguished  by  the  names  of  cirro- 
stratus,  cirro-cumulus,  and  cumulo-stratus. 

The  cirrus  (cirrus,  earl)  usually  resembles  a  disheveled  lock  of  hair,  being 
composed  of  streaks  or  feathery  filaments,  assuming  every  variety  of  "figure. 
The  cirrus  floats  at  a  higher  elevation  than  other  clouds,  and  probably  is  often 
composed  of  snow-flakes.  It  is  among^l^r  cirri  that  halos  and  parhelia  are 
formed.  ^K, 

The  cumulus  (cumulus,  heap")  appears^often  in  the  form  of  a  hemisphere, 
resting  on  a  horizontal  base ;  sometimes  in  detached  masses,  gathered  in  one 
vast  cloud,  near  the  horizon.  When  lighted  up  by  the  sun,  they  present  the 
appearance  of  mountains  of  snow.  The  cumulus  is  the  cloud  of  day ;  in  the 
fine  days  of  summer  it  is  most  perfect. 

The  name  of  cirro-cumulus  is  given  to  little  rounded  clouds. 

The  cumuli  owe  their  existence  to  ascending  currents  ;  their  height  varies 
greatly,  but  it  is  always  less  than  that  of  the  cirri. 

Tho  stratus  (stratus,  covering)  ccnsists  of  sheets  of  cloud,  or  layers  of  vapor, 


656  APPENDIX. 

stretching  along  and  resting  upon  the  horizon.    It  forms  about  sunset,  increases 

719 


Stratus.        Cirro-cumulus.  Cirrus. 

during  the  night,  and  disappears  about  sunrise.  It  floats  at  a  moderate  eleva- 
tion above  the  earth. 

The  cirro-stratus  partakes  of  the  character  of  the  cirrus  and  stratus.  It  is 
remarkable  for  its  length  and  thickness.  It  appears,  sometimes,  as  a  long  and 
narrow  band;  at  other  times,  as  composed  of  small  rows  of  clouds  or  bars  of 
vapor.  Cumuli,  heaped  together,  pass  into  the  condition  of  cumulo-stratus, 
which  consists  of  a  horizontal  stratum  of  vapor,  from  which  rise  masses  of 
cumuli.  These  often  assume,  at  the  horizon,  a  dark  tint,  and  pass  into  the 
nimbus  state. 

The  nimbus,  or  rain-cloud  (nimbus,  storm).  This  has  a  characteristic  storm- 
like  form ;  it  is  distinguished  from  others  by  its  uniform  gray  or  blackish  tint, 
and  its  edges  fringed  with  light. 

980.  Rain  is  the  vapor  of  clouds,  or  of  the  air,  precipitated  to  the 
earth  in  drops.  Rain  is  generally  produced  by  the  rapid  union  of  two 
or  more  volumes  of  humid  air,  differing  considerably  in  temperature ; 
the  several  portions,  when  mingled,  being  incapable  of  absorbing  the 
same  amount  of  moisture  that  each  would  retain  if  they  had  not  united. 
If  the  excess  is  great,  it  falls  as  rain  ;  if  it  is  of  slight  amount,  it 
appears  as  cloud.  The  productian  of  rain  is  the  result  of  the  law,  that 
the  capacity  of  air  for  moisture  decreases  in  a  higher  ratio  than  the 
temperature. 

Rain-gauges. — Instruments  for  determining  the  quantity  of  rain,  are 
called  rain-gauges,  ombrometers,  hyctometers,  &c.  They  are  of  very 
various  construction. 

One  of  the  simplest  rain-gauges  consists  of  a  cylindrical  copper  vessel,  fur- 
nished with  a  float;  the  rain  falling  into  the  vessel,  the  float  rises.  The  stem 


METEOROLOGY.  657 

of  the  float  is  accurately  graduated,  so  that  an  increase  in  the  depth  of  the  water 
of  one  one-hundredth  of  an  inch,  is  easily  measured. 

Another  rain-gauge,  a  section  of  which  is  represented  in  fig.  720,  consists  of 
a  cylindrical  copper  vessel,  M,  closed  by  a  cover,  B,  shaped 
like  a  funnel,  with  an  aperture  in  the  centre,  through 
which  the  water  passes  into  the  interior.  This  cover  pre- 
vents loss  by  evaporation.  A  lateral  glass  tube,  A,  care- 
fully graduated,  rises  from  the  base  of  the  vessel.  The 
water  rises  in  the  tube  to  the  same  height  as  in  the  copper 
cylinder.  If  the  apparatus  has  been  placed  in  an  exposed 
situation,  for  a  certain  time,  as  a  month,  and  the  gauge 
shows  three  inches  of  water,  this  indicates  that  the  rain 
that  has  fallen  during  the  interval  would  cover  the  earth 
to  the  depth  of  three  inches,  if  it  were  not  diminished  by 
evappration,  or  infiltration. 

From  a  series  of  experiments  made  at  the  Smithsonian 
Institution,  and  continued  for  several  years,  it  is  found 
that  a  small  cylindrical  gauge,  of  2  inches  in  diameter,  and  about  six  inches  in 
length,  connected  with  a  tube  of  half  the  diameter,  to  retain  and  measure  the 
water,  gives  the  most  accurate  results.  In  still  weather,  it  indicates  the  same 
amount  of  water  as  the  larger  gauges ;  but  when  the  wind  is  high,  it  receives 
more  rain ;  for,  on  account  of  its  small  size,  the  force  of  the  eddy  which  is  pro- 
duced, is  much  less  in  proportion  to  the  drops  of  water.  This  gauge  may  be 
still  further  improved  by  cutting  a  hole  of  the  size  of  the  cylinder,  in  a  circu- 
lar plate  of  tin,  of  4  or  5  inches  in  diameter,  and  soldering  this  to  the  cylinder, 
like  the  riin  of  an  inverted  hat,  three  or  four  inches  below  the  orifice  of  tho 
gauge. 

981.  Distribution  of  rain. — Rain  is  not  equally  distributed  over 
the  surface  of  the  earth.     As  a  general  rule,  it  may  be  stated  that,  the 
higher  the  average  temperature  of  a  country,  the  greater  will  be  the 
amount  of  rain  that  falls  upon  it.     Local  causes,  however,  produce 
remarkable  departures  from  this  rule. 

In  the  tropics,  the  average  yearly  rain  fall  is  ninety-five  inches  ;  in  the  tempe- 
rate zone  it  is  thirty-five  inches.  Within  the  tropics,  the  greatest  quantity  of 
rain  falls  when  the  sun  is  at  its  zenith,  that  is,  in  the  season  corresponding  to 
our  summer.  North  of  the  tropics  it  rains  more  abundantly  in  winter. 

In  certain  regions  there  is  a  periodical  season,  when  rain  is  very  abundant 
for  six  months,  called  the  rainy  season.  During  the  remainder  of  the  year, 
called  the  dry  season,  it  seldom  rains. 

Many  regions  are  destitute  of  rain.  In  Egypt,  it  scarcely  ever  rains. 
Along  the  coast  of  Peru,  is  a  long  strip  of  land  upon  which  no  rain  ever 
descends.  A  similar  destitution  of  rain  .occurs  on  the  coast  of  Africa,  and 
some  parts  of  North  America;  the  intervals  between  the  showers  being  six  or 
seven  years. 

In  Guiana  it  rains  during  a  great  part  of  the  year.;  this  is  also  the  case, 
according  to  Davison,  at  the  Straits  of  Magellan.  In  the  Island  of  Chiloe  (S. 
lat.  43°),  there  is  a  proverbial  saying,  tha.  it  rains  six  days  of  the  week,  and  is 
cloudy  on  the  seventh. 

982.  Days  of  rain. — The  rainy  days  are  more  numerous  in  high 
than  in  low  latitudes,  as  is  seen  in  the  following  table,  although  the 

68 


658  APPENDIX. 

annual  amount  of  rain  which  falls  is  smaller.  Consequently,  the  ordi- 
nary rains  of  the  tropical  regions  are  more  powerful  than  those  of  the 
temperate  regions. 

N.  latitude.  Mean  annual  number  of  rainy  days. 

From  12°  to  43°  78 

"      43°  «  46°  103 

"     46°  "  50°  134 

«      50°  «  60°  161 

In  the  northern  part  of  the  United  States  there  are,  on  the  average, 
about  134  rainy  days  in  the  year ;  in  the  southern  part,  about  103. 

983.  Annual  depth  of  rain. — The  greatest  annual  depth  of  rain 
occurs  at  San  Luis,  Maranham,  280  inches ;  the  next  in  order  are  Vera 
Cruz,  278;  Grenada,  126;  Cape  Francois,  120;  Calcutta,  81;  Rome, 
39;  London,  25  ;  Uttenberg,  12'5.     In  our  country,  the  annual  average 
fall  is  39-23  inches  ;  at  Hanover,  N.  H.,  38  ;  New  York  State,  36  ;  Ohio, 
42  ;  Missouri,  38*265. 

984.  Snow  is  the  frozen  moisture  that  descends  from  the  atmosphere, 
when  the  temperature  of  the  air  at  the  surface  of  the  earth  is  near,  or 
below,  the  freezing  point.     The  largest  flakes  of  snow  are  produced 
when  the  atmosphere  is  loaded  with  moisture,  and  the  temperature  of 
the  air  is  about  32° ;  as  the  cold  increases,  the  flakes  become  smaller. 

The  bulk  of  recently  fallen  snow  is  ten  or  twelve  times  greater  than  that  of  the 
water  obtained  from  it.  Snow  flakes  are  crystals  of  various  forms.  Scoresby  has 
enumerated  six  hundred  forms,  and  figured  721 

ninety-six.  Kaemtz  has  met  with  at  least 
twenty  forms  not  figured  by  Scoresby.  Crys- 
tals of  snow  are  not  solid,  else  they  would  be 
transparent  as  ice ;  they  contain  air.  It  is 
to  the  reflection  of  light  from  the  assem- 
blage of  crystals,  that  its  brilliant  whiteness 
is  due.  Snow  crystals  are  produced  with 
most  regularity  during  calm  weather,  without  | 
fog.  Fig.  721  represents  a  few  of  the  beautiful  forms  assumed  by  snow  crystals. 

985.  Colored  snow  is  mentioned  by  Pliny.     It  occurs  under  two 
very  different  circumstances, — either  while  the  snow  is  falling,  or  some 
time  after  its  descent. 

In  1808,  rose-colored  snow  fell  in  the  Tyrol  and  in  Carinthia.  Its  color  was 
owing  to  an  earthy  powder,  composed  of  iron,  silex,  and  alumina.  Of  a  similar 
composition  was  a  red  snow  that  fell  on  the  mountain  of  Toual,  in  Italy,  in 
1816.  These  facts  prove  conclusively  that,  at  times,  snow  tinged  with  mineral 
ingredients,  falls  upon  the  earth.  That  the  color  is  sometimes  (and  generally) 
produced  by  the  presence  of  minute  organisms,  is  no  less  conclusively  demon- 
strated. Captain  Ross,  in  1819,  discovered  a  crimson  snow  clothing  the  sides 
of  the  mountains  at  Baffin's  Bay.  It  has  been  observed  on  the  Pyrenees,  Aips, 
and  Apennines ;  in  Scotland,  Sweden,  Norway,  &c.  Certain  French  meteorolo- 
gists, at  Spitsbergen,  in  1838,  passed  over  a  field  covered  with  snow,  which 


METEOROLOGY.  659 

appeared  of  a  green  hue,  whenever  pressed  upon  by  the  foot.  Agassiz  regarda 
these  colors  as  animal  products,  believing  them  to  be  the  ova  of  a  rotiferous 
animalcule.  The  more  common  belief  is,  that  (generally,  at  least)  these  hues 
are  owing  to  the  presence  of  a  certain  class  of  microscopic  plants,  the  different 
colors  representing  different  stages  of  development.  Martini  gives,  perhaps, 
the  correct  explanation  :  that  this  product  is  a  vegetable  cell,  enclosing  fluid,  in 
which  multitudes  of  infusoria  find  a  nidus  and  support. 

986.  Hail  is  the  moisture  of  the  air  frozen  into-  globules  of  ice. 
Hail-stones  are  generally  pear-shaped ;  they  are  formed  of  alternate 
layers  of  ice  and  snow,  around  a  white,  snowy  nucleus.    It  is  necessary 
for  the  production  of  hail,  that  a  warm,  humid  body  of  air,  mingle 
with  another  so  extremely  cold,  that,  after  uniting,  the  temperature 
shall  be  below  the  freezing  point.     The  difficulty  of  explaining  the 
phenomena  of  hail-storms,  consists  in  accounting  for  this  great  degree 
of  cold. 

Hail-storms  are  most  frequent  in  temperate  climates.  They  rarely  occur  in 
the  tropics,  except  near  high  mountains,  whose  summits  are  above  the  snow- 
line.  It  is  in  great  part  during  the  summer,  and  in  the  hottest  part  of  the  day, 
that  hail  falls.  Hail-storms  rarely  occur  at  night.  Hail-stones  are  often  of 
considerable  size ;  the  largest  are  frequently  an  aggregation  of  several  frozen 
together.  Sleet  is  frozen  rain ;  it  occurs  only  in  cold  weather ;  it  falls  only 
during  gales,  and  when  the  weather  is  variable. 

g  4.   Electrical  Phenomena. 

987.  Free  electricity  of  air. — The  general  laws  of  atmospheric 
electricity  have  been  considered  in  a  previous  paragraph  (861). 

It  is  common  to  refer  the  free  atmospheric  electricity  to  several 
causes,  always  at  work  on  the  earth's  surface,  as,  1.  Evaporation, 
especially  of  impure  water;  2.  Condensation;  3.  Vegetation  (945); 
4.  Combustion ;  and,  5.  Friction  ;  without  doubt  these  are  all  causes 
of  electrical  excitement  in  the  air.  But  far  more  important  than  them 
all  is  the  powerful  inductive  influence  of  the  negatively  excited  earth 
upon  its  gaseous  envelope.  The  dense  air  near  the  earth's  surface 
is  like  the  dielectric  of  the  ^Epinus  condenser,  and  the  constant  pre- 
sence of  positive  electricity  in  the  air  is  a  fact  not  explicable  on  any 
other  hypothesis  than  that  of  induction  from  the  negative  earth. 

In  addition  to  the  laws  already  announced  in  §  861,  may  be  added 
the  fact  that  atmospheric  electricity  is  more  abundant  in  summer  than 
in  winter. 

988.  Thunder-storms  are  most  frequent  and  violent  in  the  equato- 
rial regions.     They  decrease  in  frequency  towards  either  pole,  and  are 
more  frequent  in  the  summer  than  in  the  winter  months,  and  after  mid- 
day than  in  the  morning.     They  are  produced  in  the  same  manner  as 
ordinary  storms ;  but  they  differ  from  them  in  their  local  character, 


660  APPENDIX. 

in  the  rapidity  and  extent  of  the  condensation  of  the  atmospheric  vapor, 
and  in  the  accumulation  of  electricity. 

Thunder-storms  are  usually  attended  by  an  alteration  in  the  direction  of  the 
wind.  Of  one  hundred  and  sixteen  thunder-storms  recorded  in  the  Meteorolo- 
gical Register  of  the  Connecticut  Academy,  ninety-nine  were  either  preceded  or 
followed  by  an  alteration  in  the  direction  of  the  wind. 

Thunder-storms  generally  prevail  in  the  lower  regions  of  the  atmo- 
sphere. They  are,  however,  not  unfrequently  observed  at  great  eleva- 
tions. Kaeratz  notices  one  on  the  mountains  of  Switzerland  which 
rose  to  the  height  of  more  than  10,000  feet. 

The  geographical  distribution  of  thunder-storms  has  been  lately 
discussed  by  Prof.  Loomis  (Am.  Jour.  Sci.  [2]  XXX.  94),  whose  results 
confirm  the  general  statement  already  made  with  reference  to  latitude, 
thus : — 

Between  latitude    0°  and  latitude  30°  ^  (  51-6 

"  "        30       "         "         50          The  average  number        19-9 

"  "        50       "         "         60      t       of  thunder-storms  \    14-9 

"  "        60       «         "         70  annually  is  4- 

Beyond        "70  J  [    0- 

Maury's  storm  and  rain  charts,  however,  show  that  the  frequency 
of  lightning  depends  on  other  circumstances  than  simply  latitude,  since 
throughout  the  western  half  of  the  Atlantic  Ocean  lightning  is  three 
times  as  frequent  as  over  the  eastern  half  of  that  ocean,  and  two  and  a 
half  times  as  frequent  in  the  North  Atlantic  as  in  the  South  Atlantic. 

The  origin  of  thunder-clouds  appears,  by  both  theory  and  obser- 
vation to  be  due,  in  this  country,  to  the  rushing  up  of  the  lighter  air 
to  restore  the  normal  equilibrium  of  the  atmosphere,  which  had  been 
disturbed  or  rendered  unstable  by  the  gradual  introduction,  next  to 
the  ground,  of  a  stratum  of  warm  and  moist  air.  The  upper  end  of 
Buch  an  ascending  column  of  air,  on  the  principle  of  Peltier  (861), 
must  be  negatively  electrized,  as  its  lower  end  receives  positive  induc- 
tion from  the  negative  earth.  As,  by  the  principles  established  by 
Espy,  the  excess  of  watery  vapor  in  such  a  cloud  will  be  precipitated 
as  it  rises,  it  follows,  that  the  ascending  column  becomes  a  conduc- 
tor, and  a  series  of  electrical  discharges  will  take  place  between  the 
upper  and  lower  parts  of  the  cloud.  The  hour-glass  form,  which  the 
aeronaut  Wise  asserts  is  the  shape  of  a  thunder-cloud,  when  seen  from 
one  side,  in  a  balloon,  confirms  this  view.  (Consult  Professor  Henry's 
paper  on  Meteorology,  in  the  Report  of  the  Patent  Office  for  1859, 
Agriculture. ) 

989.  Thunder. — As  lightning  passes  through  the  air  with  amazing 
velocity,  it  violently  displaces  it,  leaving  void  a  space  into  which  the  air 
rushes  with  a  loud  report;  this  is  thunder. 


.METEOROLOGY.  661 

The  rolling  of  thunder  is-  generally  ascribed  to  the  reverberation  of  the  sound 
from  clouds  and  adjacent  mountains.  It  is  also  considered  that  as  the  lightning 
darts  to  a  great  distance  with  immense  velocity,  thunder  must  be  produced  at 
every  point  along  its  course,  and  the  sounds  not  reaching  the  ear  at  the  same 
time  that  elapses  between  lightning  and  its  thunder,  we  are  enabled  to  calculate 
the  distance  of  the  former.  According  to  Mr.  Earnshaw,  the  sound  of  a  thunder 
clap  is  propagated  with  much  greater  velocity  than  ordinary  sounds.  See 
Appendix,  p.  668. 

990.  Lightning. — It  has  already  been  stated,  that  air  subjected  to 
compression  emits  a  spark.     The  production  of  lightning  is  by  some 
attributed  to  the  energetic  condensation  of  the  atmosphere  before  the 
electric  fluid,  in  its  rapid  progress  from  point  to  point.    When  lightning 
is  emitted  near  the  earth,  the  flashes  are  of  a  brilliant  white  color  ;  when 
the  storm  is  higher,  and  therefore  in  a  rarefied  atmosphere,  their  color 
approaches  to  violet.     Clouds  appear  to  collect  and  retain  electricity. 
When  a  cloud  overcharged  with  electricity  approaches  another  less 
charged,  the  electric  fluid  rushes  from  the  former  to  the  latter.     In  the 
same  manner  the  electric  fluid  may  pass  from  the  clouds  to  the  earth. 
In  such  cases,  elevated  objects,  as  trees,  high  buildings,  church  steeples, 
&c.,  often  govern  its  direction.     It  is  unnecessary  to  dwell  upon  the 
powerful  and  destructive  effects  of  lightning. 

991.  Classes  of  lightning. — Lightning  has  been  divided  by  Arago 
into  three  classes,  viz. :  zigzag  or  chain  lightning,  sheet  lightning,  and 
ball  lightning.   We  may  add  heat  lightning  and  volcanic  lightning.   This 
classification  is  convenient,  and  is  universally  adopted. 

Zigzag  or  chain  lightning  is  supposed  to  owe  its  form  to  the  resistance 
of  the  air  compressed  before  it.  The  lightning  takes  the  path  of  least  resist- 
ance; then  moves  forward  until  it  meets  with  a  like  opposition,  and  so  continues 
glancing  from  side  to  side  until  it  meets  the  object  it  seeks.  Sometimes  the 
flashes  divide  into  two,  and  sometimes  into  three  branches ;  it  is  then  called 
forked  lightning. 

Sheet  lightning  appears  during  a  storm  as  a  diffuse  glow  of  light  illumi- 
nating the  borders  of  the  clouds,  and  occasionally  breaking  out  from  the  central 
part. 

Heat  lightning  as  it  is  called,  appears  often  in  serene  weather  during 
summer,  near  the  horizon;  it  is  generally,  if  not  always,  unattended  with 
thunder;  heat  lightning  is  the  reflection  in  the  atmosphere  of  lightning  very 
remote,  or  not  distinctly  visible.  By  many,  this  phenomenon  is  supposed  to  be 
occasioned  by  the  feeble  play  of  electricity  when  the  air  is  rarefied,  and  the 
pressure  upon  the  clouds  is  so  much  diminished  that  the  electric  fluid  cannot 
accumulate  upon  their  surface  beyond  a  certain  point,  and  escapes  in  noiseless 
flashes  to  the  earth. 

Ball  lightning  appears  in  the  form  of  globular  masses,  sometimes  remain- 
ing stationary,  often  moving  slowly,  and  which  in  a  little  time  explode  with  great 
violence.     This  form  of  lightning  is  of  very  rare  occurrence,  and  philosophers 
have  not  as  yet  been  able  to  account  for  it. 
58* 


662  APPENDIX. 

Volcanic  lightning. — The  clouds  of  dust,  ashes,  and  vapor,  that  issue 
from  active  volcanoes,  are  often  the  scene  of  terrific  lightning  and  thunder. 
Volcanic  lightning  is  probably  caused  by  rapid  condensation  of  the  vast  volumes 
of  heated  vapor  thrown  into  the  air. 

The  rapidity  of  lightning  of  the  first  two  classes  is  probably  not  less 
than  two  hundred  and  fifty  thousand  miles  per  second.  Arago  has 
demonstrated  that  the  duration  of  a  flash  of  lightning  does  not  exceed 
the  millionth  part  of  a  second.  The  waving  trees  illuminated  at  night 
by  a  single  flash  of  lightning  during  a  storm  appear  motionless ;  the 
duration  of  the  flash  is  so  short,  that,  during  its  continuance,  the  trees 
have  not  sensibly  moved. 

992.  Return  stroke. — -When  a  highly  charged  thunder-cloud  ap- 
proaches the  earth,  it  induces  the  opposite  kind  of  electricity  upon  the 
ground  below,  and   repels   that  of  the  same  kind.     If  the   cloud  is 
extended,    and   comes   within   striking   distance  of  the    earth,   or  of 
another  cloud,  a  flash  at  one  extremity  is  often  followed  by  a  flash 
at  the  other.     This  latter  is  called  the  return  stroke,  and  sometimes 
is  of  such  violence  as  to  prove  fatal,  even  at  a  distance  of  several  miles 
from  the  point  of  the  first  discharge. 

993.  Lightning-rods  were  first  introduced  by  Dr.  Franklin.     He 
was  induced  to  recommend  their  adoption  as  a  means  of  protection  to 
buildings,  from  the  effects  of  lightning,  by  observing  that  electricity 
could  be  quietly  and  gradually  withdrawn  from  an  excited  surface  by 
means  of  a  good  conductor,  pointed  at  its  extremity  (826). 

Lightning-rods  are  ordinarily  made  of  wrought  iron ;  but  copper  is  prefera- 
ble, being  a  better  conductor  of  electricity,  and  less  easily  corroded.  The  size 
of  the  rod,  if  of  iron,  should  not  be  less  than  three-quarter  inch  in  diameter. 
The  upper  extremity  of  the  rod  should  be  pointed.  Three  points  is  the  usual 
number  used  in  the  United  States,  but  one  is  sufficient.  The  points  should  be 
tipped  with  silver,  gold,  or  platinum,  or  copper  gilded  by  electricity ;  these 
metals  being  unaffected  by  the  air,  which  would  corrode  the  copper  or  iron,  and 
render  them  poorer  conductors.  The  rod  should  be  continuous  from  top  to 
bottom,  and  securely  fastened  to  the  building.  Glass  or  wooden  insulators  are 
often  recommended,  but  when  once  wet  by  a  shower,  there  is  but  little  advantage 
in  them  over  metallic  supports.  When  there  are  surfaces  of  metal  about  the 
building,  as  gutters,  pipes,  <fcc.,  these  should  be  connected  with  the  cbnduetor  by 
Strips  of  metal,  as  first  recommended  by  Prof.  Henry.  The  lower  part  of  the 
rod,  where  it  enters  the  ground,  should  be  divided  into  two  or  three  branches, 
and  bent  away  from  the  building,  penetrating  so  far  below  the  surface  of  the 
earth  as  to  reach  water,  or  permanently  moist  soil.  Charcoal  is  recommended 
to  fill  the  hole  in  the  centre  as  a  means  of  effecting  a  better  conduction.  In  a 
church,  in  New  Haven,  the  lightning  has  twice  penetrated  a  twenty  inch  brick 
wall  at  a  point  opposite  a  gas-pipe,  20  feet  above  the  earth,  through  which  the 
discharge  has  escaped  to  the  earth,  although  the  conductor  of  three-quarter  inch 
iron  was  well  mounted,  but  its  connection  with  the  earth  was  less  perfect  thai? 
that  of  the  gas-pipe. 


METEOROLOGY.  663 

Protective  power. — According  to  Mr.  Charles,  a  lightning-rod  pro- 
tects a  space  around  it,  whose  radius  is  equal  to  twice  its  height  above 
the  building.  Thus,  if  a  conductor  extend  ten  feet  above  the  house,  it 
affords  protection  to  a  circular  space  forty  feet  in  diameter,  the  rod 
boing  in  the  centre. 

Conductors  do  not  attract  the  lightning  toward  the  building  upon  which  they 
are  placed.  They  simply  direct  the  course  and  facilitate  the  passage  of  the 
electricity  to  the  earth,  which  otherwise  might  have  been  effected  in  a  powerful 
and  destructive  discharge  through  the  building.  It  is  indeed  considered  by 
Arago,  that  "lightning-rods  not  only  render  strokes  of  lightning  inoffensive, 
but  considerably  diminish  the  chance  of  their  being  struck  at  all." 

994.  Aurora  borealis. — Under  this  name  are  comprised  the  luminous 
phenomena  seen  frequently  in  the  northern  sky;  and  also,  although 
more  rarely,  in  the  neighborhood  of  the  south  pole ;  they  are  then  called 
aurora  australis.     They  present,  when  in  full  display,  a  spectacle  of 
surpassing  splendor  and  beauty.   The  cause  of  the  aurora  borealis  is  yet 
involved  in  obscurity.     Although  it  is,  evidently,  intimately  connected 
with  terrestrial  magnetic  electricity,  it  is  impossible  at  present  to  say 
exactly  what  this  connection  is.     It  has  been  ascribed  to  the  passage 
of  electrical  currents  through  the  upper  regions  of  the  atmosphere,  the 
different   colors   being   manifested   by  the  passage  of  the   electricity 
through  air  of  different  densities. 

Appearance  of  auroras. — Before  the  aurora  appears,  the  sky  in  the 
northern  hemisphere  usually  assumes  a  darkish  hue,  which  gradually 
deepens,  until  a  circular  segment  of  greater  or  less  size  is  formed.  This 
dark  segment  is  bounded  by  a  luminous  arc,  of  a  brilliant  white  color, 
approaching  to  blue. 

The  lower  edge  of  this  arc  is  clearly  defined;  its  upper  edge  gradually  blends 
with  the  sky.  When  this  luminous  arc  is  formed,  it  frequently  remains  visible 
for  many  hours,  but  it  is  always  in  motion.  It  rises,  falls,  and  breaks  in 
various  places.  Clouds  of  light  are  suddenly  disengaged,  separating  into  rays, 
which  stream  upwards  like  tongues  of  fire,  moving  backwards  and  forwards. 
AVhen  the  luminous  rays  are  numerous,  and  their  palpitating  lights  pass  to  the 
zenith,  they  form  a  brilliant  mass  of  light,  called  the  corona  or  crown,  whose 
centre  is  the  point  towards  which  the  dipping-needle  at  the  place  is  directed. 
The  aurora  is  then  seen  in  its  greatest  splendor  ;  the  sky  resembles  a  fiery  dome, 
supported  by  waving  columns  of  different  colors.  When  the  rays  are  darted 
less  visibly,  the  aurora  soon  disappears,  the  lights  momentarily  increase,  then 
diminish,  and  finally  disappear.  It  is  asserted  that  sounds,  like  the  rustling  of 
silk,  often  accompany  the  display  of  auroras,  but  this  is  extremely  problemati- 
cal ;  the  most  celebrated  polar  navigators  never  heard  any  noises  which  they 
could  certainly  ascribe  to  the  auroras. 

995.  Remarkable  auroras. — The  aurora  is  not  a  local  phenomenon  ; 
it  is  often  seen  simultaneously  in  places  far  apart,  as  in  Europe  and 
America. 


604 


APPENDIX. 


Tn  1796,  a  beautiful  aurora  was  observed  simultaneously  in  Pennsylvania  and 
F«-vnce.  The  aurora  of  January  7th,  1831,  was  observed  in  all  central  and 
t  -them  Europe,  and  at  Lake  Erie.  The  aurora  of  November  17th,  1848,  is  one 

722 


Auroral  display,  seen  at  Bossekop,  70°  N.,  1838-9. 

of  the  most  remarkable  previously  recorded.  It  was  seen  from  Odessa,  on  the 
Black  Sea,  lat.  46°  35',  long.  30°  35'  E.  to  San  Francisco  (California),  38°  N.  lat, 
1 22°  W.  long.,  and  as  far  south  as  Cuba.  It  seems  everywhere  to  have  had  a 
prevailing  red  hue,  mistaken  in  many  places  for  a  conflagration.  (Am.  Jour, 
gci.  [2]  VII.  203.) 

More  remarkable  than  all,  however,  was  the  aurora  of  August  28th  to  Sep- 
tember 4th,  1859,  for  the  great  extent  of  territory  over  which  it  was  seen,  for  its 
long  duration,  and  for  the  brilliancy  of  its  colors,  the  intensity  of  its  illumination, 
and  the  rapidity  of  its  changes.  It  was  equally  remarkable  for  the  accompany- 
ing magnetic  disturbances,  recorded  not  only  by  the  usual  magnetic  instruments, 
but  over  the  whole  system  of  telegraph  wires  both  in  America  and  Europe. 
This  aurora  was  seen  as  far  west  as  the  Sandwich  Islands,  lat.  20°,  long.  157° 
W.,  and  east  as  far  as  Barnaul,  Russia,  long.  83°  27'  E.,  a  circuit  of  240°  about 
the  earth.  The  observations  seem  to  justify  the  inference  that  it  was  as  vivid 
iu  the  southern  as  in  the  northern  hemisphere.  It  was  seen, off  Cape  Horn  and 
in  Australia,  in  the  southern  hemisphere,  up  to  Concepcion,  Chili  (lat.  06°  -16'  S-), 
and  from  about  lat.  60°  N.,  in  North  America,  to  San  Salvador  in  13°  18'  N. 
For  full  details  of  this  aurora,  see  Am.  Jour.  Sci.  [2]  Vols.  XXVIII.,  XXIX., 
and  XXX. 

996.  Height  of  auroras. — Many  astronomers  have  endeavored  to 
determine  the  height  of  auroras,  but  the  results  of  their  calculations 
are  not  certain.  Earlier  philosophers  computed  their  altitude  at  several 
hundred  miles;  a  lower  limit  is  assigned  by  later  observers.  A  bril- 
liant auroral  arch  was  observed  in  the  Northern  and  Middle  States, 


METEOROLOGY.  665 

April  7th,  1847  ;  from  the  observations  made  at  Hartford  and  New 
Haven,  Conn.,  its  height  was  computed  by  Mr.  E.  C.  Herrick,  of  the 
latter  place,  to  be  nearly  one  hundred  and  ten  miles.  Another,  seen 
April  29th,  1859,  is  by  the  same  observer  estimated  approximately  at 
much  over  100  miles  in  height.  (Am.  Jour.  Sci.  [2]  XXVIII.  154.) 

Prof.  Loomis  calculates  the  height  of  the  base  of  the  auroral  curtain, 
August  28th,  1849,  as  about  forty  miles,  but  the  same  observer  esti- 
mates the  height  of  the  belts  of  this  aurora  in  other  places  as  over  one 
hundred  and  fifty  miles. 

Frequency  of  auroras. — Auroras  are  perhaps  rather  more  fre- 
quently seen  in  winter  than  in  summer ;  but  this  circumstance  does 
not  indicate  that  during  the  former  season  there  are  actually  a  greater 
number,  for  the  increased  length  of  night  would  render  a  greater  num- 
ber visible,  even  if  they  were  equally  distributed  throughout  the  year. 
During  the  summer  of  1860,  auroras  have  been  uncommonly  frequent 
in  the  N.  United  States.  About  the  period  of  the  equinoxes  they  appear 
to  be  more  frequent  than  at  other  times.* 

In  addition  to  the  annual  period,  there  appears  to  be  another,  a  secular  period, 
extending  through  a  number  of  years.  One  of  these  periods  was  comprised  be- 
tween 1717  and  1790;  its  maximum  was  obtained  in  1752.  An  increase  in  the 
frequency  of  auroras  began  again  in  1820.  Prof.  Olmsted,  in  an  important  paper 
on  this  subject,  in  the  Contrib.  of  Smithson.  Inst.,  vol.  8,  selects  one  of  these 
secular  periods  between  August  27th,  1827,  and  November,  1848,  or  a  little  later. 
The  number  of  auroras,  observed  for  a  period  of  about  sixteen  years,  at  New 
Haven,  by  Mr.  E.  C.  Herrick,  is  given  in  the  following  table : — 

AURORAS    OBSERVED    AT    NEW    HAVEN    DURING    SIXTEEN    YEARS. 


Number  of  auroras.                  Number  of  auroras. 

Al 

ril  1837  to  April  1838,    42     !  April  1845  to  April  1846,    21 

1838  ' 

' 

1839,    34        «  1846 

"   1847,    25 

1839  < 

( 

1840,    43        "  1847 

"   1848,    30 

1840  < 

' 

1841,    48        "  1848 

"   1849,    42 

1841  < 

1 

1842,    29        "  1849 

"   1850,    18 

1842  ' 

t 

1843,     9        "  1850 

March  1851,    15 

1843  < 

< 

1844,     7       Oct.  1851 

Oct.  1852,    33 

"  1844  "   ' 

1845,    10        "  1852 

"   1853,    24 

997.  Geographical  distribution  of  auroras. — Prof.  Loomis  has 
lately  (Am.  Jour.  Sci.  [2],  XXX.,  89)  published  a  chart  showing  the 
distribution  of  auroras  in  the  northern  hemisphere.  He  shows  from  a 
tabular  comparison  of  record  ed  observations,  that  near  the  parallel  of 
40°  N.,  on  the  meridian  of  Washington,  there  are  only  10  auroras 
annually ;  nearly  42°  N.,  the  average  is  20  annually ;  near  45°  it  is 

*  See  a  paper  on  Huxham's  Observations  (Am.  Jour.  Sci.  [1],  XXXIII.,  301), 
showing  that  the  A.  B.  is  as  abundant  in  summer  as  in  winter. 


666  APPENDIX. 

40 ;  and  near  the  parallel  of  50°  it  is  80  annually.  Between  this  and 
the  parallel  of  62°,  auroras  are  seen  almost  every  night,  appearing 
high  in  the  heavens,  and  as  often  to  the  south  as  to  the  north.  Above 
62°  they  are  seldom  seen,  except  in  the  south,  and  from  this  point  they 
diminish  in  frequency  and  brilliancy  as  we  advance  towards  the  pole. 
On  the  meridian  of  St.  Petersburg  a  similar  comparison  gives  a  like 
result,  except  that  the  auroral  region  is  situated  further  north  than  it 
is  in  America,  the  zone  of  80  auroras  annually  being  from  66°  to  75°  N. 
Prof.  Loomis's  chart  (loc.  cit.}  shows  that  the  region  of  greatest  auroral 
activity  is  an  elliptical  belt,  having  one  focus  near  the  north  pole,  and 
the  other  near  the  pole  of  magnetism,  and  whose  major  axis  crosses  the 
meridian  of  Washington,  near  lat.  56°,  and  the  meridian  of  St.  Peters- 
burgh,  in  lat.  71°.  Accordingly,  auroras  are  more  frequent  in  the 
United  States  than  in  the  same  latitudes  of  Europe.  Thus,  on  the  line 
of  50°,  we  find  in  North  America  40  auroras  annually,  but  in  Europe 
less  than  10  on  the  same  parallel. 

998.  Magnetic  disturbances  during  auroral  displays. — During 
the  prevalence  of  auroras,  all  the  magnetic  elements  show  great  dis- 
turbance, simultaneously,  at  the  most  distant  stations.    This  statement 
is  confirmed  by  comparing  the  observations  at  Toronto,  Canada  West, 
lat.  43°  59/  35"  N.,  long.  79°  2V  30"  W.,  with  those  at  St.  Petersburgh, 
Russia,  lat.  59°  56'  30"  N.,  Ion.  30°  19'  E.,  on  the  2d  and  3d  of  Sep- 
tember,  1859,  during  the  great  aurora  already  described,  when,  on 
several  occasions,  the  magnets  in  the  several  instruments  oscillated 
completely  beyond  their  scales — equal  to  a  total  deflection  of  over  5£° 
of  arc.     (Am.  Jour.  Sci.  [2],  XXVIII.,  390,  and  XXX.,  80.) 

The  magnetic  oscillations  sympathize  with  the  auroral  streamers  ; 
when  the  arc  is  quiet,  the  needle  rests.  During  the  grand  aurora  of 
November  14,  1837,  the  range  of  oscillation,  as  observed  at  New  Haven 
by  Messrs.  Herrick  and  Haile,  was  6°. 

999.  Effect  of  the  aurora  on  telegraphic  wires. — This  phenome- 
non, already  alluded  to  (994),  is  entirely  distinct  from  the  induction 
of  static  electricity  during  thunder-storms  from  the  atmosphere  (860). 
Duringthe  aurora  of  August-September,  1859,  several  of  the  telegraphic 
lines  in  the  United  States  were  worked,  for  hours  together,  entirely  by 
the  magnetic  current  induced  from  the  aurora,  the  batteries  being 
detached.     Chemical  decompositions,  and  powerful  heating  and  lumi- 
nous effects,  have  been  often  observed  from  the  currents  induced  during 
auroral  disturbances.      Those  facts  were  first  noticed  by  Mr.  G.  B. 
Prescott,  at  New  Haven,  in  1847.     In  Europe,  during  the  great  aurora 
of  1859,  the  same  disturbances  of  the  telegraphic  lines  were  observed 
as  in  this  country. 


METEOROLOGY.  667 

While  all  the  lines  were  more  or  less  affected,  whatever  their  direc- 
tion, it  appears  that  the  disturbances  were  more  marked  on  the  north 
and  south  going  lines,  than  on  those  going  east  and  west:  and  in 
Tuscany,  Prof.  Matteucci  observed,  that  where  there  were  several  par- 
allel lines,  one  above  the  other,  the  'upper  wires  were  most  affected, 
and  those  nearest  the  earth,  least ;  and  that  the  inductive  effects  were 
stronger  on  the  longest  lines. 

1000.  Reversal  of  polarity  in  the  auroral  current. — Mr.  Prescott 
first  determined,  by  observation  on  the  aurora  of  July  19,  1852,  that 
the  auroral  current  invariably  changes  its  polarity  with  every  wave. 
First,  a  positive  current,  producing,  on  Bain's  system,  a  deep  blue 
mark,  light  at  first,  and  then  stronger,  until,  having  attained  the  inten- 
sity of  at  least  200  Grove's  cups,  it  subsided,  and  was  followed  by  a 
current  of  reverse  polarity,  which  bleached  instead  of  coloring  the 
paper.  Sometimes  a  flame  of  fire  followed  the  steel  stylus,  and  burned 
through  a  dozen  thicknesses  of  the  prepared  paper.  Free  or  atmo- 
spheric electricity,  when  it  is  induced  on  the  telegraph  wires,  produces 
no  color  on  the  paper.  (Am.  Jour.  Sci.  [2],  XXIX.,  92  and  391.) 


Problems  on  Electricity. 

243.  Compare  the  force  of  electricity  on  two  similar  balls,  of  which  one  repels 
the  needle  of  the  torsion  electrometer  45°  and  the  other  100°. 

244.  The  extreme  plates  of  a  voltaic  battery,  being  placed  in  contact,  there 
was  no  exterior  resistance,  and  the  electro-motive  force  manifested  by  the  evo- 
lution of  hydrogen  was  reckoned  as  unity,  or,  E  =  1,  r  =  1,  $  881.     A  pair 
of  electrodes  having  then  been  united  to  the  poles,  and  the  bath  arranged  for 
electrotyping,  the  gas  evolved  was  found  to  be  only  one-twentieth  as  much  as 
before.     Calculate  the  relative  value  of  r  and  L,  and  also  the  intensity  of  the 
battery. 

245.  In  the  case  of  a  Voltaic  battery,  so  constructed  that,  when  in  use,  the 
exterior  resistance  L  is  equal  to  nineteen  times  the  resistance  of  the  battery  r, 
what  would  be  the  effect  of  doubling,  trebling,  and  quadrupling  the  dimensions 
of  all  the  plates  in  the  battery  ? 

246.  With  the  same  conditions  as  in  the  preceding  case,  L  =  19r,  how  would 
the  intensity  of  the  current  be  changed  by  doubling  the  number  of  couples  in 
the  battery  ? 

247.  In  a  battery  in  which  L  =  r,  or  the  external  resistance  is  equal  to  the 
resistance  of  the  battery,  how  will  the  intensity  vary  by  doubling  the  number 
of  couples  of  the  same  dimensions  in  the  battery  ? 

248.  When  L  =  4r,  what  advantage  would  be  gained  by  uniting  two  similar 
batteries  in  a  single  series? 

249.  If  in  the  use  of  a  Voltaic  battery  of  100  pairs  of  plates,  arranged  in  a 
series,  the  exterior  resistance,  Z,  is  found  to  be  six  times  the  resistance  of  the 
battery,  r,  what  change  of  intensity  will  be  produced  by  so  uniting  the  couples 
as  to  form  only  four  groups,  each  having  twenty-five  times  the  previous  extent 
of  surface  ? 


668  APPENDIX. 


ADDENDA. 

NOTE  TO  §  369.— Uniform  musical  pitch.— A  general  congress,  called 
together  by  the  Society  of  Arts,  at  London,  June  8,  1860,  of  musicians,  ama- 
teurs, and  otters  interested  in  music,  have  accepted  the  report  of  a  committee 
appointed  in  1859,  to  consider  the  subject  of  uniform  musical  pitch.  This  com- 
mittee recommend  a  pitch  of  528  full  vibrations  for  C'  =  440  for  A,  basing  their 
calculations  on  33  single  vibrations  of  an  organ  pipe  32  feet  high,  in  place  of  32 
vibrations,  the  actual  number.  The  following  is  the  scale  at  this  pitch — the 
only  one  yet  proposed  which  gives  all  the  sounds  in  whole  numbers  : — 

CDEFGABC' 
264     297     330     352     396     440     495     528 

This  pitch  is  but  16  vibrations  per  second  higher  than  the  normal  Diapason, 
C'  =  512,  or  "  Stuttgard  pitch,"  and  18  vibrations  lower  than  the  present  pitch 
of  546.  It  is  therefore  nearly  half  way  between  the  two,  being  a  quarter  tone 
above  one,  and  the  same  quantity  below  the  other. 

The  commission  recently  appointed  to  report  on  the  pitch  in  France  have 
advised  the  following  scale : — 

CDEFGABC' 
2~61     2~98l     3261     348     391$     435     489f     522 

The  following  is  a  list  of  the  several  pitches  considered  in  this  report : — 
Handel's  Tuning  Fork  (C.  1740)  A  at  416    =  C  at  499£ 


Theoretical  Pitch  A 

Philharmonic  Society  (1812-42)  A 

Diapason  Normal  (Paris,  1859)  A 

Stuttgard  Congress  (1834)  A 

Italian  Opera,  London  (1859)  A 


426|  =  C 
433  =  0 
435  =  C 

440  =  C 
455  =  C 


512 

518f 

522. 

528 

546 


(Journal  of  the  Society  of  Arts,  June  8,  1860.) 

NOTE  TO  §  343. — The  velocity  of  all  sounds  not  the  same. — Rev. 
E.  S.  Earnshaw,  of  Sheffield,  England,  lately  brings  good  evidence,  both  mathe- 
matical and  physical,  to  show  that  the  accepted  views  stated  in  $  343  are  correct 
only  for  sounds  having  no  very  great  difference  of  intensity.  Every  note  in  music 
may  be  formed  by  two  kinds  of  vibrations  of  the  same  rapidity,  but  differing  in 
wave-length  and  velocity  of  transmission.  Only  one  variety  of  these  waves  is 
supposed  in  general  to  be  sensible  by  human  ears.  The  velocity  of  sounds  of 
all  kinds  is  a  certain  function  depending  upon  the  rapidity  and  length  of  vibra- 
tion. In  the  case  of  violent  thunder  the  numerical  value  of  this  function  becomes 
much  greater  than  for  ordinary  sounds.  These  and  other  remarkable  conclu- 
sions are  sustained  by  mathematical  reasoning.  The  author  of  the  memoirs  also 
cites  evidence  to  show  that  the  crash  of  violent  thunder-claps  has  been  often 
heard  almost  simultaneously  with  the  flash  of  lightning,  although  the  stroke 
fell  several  miles  distant.  (London,  Edinburgh,  and  Dublin  Phil.  Mag.,  June, 
July,  Sept.  1860.) 

NOTE  TO  §  392. — Sounds  produced  by  insects. — Burmeister  has  shown 
that  the  usual  opinion  of  naturalists  (expressed  in  g  392)  is  erroneous,  and  that  the 
sounds  produced  by  insects  are  formed  by  the  expansion  and  contraction  of  their 
air  tubes,  the  sound  being  formed  by  the  passage  of  air  through  the  orifices  of 
the  tubes,  which  act  like  a  whistle.  (  Taylor's  Scientific  Memoirs,  Vol.  I.,  p.  377.) 


CHAPTER  II. 
PHYSICAL  TABLES. 

TABLE  I. 
MEASURES    AND    WEIGHTS. 


ENGLISH  MEASURES. 

Measures  of  Length. 

THE  inch  is  the  smallest  lineal  integer  now  used.  For  mechanical 
purposes  it  is  divided  either  duodecimally  or  by  continual  bisection  ;  but 
for  scientific  purposes'  it  is  most  convenient  to  divide  it  decimally.  The 
larger  units  are  thus  related  to  it  :  — 

Mile.  Furlongs.  Chains.  Rods.  Fathoms. 

1=8  =  80  =  820  =  880      =1760 
1=10=   40  =  110      =   220 
lrr=     4=    11      == 
1=     2-75= 
1       = 


•000126  =-001  =  -01=  -04=  -11= 


is.           Feet.             Links.             Inches. 
10    =6280      =8000     =63360 

10    =   660      =1000     = 

7920 

12     = 

66      = 

100     = 

792 

6-5  = 

16-5   = 

25      = 

198 

2     = 

6      = 

9^  = 

72 

1     = 

3       = 

4T«T  = 

36 

1       = 

iH  = 

12 

•22^- 

0-66  = 

•i        

7-92 

Acre. 

1 


Roods. 

4 

1 


Measures  of  Surface. 


Square  Chains. 

10 

2-5 
1 


Square  Yards.  Square  Feet. 

4840   =  43,560 

1210   =  10,865 

484   =  4,356 

1   =  9 


Measures  of  Volume. 


Cubic  Yard. 
1 


Cubic  Feet. 

27 

1 


Cubic  Inches, 

46,656 

1,7J8 


69 


(669) 


670 


APPENDIX. 


Imperial  Measure. 

The  Imperial  Standard  Gallon  contains  ten  pounds  avoirdupois  weight 
of  distilled  water,  weighed  in  air  at  62°  Fahr.  and  30  in.  Barom.,  or  12 
pounds,  1  ounce,  16  pennyweights,  and  16  grains  Troy,  =  70,000  grains' 
weight  of  distilled  water.  A  cubic  inch  of  distilled  water  weighs 
252*458  grains,  and  the  imperial  gallon  contains  277*274  cubic  inches. 

Distilled  Water.. 


Grains.       ^Avoir.  Ib.         Cubic  Inches.        Pint.      Quart.    Galls.  Pecks.  Bush.    Qr. 
8,750=      1-25=         34-659=     1 
17,500=      2-5    =         69-318=     2=      1 
70,000  =    10      =       277-274  =     8  =     4=1 

140,000  = 

20 

= 

554 

548  = 

16  = 

Q    

0    

1 

560 

,000  = 

80 

n 

,218 

192  = 

64  = 

32  = 

8  = 

4 

i 

4,480,000  =  640      =  17,745-536  =  512  =  256  =  64  =  32  =  8  =  1 


Apothecaries'  Measure. 

The  gallon  of  the  former  wine  measure  and  of  the  present  Apotheca- 
ries' measure  contains  58,333*31  grains'  weight  of  distilled  water,  or 
231  cubic  inches,  the  ratio  to  the  imperial  gallon  being  nearly  as  5  to  6, 
or  as  0-8331  to  1. 


Gallon.    Pints. 

1    =    8    = 
1    = 


Ounces.        Drachms. 
128    =    1024    = 
16    =      128    = 
l    =         8    = 


Minims.         Gr.  of  Dist.  Wat.     Cub.  Inch. 

61,440  =    58,333-31    =    231 

7,680  =      7,291-66    =     28-8 

480  =         455.72    =        1-8 

60  =          66-96    =       0-2 


ENGLISH  WEIGHTS. 


Pound. 
1 


Avoirdupois  Weight. 


Ounces. 

16 

1 


Drachms. 
256 
16 
1 


Chains. 
7000 
437-6 
27-34375 


Apothecaries'  l~oy  Weight. 


Peund. 

1 


Ounces. 
12 

1 


Drachms. 

96 

8 

1 


Scruples. 

288 

24 

3 

1 


Grains. 

5760 

480 

60 

20 


PHYSICAL   TABLES. 


671 


FRENCH  MEASURES. 


Measures  of  Length. 

1  Kilometre      —     1000  Metres. 
1  Hectometre    =       100      " 
1  Decametre     t=         10      " 
1  Metre             =          1      " 

1  Metre             =    1  -000  Metre. 
1  Decimetre       =     0-100       " 
1  Centimetre     =    0-010       " 
1  Millimetre      =    0-001 

1  Kilometre       =     0  6214  Mile. 
1  Metre             —    3  2809  Feet. 

1  Centimetre     =.     0-3937  Inch. 
2-539954  c.  m.  —              1  Inch. 

Comparison  of  Standard  Measures. 

1  Metre  =  3-28089917  English  Feet,  =    3-28070878  American  Feet. 
1  Metre  =  3-07844400  Paris  Feet,      =  39-36850535  American  Inches. 

Measures  of  Volume. 

1  Cubic  Metre          =  1000-000  Litres.         1  Litre>=  0-22017  Gallon. 
1  Cubic  Decimetre    =        1-000      "  1  Litre  =;  0-88066  Quart. 

1  Cubic  Centimetre  =        0-001      "  1  Litre  =  1-76133  Pints. 

1  Cubic  Metre  =    35-31660  Cubic  Feet. 

1  Cubic  Decimetre     =    61-02709  Cubic  Inches. 
1  Cubic  Centimetre   —      0-06103     "          " 


]  Kilogramme 
1  Hectogramme 
1  Decagramme 
1  Gramme 


FRENCH  WEIGHTS. 

1000  Grammes. 
100 

10         " 
1 


1  Gramme  =  1-000  Gramme. 

1  Decigramme    =  0-100        " 

1  Centigramme  =  0-010       " 

1  Milligramme   =  0-001        " 


1  Kilogramme  =  2-67951  Pounds  (Troy),  =  2-20485  Pounds  (Avoirdupois). 
1  Gramme        =  15-44242  Grains. 

To  convert  French  metrical  quantities  into  English  measures  and 
weights  consult  Table  II. 

To  convert  Grams  into  Grammes. 
Log.  Grains  -f  ( —  2-8115680)  =  Log.  Grammes. 

To  convert  Cubic  Inches  into  Cubic  Centimetres. 
Log.  Cubic  Inches  -f  1-2144993  =  Log.  Cubic  Centimetres. 

To  convert  Inches  into  Millimetres. 
Log.  Inches  +  1-4048337  =  Log.  Millimetres. 


672 


APPENDIX. 


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PHYSICAL    TABLES. 


673 


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674 


APPENDIX. 


TABLE  III. 

EXPANSION  OF  SOLIDS. 


1,000,000  parts  at  32C  F. 

At  212°  F. 
become 

Expansion. 
In  length.          In  bulk. 

Authority. 

English  Flint  Glass    . 

1,000,811 

1  in  1248 

1  in    316 

(    Lavoisier 
\  &  Laplace. 

Glass  tube  (French)  . 

1,000,861 

1  in  1148 

1  in    382 

{   Dulong  & 

Platinum      .... 

1,000,884 

1  in  1131 

1  in    377 

\       Petit. 

Palladium    .... 

1,001,000 

1  in  1000 

1  in    333 

Wollaston. 

Tempered  Steel     .     . 

1,001,079 

1  in    926 

1  in    309 

f    Lavoisier 
\  &  Laplace. 

Antimony     .... 

1,001,083 

1  in    923 

1  in    307 

Smeaton. 

Iron 

1  001  182 

1  in    846 

1  in    282 

f   Dulong  & 

\       Petit. 

Bismuth  

1,001  392 

1  in    718 

1  in    239 

Smeaton 

Gold 

1  001  466 

1  in    682 

1  in    227 

Copper 

1  001  718 

1  in    582 

1  in    194 

Brass       

1,001,866 

1  in    536 

1  in    179 

Lavoisier 

Silver      

1,001,909 

1  in    524 

1  in    175 

&  Laplace. 

Tin     

1  001  937 

1  in    516 

1  in    172 

Lead  

1,002,848 

1  in    351 

1  in    117 

Zinc 

1,002,942 

1  in    340 

1  in    113 

Smeaton. 

INCREASE  OF  MEAN  EXPANSION  BY  HEAT. 


Glass     . 

Expansion  for  each  degree  F. 

Between 
32°  and  212°. 

Between 
32°  and  392°. 

Between 
32°  and  572°. 

1  in  69660 
1  in  67860 
1  in  50760 
1  in  34920 
1  in    9990 

1  in  65340 
{  in    9965 

1  in  59220 
1  in  65340 
1  in  40860 
1  in  21060 
1  in    9518 
\ 

Platinum  

,    Iron      
Copper                                     . 

Mercury    

1,000,000  parts  at  62°  F. 

At  212°  F. 

At  662C  F. 

At  Freezing  Point. 

Black  lead  ware    . 

1,000,244 

1,000,703 

Wedgewood  ware  . 

1,000,735 

1,002,995 

Platinum      .     .     . 

1,000,735 

1,002,995 

f  1,009,926  maximum,  but 
\     not  fused. 

Cast  iron      .     .     . 

1,000,893 

1,003,943 

1,016,389 

Wrought  iron   .     . 

1,000,984 

1,004,483 

f  1,018,378  to  the  fusing 
\      point  of  cast  iron. 

Copper    .... 

1,001,430 

1,006,347 

1,024,376 

Silver      .... 

1,001,626 

1,006,886 

1,020,640 

Zinc    

1,002,480 

1,008,527 

1,012,621 

Lead 

1  002  323 

1  009,072 

Tin     .... 

1  001,472 

1,037,980 

PHYSICAL   TABLES. 


675 


TABLE  IV. 
EXPANSION  OF  LIQUIDS. 

BETWEEN  32°  AND  212°  F. 


1,000,000  parts  mercury  become        .     . 

,018,153 

1  in  55 

Regnault. 

"           "     pure  water  become 

,046,600 

1  in  21  -3 

Dalton. 

"           "     sulphuric  acid  become 

,058,823 

1  in  17 

Dalton. 

"           "     chlorohydric  acid  become 

,058,823 

1  in  17 

Dalton. 

"           "     oil  turpentine  become 

,071,428 

1  in  14 

Dalton. 

"           "     sulphuric  ether  become 

1,071,428 

1  in  14 

Dalton. 

"           "     fixed  oils  become       .     . 

1,080,000 

1  in  12-5 

Dalton. 

"           "     alcohol  become     .     .     . 

1,111,000 

1  in    9 

Dalton. 

"           "     nitric  acid  become    .     . 

1,111,000 

1  in    9 

Dalton. 

EXPANSION  OF  LIQUIDS  OF  SIMILAR  CHEMICAL  COMPOSITION. 


Aldehyde. 

Butyric  Acid. 

Acetate  of  Ethyl. 

CiliiOa. 

C8H804. 

C8H804. 

°c. 

Pierre. 

Kopp. 

Pierre. 

Kopp. 

Pierre. 

Kopp. 

(B.  P.  22°.) 

(20-8°.) 

(163°.) 

(157°.) 

(74-1°.) 

(74-3°.) 

0 

10000 

10000 

10000 

10000 

10000 

10000 

10 

9817 

9830 

9872 

9867 

9846 

9843 

25 

9567 

9596 

9688 

9667 

9629 

9622 

45 

9284 

9453 

9439 

9359 

9352 

60 

9094 

9288 

9271 

9172 

9165 

75 

9128 

9112 

8996 

8988 

110 

8781 

8765 

8633 

Chlorid 
of 
Ethylene. 

Monochlo- 
rinated 
Chlorid 

Monochlo- 
rinated 
Chlor.  of 

Bichlori- 
nated 
Chlorid 

Formiate  of  Ethyl. 
CeHsOi. 

Acetate  of  Methyl. 

°0. 

C4H4C12. 

of  Ethyl. 
C4H4C12. 

Ethylene. 
C4H3C13. 

of  Ethyl. 
C4H3C13. 

Pierre. 

Pierre. 

Pierre. 

Pierre. 

Pierre. 

Kopp. 

Pierre. 

Kopp. 

(84-9°.) 

(64-8°) 

(114-2°.) 

(74-9°.) 

(52-9°.) 

(54-9°) 

(59-5°.) 

(56-3°) 

0 

10000 

10000 

10000 

10000 

10000 

10000 

10000 

10000 

25 

9667 

9669 

9693 

9648 

9632 

9631 

9633 

9631 

55 

9331 

9300 

9350 

9267 

9241 

9243 

9243 

9243 

80 

9068 

9003 

9090 

8988 

8953 

8955 

676 


APPENDIX 


TABLE  V. 
EXPANSION  OF  GASES. 

EXPANSION  FOR  A  CONSTANT  VOLUME.* 


Air. 

Carbonic  Acid. 

Pressure  at 

Pressure  at 

Expansion  for 

Pressure  at 

Pressure  at 

Expansion  for 

32°  F. 

212°  F. 

180°  F. 

32°  F. 

212°  F. 

180°  F. 

m.m. 

m.m. 

m.m. 

m.m. 

109-72 

149-31 

0-36482 

758-47 

1034-54 

0-36856 

174-36 

237-17 

0-36513 

901-09 

1230-37 

0-36943 

266-06 

395-07 

0-36542 

1742-93 

2387-72 

0-37523 

374-67 

510-35 

0-36587 

3589-07 

4759-03 

0-38598 

375-23 

510-95 

0-36572 

760-00 

« 

0-36650 

1678-40 

2286-09 

0-36760 

1692-53 

2306-23 

0-36800 

2144.18 

2924-04 

0-36894 

3655.66 

4992-09 

0-37091 

EXPANSION  FROM  32°  TO  212°  F.  AT  A  CONSTANT  PRESSURE.* 


Hydrogen.                            Air. 

Carbonic  Acid. 

Sulphurous  Acid. 

^eO     0-36613 
2545     0-36616 

760     0-36706 
2525     0-36944 
2620     0-36964 

m.m. 
760    0-37099 
2520    0-38455 

m.m. 
760      0-3902 
980      0-3980 

TABLE  VI. 

RADIATING  POWER  ACCORDING  TO  PROVOSTAYE,  DESAINS, 
AND  MELLONI. 


Lampblack  being     .     . 
Pure  rolled  silver    .     . 
Pure  burnished  silver  . 
Rolled  platinum       .     , 
Gold  in  leaf 

.  100 

.       3-00 
.       2-50 
10-80 

4-28 

Rough   silver  (deposited 
copper)      
Burnished  silver  (pure)  . 
Burnished  platinum    .     . 
Sheet  copper 

on 
.  5-36 
.  2-25 
.  9-50 
4-90 

*  Cours  de  Physique.     Par  M.  J.  Jamin.     Tome  ii.  p.  70. 


PHYSICAL   TABLES. 


677 


TABLE  VII. 


CONDUCTING  POWER  OF  METALS  AND  BUILDING  MATERIALS. 


A. — CONDUCTING  POWER  OF  METALS. 


1 

Name  of  Metal. 

Despretz. 

Wiedemann 
&  Franz. 

Becquerel. 

Gold                    .                              .      . 

1000-0 

1000 

1000 

Platinum    ...                ... 

981-0 

158 

124-91 

Silver 

973-0 

1880 

1451-37 

Copper                            .... 

898-2 

1383 

1383-61 

Brass     

444 

Steel 

218 

Iron                                           .     . 

374-3 

224 

188-3 

Zinc             

363  0 

375-3 

Tin         

303-9 

273 

212-09 

Lead 

179-6 

160 

128-65 

118 

217-08 

Bismuth      

34 

Marble  .     

23-6 

Porcelain 

12-2 

Brick  clay                 

11-4 

B. CONDUCTING  POWER  OF  BUILDING  MATERIALS. 


Name  of  Substance. 

Conducting 
power  referred 
to  slate  =  100. 

Name  of  Substance. 

Conducting 
power  referred 
to  slate  =  100. 

Plaster  and  sand  .  . 
Keene's  cement  .  . 
Plaster  of  Paris  .  . 
Roman  cement  .  . 
Lath  and  plaster  .  . 
Fir  wood  .... 
Oak  wood  .... 
Asphalt  

18-70 
19-01 
20-26 
20-88 
25-55 
27-61 
33'66 
45-19 

Bath  stone    .... 
Fire  brick     .... 
Paniswick  stone,  H.  P. 
Malen  brick      .     .     . 
Portland  stone  .     .     . 
Lunelle  marble       .     . 
Balsover  stone,  H.  P. 
Norfal  stone,  H.  P.     . 

61-08 
61-70 
71-36 
72-92 
75-10 
75-41 
76-35 
95-36 

Chalk  (soft) 

56-38 

Slate        

100-00 

Napoleon  marble  .  . 
Stack  brick 

58-27 
60-14 

Yorkshire  flag  .     .     . 
Lead                        .     . 

110-94 
521-34 

678 


APPENDIX. 


TABLE  VIII.       . 

ABSORPTIVE  POWER  OF  DIFFERENT  BODIES. 


Names. 

Absorptive 
Power. 

Reflective 
Power. 

Smoke  blackened  surface                            •     . 

100 

o 

Carbonate  of  lead     

100 

o 

98 

2 

Glass     

90 

10 

China  ink  

85 

15 

72 

28 

Silver  foil  on  glass  ....          .... 

27 

73 

25 

75 

Wrought  iron  polished      .               ... 

23 

77 

Mercury     

23 

77 

19 

81 

Steel                     

17 

83 

Platinum,  thick  coat,  imperfectly  polished   . 
"          on  copper                               • 

24 
17 

76 
83 

«         leaves           .     •          .     •     .     .     . 

17 

83 

14 

80 

Metallic  mirrors,  a  little  tarnished      .     .     . 
"            "        nearly  polished    .... 
Brass,  cast,  imperfectly  polished     .... 
*       hammered,  imperfectly  polished     .     . 
<               "           highly  polished  .... 
«        cast,                 "             "        .... 

17 
14 
11 
9 
7 
7 
7 

83 
86 
89 
91 
93 
93 
93 

14 

86 

'       hammered  or  cast      

7 

93 

Gold  plating  

6 

95 

Gold  deposited  on  polished  steel      .... 
Silver,  hammered,  and  well  polished   .     .     . 
Silver,  cast,  and  well  polished    

3 
3 
3 

97 
97 
97 

TABLE  IX. 

ABSORPTIVE  POWER  FOR  HEAT  FROM  DIFFERENT  SOURCES. 


Name  of  Substance. 

Incandescent 
Platinum. 

Copper  at 
400°. 

Copper  at 
100°. 

Lampblack      

100 

100 

100 

Carbonate  of  lead     
China  ink  

56 
95 

89 

87 

100 
85 

Isinglass 

54 

64 

91 

Lac    

47 

70 

72 

Metallic  surface  

13-5 

13 

13 

PHYSICAL   TABLES. 


679 


TABLE  X. 

DIATHERMANCY  OF  DIFFERENT  LIQUIDS. 


Of  100  incident  rays. 

Trans- 
mitted 

Trans- 
mitted 

Bisulphid  of  carbon  (colorless] 
Bichlorid  of  sulph.  (red  brown) 
Terchlorid  of  phosphorus 
Essence  of  turpentine  .     .     . 
Colza  oil  (yellow)     .... 
Olive  oil  (greenish)      .     .     . 

63 
62 
62 
31 
30 
30 

Ether 

21 

17 
17 
14 
15 
11 

Sulphuric  acid  (colorless)     . 
Sulphuric  acid  (brown)    .     . 
Nitric  acid 

Alcohol               .... 

Distilled  water  

TABLE  XI. 

[Ratio  of  Specific  Heat  to  Atomic  Weight.] 

SPECIFIC  HEAT. 

A. — SOLIDS. 


1 

Water  =  1.00. 

Names. 

Specific  Heats. 
C. 

Atomic  Weights. 
P- 

Product, 

CXP. 

Aluminum   

0-2143 

13-7 

2-94 

Sulphur  

0-2026 

16 

3-24 

0-1138 

28 

3-19 

Cobalt                

0-1070 

29-5 

3-16 

Nickel     . 

0-1086 

29-6 

3-21 

Copper         .          .... 

0-0952 

31-7 

3-02 

Zinc   

0-0956 

32-6 

3-12 

Selenium                .               . 

0-0762 

40 

3-04 

Tin          

0-0562 

59 

3-31 

Platinum 

0-0324 

98-7 

3-20 

Lead             

0-0314 

103-7 

3-26 

Phosphorus       
Arsenic                         .          . 

0-1887 
0-0814 

31 
75 

5-85 
6-10 

Silver      

0-0570 

108 

6-16 

Iodine 

0-0541 

127 

6-87 

Antimony    
Gold 

0-0508 
0-0324 

120-3 
197 

6-11 
6-38 

Bismuth  .     .     .  *  .     .     .     . 

0-0308 

208 

6-41 

] 

5.  LIQUIDS. 

Mercury  (liquid)  .... 
Mercury  (solid)     ...     .     . 
Bromine  (liquid)  .... 
Bromine  (solid)  28°  C.  .     . 

0-03331 
0-03241 
0-11094 
0-08432 

100 
100 
80 
80 

3-33 
3-24 

6-74 

680 


APPENDIX. 


TABLE  XI—  (Continued.) 
SPECIFIC  HEAT. 

C. — GASES  AND  VAPORS. 


Name  of  Substance. 

Capacity  for 
equal  weights. 

Water  —  1. 

Capacity  for 
equal  volumes. 
Water  of  equal 
weight  being  =  1. 

Specific  Gravity. 

Atmospheric  air*  .... 
Oxvsren 

0-2379 
0-2182 

0-2412 

1-0000 
1-1056 

0-2440 

0-2370 

0-9713 

Hydrogen              .... 

3-4046 

0-2356 

0-0692 

0-1214 

0-2967 

2-4400 

0-0552 

0-2992 

6-3900 

Nitrous  oxyd    

0-2238 

0-3413 

1-5250 

0-2315 

0-2406 

1  -0390 

Carbonic  oxyd       .... 

0-2479 
5-2164 

0-2399 
0-3308 

0-9674 
1-5290 

Sulphid  of  carbon      .     .     . 
|  Sulphurous  acid    .... 
Ammonia  gas   
Olefiant  gas      

0-1575 
0-1553 
0-5080 
0-3694 
0-4750 

0-4146 
0-3489 
0-2994 
0-3572 
0.2950 

2-6325 
2-2470 
0-5894 
0-9672 
0-6210 

0-4513 

0.7171 

1-5890 

0-4810 

1-2296 

2-5563 

Chloroform       
Vapor  of  mercury      .     .     . 
Vapor  of  Iodine     .... 

0-1568 

0-8310 

5-3000 
6-9760 
8-7160 

TABLE  XII. 

FREEZING  MIXTURES. 


Substances. 

Parts  by 
Weight. 

Cooling  in  Degrees  F. 

Sulphate  of  soda 

8) 

Hydrochloric  acid  

4 

from  +  50°  to      0° 

Snow  or  ice 

21 

Common  salt      

l} 

«     x          «_5° 

Sulphate  of  soda 

81 

Dilute  nitric  acid    

9} 

"   _|_  50°  "  —  3° 

Sulphate  of  soda     
Nitrate  of  ammonia     
Dilute  nitric  acid    .     .               .     . 
Snow  or  ice  ....          ... 

CO  »0  TjH  « 

«   _|_  50°  «  —  14° 

Chloride  of  calcium     

4) 

"    -f  20°  "  —  14° 

*  De  la  Roche  and  Berard. 


PHYSICAL   TABLES. 


681 


TABLE  XIII. 

DIATHERMANCY  OF  DIFFERENT  SOLIDS. 


Substance  of  Screens. 

Sources 

of  Heat. 

[Each  plate  was  2-62  m.  m.  (0-1  in.)  in  thick.] 

.    Naked 
Flame. 

Ignited 
Platinum. 

Copper 
750°  F. 

Copper 
212°  F. 

Kock  salt  (limpid) 

92-3 

92-3 

92-3 

92-3 

Silician  sulphur  (yellow)  .     .     . 
Fluor  spar  (limpid)      .... 
Rock-salt  (cloudy)        .... 
Beryl  (greenish  yellow)    .     .     . 
Iceland  spar  (limpid)  .... 
Plate  glass 

74 

72 
65 
46 
39 
39 

77 
69 
65 
38 
28 
24 

60 
42 
65 
24 
6 
g 

54 
53 
65 
20 
0 

o 

Quartz  (limpid)  

38 

28 

6 

3 

Quartz  (smoky)  

37 

28 

6 

3 

White  topaz    .     .     . 

33 

24 

4 

o 

Tourmaline  (dark  green)  .     .     . 

18 
11 

16 

2 

8 

0 

0 

o 

Alum     

9 

2 

o 

o 

Sugar  candy  (limpid)  .... 

8 

1 

0 

0 

TABLE  XIV 

TENSION  OF  VAPORS  AT  EQUAL  DISTANCES  ABOVE  AND  BELOW 
THE  BOILING  POINTS  OF  THEIR  RESPECTIVE  LIQUIDS. 


Regnault. 

Ure. 

Ure. 

Marx. 

Avogadro. 

Number  of  de- 
grees above  or 
below  boiling. 

Water. 

Alcohol. 
Sp.  Or.  0-813. 

Ether. 

Sulph't  Carbon. 

Mercury. 

Temp. 

Pressure 

Temp. 

Pressure 

Temp. 

Pressure 

Temp.  Pressure 

Temp. 

Pressure 

+  40° 

252 

63-14 

+  20° 

232 

44-06 

124 

42-64 

137 

40-19 

Boiling  p't. 

212 

30-00 

173 

30-00 

104 

30-00 

117 

29-87 

680 

30-00 

—  20° 

192 

19-87 

153 

19-30 

84 

20-90 

97 

20-65 

—  40° 

172 

12-78 

133 

11-60 

64 

13-00 

77 

13-89 

630 

19-85 

—  60° 

152 

7-94 

113 

6-70      44 

8-10 

57 

9-07 

—  80° 

132 

4-67 

93 

3-67 

37 

5-73 

590 

14-08 

682 


APPENDIX. 


TABLE  XV. 

MELTING  POINTS  AND  LATENT  HEAT  OF  FUSIDN  OP  DIFFERENT 

BODIES. 


Substances. 


Melting  Point. 


Latent  Heat.* 

Of. 


Water  =  1. 


Mercury —  39 

Oil  of  vitriol  .....  —30 

Bromine —    4 

Water 

Phosphorus -f-  111 

Potassium  (about)  .     .     .  131 

Yellow  wax 143 

Sodium 190 

Iodine 224 

Sulphur 239 

Tin 455 

Bismuth 518 

Lead 630 

Zinc 761 

Antimony 963 

Silver 1873 

Copper f2143 

Gold 2016 

Cast  iron  (above)     .     .     .  2786 

Wrought  iron      ....  3280 

Platinum  ......  4591 

Nitrate  of  soda    ....  691 

Nitrate  of  potash     ...  642 
Nitrate  of  silver 


5-11 


142-1 
8-08 

78-32 


16-51 
25-74 
22-30 
9-27 
49-43 

37-92 


113-36 

83-12 

113-34 


0-035 


1-000 
0-056 

0-551 


0-116 
0-180 
0-156 
0-065 
0-347 

0-265 


•797 
•584 
•704 


TABLE  XVI. 

BOILING  POINT  OF  WATER  UNDER  DIFFERENT  PRESSURES. 


Boiling  Point. 


Barometer. 
Inches. 


Boiling  Point 


Barometer. 
Inches. 


184 
186 
188 
190 
192 
194 
196 
198 


16-676 
17-421 
18-196 
18-992 
19-822 
20-687 
21-576 
22-498 


200 
202 
204 
206 
208 
210 
212 
214 


23-454 
24-441 

25-468 
26-529 
27-614 
28-744 
29-922 
31-120 


*  The  numbers  in  this  column  may  be  considered  as  the  number  of  pounds  of 
water  that  could  be  raised  1°  F.  by  the  heat  emitted  during  the  congelation  of 
one  pound  of  each  of  the  substances  included  in  the  table. 

f  Plattner. 


PHYSICAL   TABLES. 


683 


TABLE  XVII. 

BOILING  POINTS  OF  LIQUIDS. 


Temperature. 

Temperature. 

Sulphurous  acid 

17.6 

Nitric  acid,  sp.  gr.  1-42 

248-0 

Chlorid  of  ethyl       . 

51-9 

Bichlorid  of  tin  .     . 

240-2 

Aldehide  .... 

69-4 

Fousel  oil  .     .     .     . 

269-8     * 

Ether    

94-8 

Terchlorid  of  arsenic 

230-0 

Bisulphid  of  carbon 

118-5 

Butyric  acid  .     .     . 

314-6 

Terchlorid  of  silicon 

138-2 

Naptha       .... 

320-0 

Ammonia,  sp.  gr.  0-945 

140-0 

Sulphurous  ether     . 

320-0 

Bromine    .... 

145-4 

Phosphorus    .     .     . 

554-0 

Wood  spirit    .     .     . 

149-9 

Oil  of  turpentine 

568-5 

Alcohol     .... 

173-1 

Linseed  oil     ... 

597-0 

Dutch  liquid  .     .     . 

184.7 

Sulp.  acid,  sp.  gr.  1  -843 

620-0 

Water  

212.0 

Mercury    .... 

662-0 

TABLE  XVIII. 

BOILING  POINT  OF  WATER  AT  DIFFERENT  PLACES  AND  THEIR 
ELEVATION  ABOVE  THE  SEA. 


Names  of  Places. 

Above  (or  be- 
low) the  level 
of  the  sea. 

Mean  height 
of  the 
Barometer. 

Thermometer. 

Donkia  (Himalaya)  
Donkia  Pass  (Himalaya)   .     .     . 
Farm  of  Antisana,  S.  A.    .     .     . 
Micuipampa  (Peru)       .... 
Quito 

Feet. 
+  17,337 
16,621 
13,455 
11,870 
9  541 

Inches. 
15-442 
15-489 
17-870 
19-020 
20-750 

Degrees. 
179-90 
181-40 
187-30 
190-20 
194-20 

Mexico  

7,471 

22-520 

198-10 

Hospice  of  St.  Gothard      .     .     . 
Black  Mountain,  N.  C.  (highest  1 
point  in  the  eastern  U.  S.)*    .  J 
Mount  Washington,  N.  H.      .     . 
Madrid  

6,808 
6,702 

6,290 
1  995 

23.070 
22-502 

22-905 
27-720 

199-20 
f!99-67 

f200-43 
208-00 

1,483 

28-270 

209-10 

Plombieres      . 

1  381 

28-390 

209-30 

Moscow      . 

984 

28-820 

210-20 

Vienna 

436 

29-410 

211-10 

Home     

151 

29-760 

211-60 

Dead  Sea  (below  Mediterranean  "» 

Seal  . 

—  1316-7 

31-496 

•f-214-44 

*  Guyot. 


f  Estimated  by  Forbes'  coefficient. 


684 


APPENDIX. 


TABLE  XIX. 

BOILING  POINT  OF  WATER  AT  DIFFERENT  ATMOSPHERIC 
PRESSURES.— REGNAULT. 


Pressure  in  atmo- 
spheres of  30  inches 
mercury. 

Boiling  Point  of 
Water. 

Pressure  in  atmo- 
spheres of  30  inches 
mercury. 

l 

Boiling  Point  of 
Water. 

1 

212     °F. 

11 

364-2  °F. 

2 

249-5 

12 

371-1 

3 

273-3 

13 

377-8 

4 

291-2 

14 

384 

5 

306-0 

15 

390 

6 

318-2 

16 

395-4 

7 

329-6 

17 

400-8 

8 

339-5 

18 

405-9 

9 

348-4 

19 

410-8 

10 

356-6 

20 

415-4 

TABLE  XX. 

LIQUEFACTION  AND  SOLIDIFICATION  OF  GASES. 


Names  of  the  Gases. 

Melting 
Point. 

°P. 

Pressure  in  Atmospheres. 

At  32°  F. 

At  60°  F. 

°F. 

Sulphurous  acid     .     .     . 
Cyanogen     

—  105° 
—    30 
—    60 
—  103 
—  122 
—  150 
—    70 
—    65 
—  124 
—  220 

1-53 
2-37 
3-97 
4.4 

10 

32 
38-5 

8-95 
26-20 

2-54 

5-86 
6-90 

13-19 

5-16  at  100° 
4-00  at  63 

10-00  at  83 
14-60  at  52 
33-40  at  35 

26-90  at       0° 
11-54  at  —  62 
40       at     50 

Hydriodic  acid      .     .     . 
Ammonia      

Sulphuretted  hydrogen  . 
Protoxid  nitrogen       .     . 
Carbonic  acid   .... 
Euchlorine   
Hydrobromic  acid      .     . 
Fluorid  of  silicon  .     .     . 
f  Chlorine 

Arseniuretted  hydrogen 
Phosphuretted  hydrogen 
Olefiant  gas  .              .     . 
Fluorid  of  boron    .     .     . 
[  Hydrochloric  acid      .     . 

PHYSICAL   TABLES. 


685 


.- 

O  ~1  Ci  Or  HJ  CO  O  ^  *>.  <i>  6<  S. 
WOrf^ 


to  --i  to 

-^HJ^CC-'lcb^osdiOo: 


II 

&i 


to  >-»  i-*  >-« 


60* 


686 


APPENDIX. 


TABLE  XXII.— LATENT  AND  SENSIBLE  HEAT  OF  STEAM. 


Temp. 

Latent  Heat. 

i 

Sum  of  Latent 
and  Sensible  Heat. 

Temp. 

i  itwnf  Tii..,t       Sum  of  Latent 
Latent  Heat.  and  gensible  Heat 

32° 

1092-6° 

1124-6° 

248° 

939  6° 

1187-6° 

68 

1067-4 

1135-4 

284 

914-4 

1198-4 

86 

1054-8 

11408 

320 

889-2 

1209-2     . 

104 

1042-2 

11462 

338 

874-8 

1212-8 

140 

1017-0 

1157  0 

374 

849-6 

1223-6 

194 

979-2 

1173-2 

410 

822-6 

1232-6 

212 

966-6 

1178-6 

446 

795-6 

1241-6 

REGNAULT'S  RESULTS.       683. 


Pressure  in  Atmo- 
spheres. 

Temperature. 

Latent  Heat. 

Sum  of  Latent  and 
Sensible  Heat. 

0-0014 

0° 

1114-0° 

1114-0° 

0-006 

32 

1091-7 

1123-7 

1-000 

212 

966-6 

11786 

8.000 

339 

877-3 

1216-8 

TABLE  XXIIL— SPECIFIC  GRAVITY  OF  SOLIDS  AND  LIQUIDS. 


Substances. 

Sp.  Gravity. 

Substances.          • 

Sp.  Gravity. 

Platinum  .     . 

21- 

2'32 

Gold     

19-24 

Sulphur    

2-03 

Tungsten  

17* 

Bone     ...          .     . 

r8-l'99 

13-60 

1/92 

Rhodium  and  Palladium 
Silver 

11- 

10-47 

Caoutchouc    .... 

0-989 
0-97 

Bismuth    .     .     ,     .     . 

9-82 

Wax      

0-97 

Copper 

8-78 

Gutta-percha 

0-966 

Arsenic     

8-60 

Ice  

0-9175 

Steel    .              ... 

7-81 

Pumice-stone 

0-92 

7-78 

Potassium      .... 

0-86 

Meteoric  iron     .     .     . 
Cast  iron 

7-26-7-79 
7-21 

Pine  wood     .... 
Cypress  wood 

0-66 
0-60 

Zinc     ...... 

6  '8  6 

Cedar  wood  .... 

0-56 

Antimony      .... 
Iodine  
Heavy  spar   .... 
Oriental  ruby     .     .     . 
Topaz  . 

6-71 
4-95 
4-43 
4-28 
3-56 

Common  poplar      .     . 
Lombardy  poplar    .     . 
Cork      

LIQUIDS. 

Sulphuric  acid   . 

0-38 
0-36 
0-24 

1-84 

Diamond 

3'50 

Nitrous  acid  .... 

1-55 

English  flint-glass 
Parian  marble    .     .     . 
Emerald 

3-33 

2-84 
2-77 

Water  from  Dead  Sea 
Nitric  acid     .... 
Milk     

1-24 
1-22 
1-03 

Pearl 

2-75 

Wine 

0-99 

Iceland  spar       .     .     . 
Common  marble     .     . 
Coral    

2-72 
2-70 

2-68 

Linseed  oil    .... 
Spirits  turpentine  .     . 
Absolute  alcohol 

0-94 
0-87 
0-79 

Quartz  

2-65 

Naphtha,  "light  oil"  . 

0-733 

Agate   . 

2-61 

Sulphuric  ether 

0'72 

2-49 

0-655 

PHYSICAL    TABLES. 


687 


TABLE  XXIV. 

VOLUME  AND  DENSITY  OF  WATER.— BY  KOPP. 


Temperature. 
C. 

Volume  of  Water 
(at  0°  =  1). 

Sf  Gr.  of  Water 
(atO°  =  l). 

Volume  of  Water 
(at4°  =  l). 

Sp.  Gr.  of  Water 
(at  4°  =  1). 

0 

1-00000 

1-000000 

1-00012 

0-999877 

1 

0-99995 

1  -000053 

1-00007 

0-999930 

2 

0-99991 

1-000092 

1-00003 

0-999969 

3 

0-99989 

1-000115 

1-00001 

0-999992 

4 

0-99988 

1-000123 

1-00000 

1-000000 

5 

0-99988 

1-000117 

1-00001 

0-999994 

6 

0-99990 

1-000097 

1-00003 

0-999973 

7 

0-99994 

1-000062 

1-00006 

0-999939 

8 

0-99999 

1-000014 

1-00011 

0-999890 

9 

1-00005 

0-999952 

1-00017 

0-999829 

10 

1-00012 

0-999876 

1-00025 

0-999753 

11 

1-00021 

0-999785 

1-00034 

0-999664 

12 

1-00031 

0-999686 

1  -00044 

0-999562 

13 

1-00043 

0-999572 

1-00055 

0:999449 

14 

1-00056 

0-999445 

1-00068 

0-999322 

15 

1-00070 

0-999306 

1-00082 

0-999183 

16 

1-00085 

0-999155 

1-00097 

0-999032 

17 

1-00101 

0-998992 

1-00113 

0-998869 

18 

1-00118 

0-998817 

1-00131 

0-998695 

19 

1-00137 

0-998631 

1-00149 

0-998509 

20 

1-00157 

0-998435 

1-00169 

0-998312 

21 

1-00178 

0-998228 

1-00190 

0-998104 

22 

1-00200 

0-998010 

1-00212 

0-997886 

23 

1-00223 

0-997780 

1-00235 

0-997657 

24 

1-00247 

0-997541 

1-00259 

0-997419 

25 

1-00271 

0-997293 

1-00284 

0-997170 

26 

1-00295 

0-997035 

1-00310 

0-996912 

27 

1-00319 

0-996767 

1-00337 

0-996644 

28 

1-00347 

0-996489 

1-00365 

0-996367 

29 

1-00376 

0-996202 

1-00393 

0-996082 

30 

•00406 

0-995908 

1-00423 

0-995787 

35 

•00570 

40 

•00753 

45 

•00954 

50 

•01177 

55 

•01410 

60 

•01659 

65 

•01930 

70 

•02225 

75 

•02541 

80 

•02858 

85 

1-03189 

90 

1-03540 

95 

1-03909 

100 

1-04299 

688 


APPENDIX. 


TABLE  XXV. 

COMPARISON  OF  THE  DEGREES  OF  BEAUME'S  HYDROMETER  WITH 
THE  REAL  SPECIFIC  GRAVITY. 

A. — FOR  LIQUIDS  HEAVIER  THAN  WATER. 


Degrees. 

Specific 
GraTity. 

Degrees. 

Specific 
Gravity. 

Degrees. 

Specific 
Gravity. 

Degrees. 

Specific 
Gravity. 

0 

1-000 

20 

1-152 

40 

1-357 

60 

1-652 

1 

1-007 

21 

1-160 

41 

1-369 

61 

1-670 

2 

1-013 

22 

1-169 

42 

1-381 

62 

1-689 

3 

1-020 

23 

1-178 

43 

1-395 

63 

1-708 

4 

1-027 

24 

1-188 

44 

1-407 

64 

1-727 

5 

1-034 

25 

1-197 

45 

1-420 

65 

•747 

6 

1-041 

26 

1-206 

46 

1-434 

66 

•767 

7 

1-048 

27 

1-216 

47 

1-448 

67 

•788 

8 

1-056 

28 

1-225 

48 

1-462 

68 

•809 

9 

1-063 

29 

1-235 

49 

1-476 

69 

•831 

10 

1-070 

30 

1-245 

50 

1-490 

70 

•854 

11 

1-078 

31 

1-256 

51 

1-495 

71 

•877 

12 

1-085 

32 

1-267 

52 

1-520 

72 

•900 

13 

1-094 

33 

1-277 

53 

1-535 

73 

•924 

14 

1-101 

34 

1-288 

54 

1-551 

74 

1-949 

15 

1-109 

35 

1-299 

55 

1-567 

75 

1-974 

16 

1-118 

36 

1-310 

56 

1-583 

76 

2-000 

17 

1-126 

37 

1-321 

57 

1-600 

18 

1-134 

38 

1-333 

58 

1-617 

19 

1-143 

39 

1-345 

59 

1-634 

B. — FOR  LIQUIDS  LIGHTER  THAN  WATER. 


Degrees. 

Specific 
Gravity. 

Degrees. 

Specific 
Gravity. 

Degrees. 

Specific 
Gravity. 

Degrees. 

Specific 
Gravity. 

10 

1-000 

23 

•918 

36 

•849 

49 

•789 

11 

•993 

24 

•913 

37 

•844 

50 

•785 

12 

•986 

25 

•907 

38 

•839 

51 

•781 

13 

•980 

26 

•901 

39 

•884 

52 

•777 

14 

•973 

27 

•896 

40 

•830 

53 

•773 

15 

•967 

28 

•890 

41 

•825 

54 

•768 

16 

•960 

29 

•885 

42 

•820 

55 

•764 

17 

•954 

30 

•880 

43 

•816 

56 

•760 

18 

•948 

31 

•874 

44 

•811 

57 

•757 

19 

•942 

32 

•869 

45 

•807 

58 

•753 

20 

•936 

33 

•864 

46 

•802 

59 

•749 

21 

•930 

34 

•859 

47 

•798 

60 

•745 

22 

•924 

35 

•854 

48 

•794 

j 

PHYSICAL   TABLES. 


689 


TABLE  XXVI. 

TENSION,  VOLUME,  AND  DENSITY  OP  AQUEOUS  VAPOR. 


Temperature 
of  Vapor. 
Degrees 
Centigrade. 

Tension  of  Vapor 
expressed  in 
Atmospheres. 

Tension 
expressed  by 
a  column  of 
mercury 
in  metres. 

Volume 
occupied  by  a 
kilogramme  of 
vapor,  in  cubic 
metres. 

Weight  of  a 
cubic  metre  of 
Aqueous  Vapor 
in  kilogrammes. 

0° 

T£s  or    0-0060 

0-00460 

205-222400 

0-00487266 

17-86 

ft  or    0-0200 

0-01520 

66-144960 

0-01512517 

29-37 

J5  or    0-0400 

0-03040 

34-364490 

0-02909000 

33-30 

ft  or    0-0500 

0-03800 

27-852530 

003590307 

37-38 

ft  or    0-0625 

0-04750 

22-578310 

0-04430600 

42-66 

ft  or    0-0833 

0-06330 

17-232270 

0-05803375 

46-25 

ft  or    0-1000 

0-07600 

14-515640 

0-06892666 

50-60 

|  or    0-1250 

0-09500 

11-769500 

0-08495800 

53-35 

I  or    0-1428 

0-10857 

10-391950 

0-09622000 

56-63 

£or    0-1666 

0-12666 

8-996440 

0-11119230 

60-40 

|  or    0-2000 

0-15184 

7-582970 

0-13185937 

65-36 

for    0-2500 

0-19000 

6-156670 

0-16240770 

81-72 

}or    0-5000 

0-38000 

3-227120 

0-30983570 

92-18 

f  or    0-7500 

0-57000 

2-215120 

0-45141000 

100- 

1    or    1-0000 

0-76000 

1-696000 

0-59130000 

106-33 

Hor    1-2500 

0-95000 

1-380541 

0-72430000 

111-83 

l|or    1-5000 

1-14000 

1-167228 

0-85670000 

116-50 

If  or    1-7500 

1-33000 

1-012619 

0-98752500 

120-64 

2    or    2-0000 

1-52000 

0-895462 

1-11571700 

124-39 

2J  or    2-2500 

1-72000 

0-798033 

1-25305700 

127-83 

2£  or    2-5000 

1-90000 

0'-729463 

1-37087500 

130-98 

2|  or    2-7500 

2-09000 

0-668363 

1-49620700 

133-91 

3    or    3-0000 

2-28000 

0-616697 

1-62038400 

136-72 

3J  or    3-2500 

2-47000 

0-573576 

1-74340000 

139-29 

3£  or    3-5000 

2-66000 

0-534694 

1-86582600 

141-72 

3|or    3-7500 

2-85000 

0-503167 

1-98731800 

144- 

4    or    4-0000 

3-04000 

0-474320 

2-10828500 

146-28 

4Jor    4-2500 

3-23000 

0-448860 

2-22780000 

148-44 

4J  or    4-5000 

3-42000 

0-426093 

2-34683300 

15035 

4|or    4-7500 

3-61000 

0-405507 

2-46605500 

152-26 

5    or    5-0000 

3-80000 

0-386960 

2-58417600 

154-15 

5J-  or    5  2500 

3-99000 

0-370170 

2-70135200 

155-94 

5|  or    5-5000 

4-18000 

0-354778 

2  81225050 

157-64 

5|or    5-7500 

4-37000 

0-340669 

2-93460000 

159-25 

6    or    6-0000 

4-56000 

0-327779 

3-05078500 

165-40 

7    or    7-0000 

5-32000 

0-284938 

3-50930700 

170-84 

8    or    8-0000 

6  -08000 

0-252423 

3-97063600 

175-77 

9    or    9-0000 

6-84000 

0-226771 

4-40770000 

180-30 

10  or  10-0000 

7-60000 

0-206248 

4-84844400 

184-60 

11  or  11-0000 

8-36000 

0-189189 

5-28325000 

188-54 

12  or  12-0000 

9-12000 

0-174952 

5-71425000 

190- 

12-4250 

9-44300 

0-169437 

5-91142800 

195- 

13-8160 

10-52000 

0-153660 

6-50428600 

200- 

15-3560 

11-68900 

0-138717 

7-31716600 

230- 

27-5340 

20-92600 

0-083115 

12-03722000 

j 

ANSWERS    TO    PROBLEMS. 


Prob.  1.  Ans.  (a.)  147640-46  yds.;  (6.)  1-021  inches;  (c.)  0-03937079  inchj 
(d.)  1-1811237. 

Prob.  2.  Ans.  (a.)  1-39697  metres;  (6.)  1131-5495  metres;  (c.)  20-921  kilo- 
metres; (d.)  4-57  metres. 

Prob.  3.  Ans.  (a.)  1  litre  and  703-258  cubic  centimetres;  (6.)  1-1  gallons; 
(c.)  31-7936  litres,-'  (d.)  0-01232931  pint. 

Prob.  4.  Ans.  (a.)  0-63499  metre;  (6.)  54-7286  Amer.  inches;  (c.)  22-86 
metres  ;  (d.)  5468-48  Amer.  yards. 

Prob.  5.  Ans.  (a.)  4258-1458  cubic  centimetres ;  (6.)  45419-4486  cubic  centi- 
metres; (c.)  0-1618  gallon. 

Prob.  6.    Ans.  0-1515  foot  per  second. 

Prob.  7.    Ans.  60  X  -  feet. 
n 

Prob.  8.     Ans.  Unit  of  time  =  0-3896  second. 

Prob.  9.  Ans.  At  an  angle  of  36°  52'  12"  with  the  component  4,  and  with  a 
velocity  =  5. 

Prob.  10.     Ans.  Speed  of  A  =  f  f  of  speed  of  B. 

Prob.  11.     Ans.  Velocity  =  180  feet  per  second;  distance  =  1800  yards. 

Prob.  12.     Ans.  20  feet  per  second. 

Prob.  13.     Ans.  Retardation  =  25  feet  per  second;  distance  =  312$  feet. 

Prob.  14.     Ans.  25142f  Ibs. 

Prob.  15.     Ans.  31,250  feet  per  second  or  5.9  miles. 

Prob.  16.     Ans.  It  would  not. 

Prob.  17.     Ans.  144  feet,  9  inches. 

Prob.  18.     Ans.  3  seconds. 

Prob.  19.  Ans.  If  h  represent  the  height  of  the  tower,  the  velocity  re- 
quired =  }/^h. 

Prob.  20.  Ans.  If  v  represents  the  vertical  velocity  of  the  balloon,  the 
height  =  —  (gt  -  t>)2. 

Prob.  21.     Ans.  The  height  =  ff~X  (*  +  —  V- 

8        \        9*J 
Prob.  22.     Ans.  396-03  feet. 
Prob.  23.     Ans.  64J  feet. 

Prob.  24.     Ans.  Height  of  bridge  =  100-52  feet ;  time  required  =  2-4  seconds. 

(691) 


692 


ANSWERS   TO   PROBLEMS. 


X  *  seconds  of  ascent  and  return. 


Prob.  25.  Ans.  402-^  feet. 

Prob.  26.  Ans.  Velocity  = 

Prob.  27.  Ans.  208-44  feet. 

Prob.  28.  Ans.  6-2  seconds. 

Prob.  29.  Ans.  96*75  feet. 

Prob.  30.  Ans.  103-37  miles  per  hour. 

Prob.  31.  Ans.  The  train  cannot  ascend  such  a  grade  without  more  steam.  It 
would  require  an  initial  velocity  of  54.69  miles  per  hour  to  overcome  such  a  grade. 

Prob.  32.  Ans.  265-099  Ibs. 

Prob.  33.  Ans.  3-3256  Ibs. 

Prob.  34.  Ans.  Twelve  times  its  present  velocity. 

Prob.  35.  Ans.  8-45  revolutions  per  second. 

Prob.  36.  Ans.  1-74  seconds. 

Prob.  37.  Ans.  31£  feet. 

Prob.  38.  Ans.  0-88  second. 

Prob.  39.  Ans.  1-003  seconds. 

Prob.  40.  Ans.  At  New  York  g  =  iPl  =  32-155399  feet. 
At  Cape  Horn  g  =  Jl  =  32-205083  feet. 
At  Boston  g  =  32-17076  (1—0-00259  cos.  2X)  =  32-163064  ft.* 
At  New  Orleans  g  =  "        "        «        «        =  32-125757  ft.* 
At  Stockholm  g  =      "        "        «        "        =  32-131002  ft.* 

Prob.  41.  Ans.  g'  =  ftg. 

Prob.  42.  Ans.  13916-25  feet  =  2-64  miles. 

Prob.  43.  Ans.  31088  feet  =  5-89  miles. 

Prob.  44.  Ans.  24-87  seconds. 

Prob.  45.  Ans.  35°  19'  43"-5  or  54°  40'  16"-5. 

Prob.  46.  Ans.  736-35  feet  per  second. 

Prob.  47.  Ans.  4|£  times  greater. 

Prob.  48.  Ans.  21-21  miles  per  hour.  m 

Prob.  49.  Ans.  As  1  to  2J. 

Prob.  50.  Ans.  50  feet. 

Prob.  51.  Ans.  As  1  to  7^. 

Prob.  52.  Ans.  2f  feet  from  the  smaller  weight. 

Prob.  53.  Ans.  Under  the  weight  7. 

Prob.  54.  Ans.  125  Ibs.  and  75  Ibs. 

Prob.  55.  Ans.  At  one  point  9§  cwt.,  at  the  other  20J  cwt. 

Prob.  56.  Ans.  Pressure  on  A  =  10-4  cwt.  ;  pressure  on  B  =  17-6  cwt. 

Prob.  57.  Ans.  40  Ibs. 

Prob.  5£.  Ans.  Diameter  of  axle  2^  inches. 

Prob.  59.  Ans.  92^  Ibs. 

Prob.  60.  Ans.  156  cwt. 

Prob.  61.  Ans.  1382-4  tons. 

Prob.  62.  Ans.  4970  Ibs. 

Prob.  63.  Ans.  3|  cwt. 

Prob.  64.  Ans.  60  Ibs. 

Prob.  65.  Ans.  12  cwt. 

Prob.  66.  Ans.  A  power  equal  to  8  cwt.  would  balance  the  train,  but  some 
additional  force  is  required  to  impart  motion  independent  of  friction,  which  is 
not  considered. 

Prob.  67.  Ans.  67858-56  Ibs. 


*  Approximate  values.     See  g  90. 


ANSWERS    TO    PROBLEMS.  693 

Prob.  68.     Ans.  79-58  Ibs. 

Prob.  69.     Ans.  10  Ibs. 

Prob.  70.     Ans.  A  force  of  18  cwt.  in  both  cases. 

Prob.  71.     Ans.  476-22  horse-power. 

Prob.  72.     Ans.  1-5874  times  greater. 

Prob.  73.     Ans.  11-94  miles  per  hour. 

Prob.  74.  Ans.  At  14°,  12321-53  kilogrammes;  at  50°,  12925-69  kilo- 
grammes; at  212°,  13885.42  kilogrammes;  at  392°,  12291.67  kilogrammes. 

Prob.  75.  Ans.  At  50°  a  rod  having  a  section  of  one  square  millimetre  would 
be  elongated  one-fourth  of  an  inch. 

Prob.  76.     Ans.  Double  the  weight  in  the  first  case. 

Prob.  77.  Ans.  Sixteen  times  as  much  as  if  the  beam  were  secured  at  one 
end  and  the  weight  applied  at  the  other  extremity. 

Prob.  78.  Ans.  Tempered  steel,  5634-95  to  7546-76  Ibs. ;  untempered  steel., 
5433-5  to  6238-7  Ibs. 

Prob.  79.     Ans.  0-07  inch. 

Prob.  80.     Ans.  3498-86  Ibs.  to  8724-71  Ibs. 

Prob.  81.     Ans.  15-474  tons  to  18-548  tons  of  2000  Ibs. 

Prob.  82.  Ans.  Considering  the  ends  secured  by  union  with  the  entire  struc- 
ture, the  breaking  weight  =  2990-18  tons ;  considering  the  ends  not  secured, 
but  merely  supported  on  the  piers,  the  breaking  weight  =  1495-09  tons. 

Prob.  83.  Ans.  If  the  ends  are  securely  fastened  the  working  load  =  532-69 
tons ;  but  if  the  ends  are  merely  supported  the  working  load  =  233-67  tons. 

Prob.  84.  Ans.  280-69  tons.  Since  the  entire  structure  forms  a  continuous 
tube,  the  ends  of  the  middle  span  are  securely  fastened. 

Prob.  85.     Ans.  59-43  tons. 

Prob.  86.  Ans.  v  =  5-85579  feet  per  second;  v'  =  8-67579  feet  per  second; 
K  =  6||  feet  per  second. 

Prob.  87.     Ans.  m  =  7W. 

Prob.  88.-  Ans.  e  =  0-6. 

Prob.  89.     Ans.  153  feet. 
1 

Prob.  90.     Ans.  r  = -. 

Prob.  91.     Ans.  25-6  feet. 

Prob.  92.     Ans.  84-3  feet  per  second. 

Prob.  93.     Ans.   Condensation  =  0-001006;  specific  gravity  =  1-001007. 

Prob.  94.     Ans.  Specific  gravity  =  1-0487. 

Prob.  95.     Ans.  0.5723  of  a  cubic  inch. 

B2 
Prob.  96.     Ans.  The  pressure  =  P  X  — :• 

A 

Prob.  97.     Ans.  Pressure  :  Power  =  4050  :  1. 

Prob.  98.  Ans.  Pressure  on  the  bottom  =  the  weight  of  the  liquid  =  half 
the  sum  of  the  pressures  on  the  four  sides. 

Prob.  99.     Ans.  0-5773  a,  0-2392  a,  and  0-1835  a. 

Prob.  100.     Ans.  P  :  P'  =  1  :  2. 

Prob.  101.     Ans.  As  the  height  of  the  cylinder  to  its  radius. 

Prob.  102.  Ans.  Pressure  of  water  ==  U01-3  Ibs.;  pressure  of  mercurj 
=  7-48888  tons. 

Prob.  103.     Ans.  Let  R  =  pressure  on   the  triangles,   the  pressure  on   the 

/ 
base  being  reckoned  as  unity.     Then  :— R  =  i  */ 

61  2Z 


694  ANSWERS    TO    PROBLEMS. 

Prob.  104.  Ans.  7138  1  grs.  =  1-0197  Ibs. 

Prob.  105.  Ans.  1-83823  feet. 

Prob.  106.  Ans.  14-4  inches. 

Prob.  107.  Ans.  500  Ibs. 

Prob.  108.  Ans.  0-03789  X  given  weight  of  the  iron. 

Prob.  109.  Ans.  11-50228  ounces. 

Prob.  110.  Ans.  Gold  =  13-8102  ounces,  silver  =  8-1898  ounces. 

Prob.  111.  Ans.  The  addition  of  10  Ibs.  of  lead  weights  under  water  to  produce 
equilibrium  shows  that  209-5  Ibs.  of  iron  are  concealed  in  the  commercial  lead. 

Prob.  112.  Ans.  5-0752  Ibs. 

Prob.  113.  Ans.  0-6028  diameter. 

Prob.  114.  Ans.  138-637  cubic  inches. 

Prob.  115.  Ans.  64-1832  cubic  feet. 

Prob.  116.  Ans.  473'538  tons. 

Prob.  117.  Ans.  67-698  tons. 

Prob.  118.  Ans.  0-9825  feet. 

Prob.  119,  Ans.  Volume  of  B  =  4795-34  cubic  inches  =  2-775  cubic  feet; 
(both  cases  assume  a  depth  of  twenty  feet  below  the  surface). 

Prob.  120.  Ans.  Specific  gravity  —  3-84. 

Prob.  121.  Ans.  Specific  gravity  of  granulated  tin  =  7-288. 

Prob.  122.  Ans.  Specific  gravity  =  3-8093. 

Prob.  123.  Ans.  Specific  gravity  of  the  fir.st  =  2-8  ;  specific  gravity  of  the 
second  =  1-0946.     The  volumes  of  the  two  bodies  are  as  1  to  14-8. 

Prob.  124.  Ans.  Specific  gravity  =  8-13. 

Prob.  125.  Ans.  Specific  gravity  =  -832. 

Prob.  126.  Ans.  23-385  gallons.     Theoretical  discharge,  37-718  gallons. 

Prob.  127.  Ans.  Actual  range,  15-187  feet. 

Prob.  128.  Ans.  Actual  velocity  =  0-3833  theoretical  velocity. 

"  Prob.  129.  Ans.  10180-217  gallons. 

Prob.  130'.  Ans.  38,450  gallons,  or  610  hogsheads. 

Note.     In  the  formula,  D  =  20-8  A  / ,  all  the  quantities,  H,  d,  and  /, 

YM-  54d 
are  to  be  taken  in  metres,  and  the  result  gives  D  in  cubic  metres  per  second. 

Prob.  131.     Ans.  97-496  feet. 

Prob.  132.     Ans.  If  the  actual  height  of  the  mercury  is  1  inch,  the  height  of 
the  alcohol  will  J)e  22'68  inches,  difference  of  level  21-68  inches. 

Prob.  133.     Ans.  63-68  miles.     This  problem  involves  the  principles  of  §  172. 

Prob.  134.     Ans.  286-1855  Ibs. 

Prob.  135.     Ans.   1156-3  Ibs. 

Prob.  136.     Ans.  0-0796  grain. 

Prob.  137.     Ans.  460-00437  grains. 

Prob.  138.     Ans.  Capacity  of  the  globe  =  148-626  cubic  feet  j  specific  gravity 
of  gas  =  0-0767. 

Prob.  139.     Ans.  31-7576  feet. 

Prob.  140.     Ans.  68  feet. 

Prob.  141.     Ans.  17-98  feet. 

Prob.  142.     Ans.  6655-85  feet. 

Prob.  143.     Ans.  Ascensional   force   with    illuminating    gas,    358-4837   Ibs.  ; 
ascensional  force  with  hydrogen,  473-0793  Ibs. 

Prob.  144.     Ans.  The  conditions  of  this  problem  require  that  the  weight  of 
the  balloon  should  be  nothing,  or  that  the  ballast  should  have  an  ascensional 


ANSWERS    TO    PROBLEMS.  095 

force  of  its  own  equal  to  the  weight  of  the  balloon,  since,  at  the  height  indicated, 
if  the  enclosed  gas  could  not  expand,  it  would  of  itself  be  in  equilibrium  with 
the  atmosphere.  If  one-half  the  gas  were  liberated  the  balloon  would  ascend ; 
to  make  it  remain  stationary  an  amount  of  ballast  must  be  added  equal  to  the 
weight  of  the  gas  liberated,  or  equal  to  one-fourth  the  weight  of  air  which  would 
fill  the  balloon  at  the  surface  of  the  earth. 

Prob.  145.     Ans.  The  tube  will  admit  no  water  by  compression  of  the  air. 

Prob.  146.     Ans.  0-016  inch. 

Prob.  147.     Ans.  45-10735  grammes. 

Prob.  148.     Ans.  76-306  centimetres. 

Prob.  149.     Ans.  Jf/,  £/,  %l,  tfl,  ftl. 

Prob.  150.     Ans.  5  Ibs.  10  oz. 

Prob.  151.     Ans.  0-09698  inch. 

Prob.  152.     Ans.  Four  times  as  long. 

Prob.  153.     Ans.  8105£  feet,  or  a  little  more  than  H  miles. 

Prob.  154.  Ans.  Velocity  at  90°  F.  =  1150-091  feet  per  second,  and  at 
_  40°  F.  =  1007-091  feet  per  second. 

Prob.  155.     Ans.  11-2  seconds. 

Prob.  156.  Ans.  In  iron,  1-59  seconds;  in  wood,  1-03  to  1-65  seconds;  in 
carbonic  acid,  21-49  seconds ;  in  hydrogen  gas,  4-44  seconds ;  in  vapor  of  alco- 
hol at  140°  F.,  21-44  seconds;  in  vapor  of  water  at  154°  F.,  13'72  seconds. 

Prob.  157.     Ans.  27  minutes,  9  seconds. 

Prob.  158.     Ans.  1677-45  feet  in  the  most  favorable  position. 

Prob.  159.     Ans.  422  feet. 

Prob.  160.     Ans.   125-69  miles. 

Prob.  161.     Ans.  13  seconds. 

Prob.  162.     Ans.  Distance  =  2294  feet;  velocity  =  764  feet  per  second. 

Prob.  163.     Ans.   fa  of  its  length. 

Prob.  164.     Ans.  101  ^  vibrations. 

Prob.  165.     Ans.  3'408  feet. 

Prob.  166.     Ans.  E  :  DJt  =  25  :  24. 

Prob.  167.     Ans.  fftff. 

Prob.  168.     Ans.  It  is  higher  by  a  comma. 

Prob.  169.  Ans.  The  chromatic  semitone  =  ^f  ^ ;  the  grave  chromatic  semi- 
tone =  |f. 

Prob.  170.     Ans.  1800  beats  per  minute. 

Prob.  171.  Ans.  Vibrations  per  minute  for  one  node,  66-56;  for  two  nodes, 
133-13;  for  three  nodes,  199-695;  for  four  nodes,  266-26  vibrations. 

Prob.  172.     Ans.  263-57. 

Prob.  173.     Ans.  Reduce  the  length  of  the  tube  to  9-343  metres. 

Prob.  174  Ans.  For  C  1,  8-0405  feet;  D  1,  7-0939  feet ;  E  1,  6-3407  feet;  F  1, 
5-9262  feet;  G  1,  5-2214  feet;  A  1,  4-6618  feet;  B  1,  41022  feet ;  C  2,  3-8326  feet. 

Prob.  175.  Ans.  11-39  in.,  10-03  in.,  8-95  in.,  8-38  in.,  7-37  in.,  6'59  in.,  5-8  in., 
5-45  in. 

Prob.  176.  Ans.  F  5  (too  flat),  A  5  (too  high  by  half  a  semitone),  and  C  6 
(also  too  high  by  half  a  semitone). 

nV 

The  formula  JV=  gives  for 

L  +  $nS* 

n  =  2  N=  2672-5  while  F  5  =  2739-2. 

n  =  3  N  =  3538-6  while  A  5  =  3424. 

n  =  4  N  =  4223-2  while  C  6  =  4108-8. 


t>yb  ANSWERS    TO    PROBLEMS. 

Prob.  177.     Ans.  8  minutes,  14-79  seconds. 

Prob.  178.     Ans.  46  years,  155  days,  10  hours,  8  minutes,  and  45  seconds. 
Prcb.  179.     Ans.  As  1  to  2J. 
Prob.  180.     Ans.  90J  per  cent. 
Prob.  181.     Ans.  22-85  candles. 
Prob.  182.     Ans.  21-43  candles. 
Prob.  183.     Ans.  60°. 

Prob.  184.     Ans.  18,  including  the  object  itself. 
Prob.  185.     Ans.  626j  inches. 
Prob.  186.     Ans.  72  inches. 
Prob.  187.     Ans.  u  =  r  j/£. 

Prob.  188.  Ans.  Once  and  a  half  the  distance  of  the  object  from  the  rtrsl 
surface. 

Prob.  189.     Ans.  39°  49'  3",  when  the  eye  is  5  feet  above  the  water. 
Prob.  190.     Ans.  6  feet,  8  inches. 
Prob.  191.     Ans.  n  =  2. 

Prob.  192.  Ans.  At  a  distance  of  2-571  feet  from  the  refracting  surface,  and 
on  the  same  side  as  the  radiant  point. 

Prob.  193.     Ans.  The  surface  is  convex,  and  r  =  7*2  inches. 
Prob.  194.     Ans.  On  the  opposite  side  of  the  lens  at  a  distance  of  3-134  inches. 
Prob.  195.     Ans.  r  :.«  =  10  :  242,   the   surface  of  shorter  curvature  being 
turned  towards  parallel  rays. 
Prob.  196.     Ans.  6-44  inches. 

Prob.  197.     Ans.  A  convex  lens  in  which  /==  4  inches. 

Prob.  198.  Ans.  A  double  convex  lens  of  crown  glass  r  =  2-955  inches, 
a  =  2-667  inches,  and  a  concavo-plane  lens  of  flint  glass  r'  =  2-667  inches,  and 
«'  =  infinity,  i.  e.  the  second  surface  is  plane. 

Prob.  199.  Ans.  They  must  converge  toward  a  point  between  the  lenses  and 
distant  f  /  from  the  first. 

Prob.  200.     Ans.  2  diameters. 

Prob.  201.     Ans.  r  =  0-449  inches,  s  =  —  1-235  inches. 
Prob.  202.     An-s.  161280  times  the  light  received  by  the  unassisted  eye. 
Prob.  203.     Ans.  Illuminating  power  =  362880  ;  penetrating  power  =  602-4. 
Prob.  204.     Ans.  Illuminating  power  =  18225 ;  penetrating  power  =  135. 
Prob.  205.     Ans.  The  illuminating  power  given  by  150°  aperture  is  2i  times, 
and  the  penetrating  power  1£  times  as  great  as  that  given  by  100°  aperture. 

Prob.  206.  Ans.  Crown  glass,  56°  43'  40" ;  plate  glass,  56°  36'  26"  j  flint 
glass,  57°  30'  18". 

Prob.  207.  Ans.  Reflected  by  crown  glass,  0-0726;  by  plate  glass,  0-0738; 
by  flint  glass,  0-0869. 

544. 

Degrees  R. 

—32°  ' 

—16 

+56 

+72 

+182-4 

-j-328-8 

+420 

+  800 

+4311-12 


Prob.  208. 

Ans.  1-544. 

Prob.  209. 

Ans.  Degrees  F. 

= 

Degrees  C. 

—40° 

= 

—40° 

—  4 

— 

—20 

- 

+158 

BBS 

+70 

+194 

= 

+90 

+442-4 

= 

+228 

+771-8 

= 

+411 

+977 

= 

+525 

+1832 

= 

+  1000 

+9732 

= 

+  5388-9 

ANSWERS    TO    PROBLEMS. 


697 


Prob.  210 


Prob.  211. 
Prob.  212. 

+290              =      +554              =     +232 
+360              =      +680              =     +288 
Ans.  18^  times. 
Ans. 

At  10°  F. 

25°  P.                              75°  F.                             100°  Jf. 

Iron  . 
Brass      .     . 
Copper  .     . 
Glass      .     . 
Platinum    . 
Silver     .     . 

3ft.  1-99002  in. 
3ft.  1-98425  in. 
3ft.  1-98550  in. 
3ft.  1-99032  in. 
3  ft.  1-99253  in. 
3  ft.  1-98387  in. 

3ft.  1-99376  in. 
3ft.  1-9901  6  in. 
3  ft.  1-99093  in. 
3ft.  1-99578  in. 
3  ft.  1-99533  in. 
3  ft.  1-98992  in. 

3  ft.  2-00623  in. 
3  ft.  2-00984  iu. 
3  ft.  2-00906  in. 
3  ft.  2-00403  in. 
3  ft.  2.00466  in. 
3ft.  2-01060  in. 

3  ft.  2-01248  in. 
3ft.  2-0  1968  in. 
3ft.  2-01812  in. 
3  ft.  2-00670  in. 
3  ft.  2.00933  in. 
3  ft.  2-02014  in. 

Prob.  213.     Ans.  1-002672  gallons. 

Prob.  214.     Ans.  0-134  inch. 

Prob.  215.     Ans.  41°-51  Fahrenheit. 

Prob.  216.     Ans.  0-04728  in. 

Prob.  217.     Ans.  At  London,  steel  92-93378  in.;  brass  53-79322  in. 

At  Paris,  steel  92-90854  in.;  brass  53-77861  in. 

At  New  York,  steel  92-84311  in.:  brass  53-74073  in. 

At  St.  Petersburgh,  steel  93.00482  in.;  brass  53-83434  in. 

Prob.  218.     Ans.  (1.)  30-0757    in.;    (2.)  29-42076    in.;    (3.)  27  8075  in.;    (4.) 
28-1778  in.;  (5.)  23-158  in.;  (6.)  24-581  in.;  (7.)  17-4228  iu.j  (8.)  15-835  in. 

Prob.  219. 
19-539  in. 
Prob.  220. 
Prob.  221. 
Prob.  222. 
Prob.  223. 


Ans.  (1.)  24-0962  in.;    (2.)  27-58513  in.;    (3.)  28-74528  in.;  (4.) 


Ans.  112-588  grains.     (Calculated  by  Table  XXIV.) 
Ans.  122°-75,  245°-5,  and  368°-25  above  its  previous  temperature. 
Ans.  1220-357  cubic  feet, 

Ans.  Water,  5500  units:    sulphur,  724-5  units;   charcoal,  9617-7 
units ;  alcohol,  525  units ;  ether,  922  units  of  heat. 

Note.     Specific  heat  of  charcoal  =  0-2415;  of  alcohol  (Sp.  Gr.  0-81)  =  0-7; 
of  ether  (Sp.  Gr.  0-76)  =  0-66. 

Prob.  224.     Ans.  68°-529  Fahrenheit. 
Prob.  225.     Ans.  4§  Ibs.  at  200°,  and  15*  Ibs.  at  50°  F. 
Prob.  226.     Ans.  88°-39  F. 
Prob.  227.     Ans.  155°-88  F. 
§>rob.  228.     Ans.  70°-79  F. 
Prob.  229.     Ans.  10-337  Ibs. 
Prob.  230.     Ans.  0-628  Ib. 

Prob.  231.     Ans.  9-26  units  of  heat  (as  in  Table  XV.). 

Note.     The  temperature  of  the  water  was  raised  to  52°-96  F.  instead  of  20°-76  C. 
Prob.  232.     Ans.  Required  for  air,  0-831  unit;    for  oxygen,  0-843  unit;   for 
carbonic  acid  gas,  27'879  units;  for  hydrogen,  0-8235  unit  of  heat. 
Prob.  233.     Ans.  3993  64  units  of  heat.     By  table  on  page  451. 
Prob.  234.     Ans.  1174-4  units  of  heat. 
Prob.  235.     Ans.  28-088  inches. 
61* 


698  ANSWERS    TO    PROBLEMS. 

Prob.  236.  Ans.  With  alcohol,  26-742  in.;  sulphuric  acid,  29-00  hi  ;  (at  75°  F. 
the  tension  of  vapor  of  sulphuric  acid  is  too  little  to  make  any  perceptible  differ- 
ence;) oil  of 'turpentine,  28*79  inches. 

Prob.  237.  Ans.  Tension  of  vapor  of  water  at  50°  F.  =  0-358  in.  mercury  ; 
at  75°  =  0-884  in.;  at  110°  =  2-682  in.;  at  175°  =  13-073  in.;  at  220°  =  35  091 
in.;  at  265°  =  78-619  in.;  at  300°  =  136-742  inches  of  mercury. 

Prob.  238.  Ans.  Boiling  points  of  water  at  the  given  pressures  =  213°-802, 
211°-709,  210°-794,  208°-679,  207°-608,  200°-51  F.  Boiling  points  of  ether  at 
the  same  pressures  =  95°'7S6,  93°  72,  92°-83,  90°-83>  89°'83,  81°-22.  Boiling 
points  of  alcohol  at  the  same  pressures,  174°-33,  172°-24,  171°-34,  169°-3J, 
168°-31,  162°-13. 

Prob.  239.  Ans.  If  the  temperature  is  not  allowed  to  change,  a  part  of  the 
steam  will  be  condensed  and  the  tension  will  remain  unchanged.  In  the  second 
case  the  tension  will  be  reduced  to  one  atmosphere. 

Prob.  240.  Ans.  457°  F.  to  460°  F.  This  tension  exceeds  the  limits  for 
which  accurate  data  are  given. 

Prob.  241.     Ans.  12  flues. 

Prob.  242.     Ans.  15  flues. 

Prob.  243.    Ans.  The  two  forces  are  to  each  other  as  1  to  10-974. 

Prob.  244.     Ans.  The  intensity  equals  -fa  of  its  original  force;  and  L  —  1'Jr. 

Prob.  24ft.     Ans.  The  intensities  are  as  1,  1-026,  1-034  and  1-039. 

Prob.  246.     Ans.  The  intensity  would  be  increased  1-9  times. 

Prob.  247.     Ans.  The  intensity  is  increased  by  one- third  its  original  amount. 

Prob.  248.     Ans.  The  intensity  is  increased  by  two- thirds  its  original  amount. 

Prob.  249.    Ans.  The  intensity  is  increased  to  1-16  what  it  was  before. 


I  N  BEX, 


'I  HE   REFERENCES    ARE   TO    SECTIONS,    NOT    TO    TAG 


ABERRATION,  chromatic,  465 ;~of  glass  covers, 

510;    of  lenses,   454;  of  mirrors,    437;    of 

sphericity,  455. 

Absolute  strength,  170;  zero,  666. 
Absorptive  power  for  heat,  6157. 
Accumulated  electricity,  843. 
Achromatic  microscope,  508,  511 ;  telescopes, 

504. 

Achromatism,  466. 
Acoustics,  335. 
Acoustic  shadow,  350. 

Action  and  reaction,  27 ;  of  a  falling  body,  77. 
Action  of  a  double  convex  lens,  447  ;  of  heat 

on  matter,  566;  of  magnetism  on  light,  919 ; 

of  surfaces  upon  heat,  G35. 
Actual  and  theoretical  velocities,  144. 
Adaptation  of  eye  to  distance,  480 ;  of  power 

to  weight,  110. 
Addenda,  page  668. 

Adhesion  distinguished  from  cohesion,  147. 
Advantage  of  friction,  141. 
Aerial  phenomena,  957  ;  waves,  332. 
Air.  buoyancy  of,  258;  impenetrability  of,  259; 

inertia  of. '260;   pump,   287;    vibrating   in 

tubes.  379. 
Amalgam.  834. 
Amalgamation  of  plates,  868. 
American  electrical   machine,  836;    turbine, 

231. 

Amorphism,  152. 

Ampere,  discoveries  and  theory,  908. 
Amusement  with  electricity.  840. 
Analogy  of  light  and  heat,  765. 
Analysis  of  central  forces.  54;  of  colors,  458; 

of  light,  456;  of  light  by  absorption,  458; 

by  prisms,  456;   of  trains  of  wheel-work, 

117. 

Anemometers,  960. 
Anemoscopes,  959. 
Aneroid  barometer.  164. 
Animal  electricity,  943;  heat,  cause  of,  756; 

strength,  130. 
Annealing,  178. 
Anode,  882. 
Aplanatic  foci,  509. 
Apparatus.  Atwood's.  72 ;  Bohnenherger's.  55 ; 

for  condensation  of  gases,  690;  for  distilla- 
tion, 687;  illustrating  barometer.  264:  Mel- 

loni's,  6-J2;  Morin'e.  72. 


Appendix,  meteorology,  946;    addenda,  page 
j      668;  physical  tables,  page  669.   • 
I  Application  of  laws  of  tailing  bodies,  73;  of 
I      levers.  115;  of  pendulum  and  measure  of 
time,  84;  of  polarized  light,  563;  of  ^flec- 
tion,  absorption,   and   radiation,    640;    of 
screw.  128  ;  of  wedge,  126. 

Appreciation  of  colors,  490;  of  distance,  481. 

Aqueous  phenomena,  972;  solutions,  maxi- 
mum density,  604. 

Arago's  experiment,  912;  polariscope,  557. 

Archimedes,  theorem  of,  205 ;  demonstrated, 
206. 

Archimedes'  screw,  298. 

Are,  18. 

Areometers,  212. 
j  Artesian  wells,  204. 

Artificial  magnets.  802;  temperature,  727. 
]  Ascent  of  liquids  in  tubes,  239. 

Astatic  needle,  787. 

Astronomical  telescope,  499. 

Atlantic  cable,  927. 

Atmosphere.  256;  tVee  electricity  in,  861. 

Atmospheric  electricity,  860;  a  source  of  heat. 
747. 

Atmospheric  engine,  708;  magnetism,  800; 
pressure.  257 ;  measure  of.  261 ;  refractions, 
538, 

Atoms.  20. 

Attraction  and  repulsion  of  light  bodies,  831. 

Attraction,  electrical.  812;  experiments,  842. 

Attraction,  magnetic,  780. 

Atwood's  apparatus,  72. 

Auditory  organs  of  man,  393. 

August's  hygrometer  or  psychrometer.  973. 

Auroral  current,  reversal  of  polarity  in,  1000. 

Auroras,  994 ;  effect  on  telegraph  wires,  999 ; 
j      geographical  distribution,  997  ;  height  and 
frequency,  996;  magnetic  disturbance,  998 
remarkable,  995. 

BA'BBAGF.'S  experiment  on  friction,  140. 

Back-ground,  476. 

Bain's  telegraph.  926. 

Balance,  spring.  37. 

Ballistic  curve.  145;  pendulum.  104. 

Balloons,  273. 

Barker's  mill,  217. 

Bath,  tempering  by,  178. 

(699) 


700 


INDEA. 


Barometer,   aneroid,  164;    at  different   alti-    Chromatic  aberration,  465. 

tudes,  265 ;  cistern,  266 ;  construction  of,    Chromatic  diagram,  491. 

263 ;  correction  for  temperature.  599 ;  errors    Chromatic  polariscope,  557. 

of,  269 ;   Fortin's,  266 ;  Gay  Lussac's,  267 ;    Chromatics.  456. 

measuring  heights,  272 ;  metallic,  163 ;  prin      ' 

ciples  of,  illustrated,  264;  wheel,  268. 
Barometric  changes   and   tbe  weather,  271 ;  '  Cistern  barometer,  266. 

height,  variations  of.  270.  '  Clarke's  magneto-electric  apparatus,  938. 

Batteries,  Smee's.  871;  trough,  870;  voltaic,    Cleavage,  157. 

869-881.  ;  Climates,  climatology,  947. 

Beams,  flexure  of,  102;  lateral  strength,  172;    Clocks,  electrical,  928. 

of  light,  401.  t  Clothing,  relations  to  heat,  625. 

Beating,  376.  ;  Clouds,  978;  classification  of.  979. 

Brume's  hydrometer,  212. 
Bellows,  281. 

Blasting  by  electricity,  937. 
Body,  defined,  1. 


Bohnenberger's  apparatus,  55. 

Binocular  vision,  484. 

Boiler  for  Gold's  steam-heater,  733. 

Boiling  point,  569;   application  in  arts.  678; 

circumstances    influencing,    676;     heights 

measured  by,  679. 
Bourdon's  metallic  barometer,  163. 
Boyden's  American  turbine.  231. 
Brachystochrome.  76. 
Bramah  press,  190. 
Breast-wheel,  230. 

Briquet's  metallic  thermometer.  580. 
Brightness  of  ocular  image,  473. 
Britannia  tubular  bridge,  172. 
Brittleness,  177. 
Bronze  tempering,  178. 
Bunseri's  photometer,  414. 
Buoyancy  of  air,  258. 
Buoyancy  of  liquids,  205. 

CAMBRIDGE  TELESCOPE,  506. 

Camera  lucida,  518. 

Capillarity,   232;    general    facts    in,   233;    a 

source  of  heat,  741 ;  influenced  by  curve  of 

surface,  236;  laws  of,  237. 
Capstan,  116. 
Calorimetry,  650. 
Camels,  206. 
Camera  obscura,  517. 
Carbon  battery,  876. 
Cartesian  devil,  206. 
Cathode,  882. 
Catoptrics.  415. 
Caustic  curves,  437. 
Centigrade  thermometer,  570. 
Centimetre,  18. 
Central  forces,  analysis,  54. 
Centre  of  gravity,  60,  62;  in  bodies  of  unequal 


Chronometers,  compensating  balance  wheels, 
596. 


Coexistence  of  sound  waves.  338. 
i  Cohesion  among  solids,  147. 
|  Cohesion  and  repulsion,  146. 
|  Cohesion  in  liquids,  gases,  and  solids,  148. 


Cold,  apparent  radiation  of.  Oo4. 

Cold  by  evaporation,  681. 

Color  blindness,  490. 

Color  dependent  on  temperature,  768. 

Colored  polarization,  555 ;  rings  in  crystals,  558. 

Colors,  analysis  of,  458  ;  ChevreuPs  classifica- 
tion of,  491  -,  complementary.  459 ;  of  grooved 
plates,  535 ;  of  thin  plates,  529 ;  study  of.  492. 

Columns,  resistance  to  pressure,  171. 

Combination  of  waves,  327. 

Combustion,  a  source  of  heat,  749;  cause  of 
heat  in,  750. 

Comparison  of  different  thermometers,  576. 

Compass,  mariner's,  787. 

Compensating  balance  wheels,  596;  pendu- 
lums, 596. 

Complementary  colors.  459. 

Components  and  resultants,  44. 

Composition  of  white  light,  457. 

Compound  chords,  372;  crystals,  156;  lenses, 
450;  levers,  114;  examples  of,  115;  micro- 
scope, 496;  achromatic.  511;  motion,  33; 
pendulum,  83 ;  pulleys,  120. 

Compressed  gases,  escape  of,  283. 

Compressibility,  21;  of  gases,  274;  of  liquids, 
188. 

Compressing  machine,  288. 

Compression  a  source  of  heat,  739. 

Concave  lenses,  448. 

Concave  mirrors,  426:  foci  of,  427-431 ;  images 
by,  433. 

Condensation  of  gases,  689,  690. 

Condenser  of  JEpinus,  844. 

Conductibility,  clothing,  625;  of  crystals.  616; 
examples  of.  622,  623;  of  gases,  620;  of 
liquids,  619;  of  metals,  615;  of  powders  or 
fibres,  624;  relative,  of  solids,  liquids  and 
gases,  621;  of  solids.  614,  622;  of  wood,  617. 


density,  68;  of  regular  figures.  64;  without  |  Conduction  of  heat,  613. 


the  body,  65. 
Centre  of  hydrostatic  pressure,  197. 
Centre  of  oscillation,  83. 
Centrifugal  and  centripetal  forces,  52. 
Centrifugal  drying  machine,  53. 
Centrifugal  forces,  demonstration,  53. 
Chain  pump,  297. 
Change  of  density,  169. 
Chart  of  magnetic  variations,  789. 
Chart  of  isoclinal  lines,  794. 
Chemical  affinity  and  molecular  attraction, 

900;  combination,  748;  effects  of  the  pile, 

history,  888 :  force,  5 ;  sources  of  heat,  748- 

757 ;  union  by  electricity,  856. 
Chemistry,  relation  of  to  physics,  9. 
Ohevreul's  classification  of  colors,  491. 
Chimneys,  draught  in,  717. 


Conjugate  mirrors,  635. 
Constitution  of  liquid  veins,  222. 
Construction  of  barometers,  263;  of  musical 

instruments,  385 ;  of  thermometers,  568. 
Convection  of  heat,  626;  of  heat  iu  liquids,  627. 
Convex  lenses,  447. 

Convex  mirrors,  426.  433;  images  by,  435. 
Cooling  by  radiation,  632. 
Copper,  tempering,  178. 
Cords,  vibration  of,  308,  309. 
Corollaries,  on  centre  of  gravity,  63. 
Coronas,  537. 
Correlation  offerees,  758. 
Coulomb  on  rolling  friction,  139;  on  starting 

friction,  138. 
Coulomb's  electrical  laws,  819 ;  laws  of  torsion, 

166. 


[NDKX.. 


701 


Couples,  48. 

Cowls,  725. 

Crystallization  by  feeble  currents,  893. 

Crystalography,  151. 

Crystals  conduct  heat,  616;  forms  of,  153, 158; 
positive  and  negative,  551. 

Cubical  expansion,  590. 

Culinary  paradox,  677. 

Currents,  in  air  and  gases,  716;  induced  by 
magnets,  938;  in  the  ocean,  028;  of  elec- 
tricity, path  and  velocity  of,  818;  produced 
by  ice,  724. 

Curve,  ballistic,  145;  influence  in  capillarity, 
236;  of  liquid  surfaces,  '234;  of  swiftest  de- 
scent, 76. 

Curvilinear  motion,  51. 

Cutoff.  712. 

Cycloidal  pendulum,  85 

Cyclones.  968. 

Cylinder  electrical  machine,  834. 

DANIELL'S  constant  battery,  874 ;  hygrometer, 

973. 

Dark  lines  in  spectrum,  461,  462. 
Declination  of  magnetic  needle,  788. 
Decimetre,  18. 
Deep-sea  thermometer,  581. 
Deflagration,  886. 

De  La  Rive's  floating  current,  909. 
Demonstration  of  Torricellian  theorem,  220. 
Density,  98 ;  changed  by  tension.  169 ;  of  gases, 

611 ;  of  the  earth  estimated  by  experiment, 

102 ;  of  vapors.  693. 
Depth  of  waves,  322. 
Depression  of  mercury  in  tubes,  238. 
Descent  on  curves,  75;  on  inclined  planes,  74. 
Despretz's  experiments,  275. 
Destructive  effects  of  impact.  112. 
Determination  of  reflective  power.  636. 
Deviation  of  light  twice  reflected,'  423. 
Dew,  975;  on  what  it  falls.  976. 
Dew-point,  674. 
Diamagnetism,  920 
Diamond  jar,  852. 
Diapason,  377;  natural.  395. 
Diathermancy .  641;  applications  of,  647 ;  causes 

which  modify,  645. 
Differential  thermometers.  587. 
Diffraction,  532. 
Diffused  light,  410. 
Dilatation  by  heat  explained,  769-.. 
Dimensions  of  the  earth,  92. 
Dioptrics,  438. 
Dipping  needle,  793. 
Direction  of  force.  40;  of  osmotic  current,  247; 

of  terrestrial  attraction,  60;  of  vibrations  of 

light,  541. 

Directive  action  of  the  earth,  911. 
Dispersion  of  light,  406. 
Displacement  of  zero-point,  573. 
Dissecting  microscope,  495. 
Distance  calculated  by  sound,  346;  of  distinct 

vision,  478;  that  sound  can  be  heard,  351. 
Distillation,  6S6. 
Distilling  apparatus.  687. 
Divisibility,  19.    . 
Double  diatonic  scale.  373;   refraction,   550; 

polarization  by,  552 ;  vision,  483. 
Downward  pressure  of  liquids,  191. 
Draught  in  chimneys,  717. 
Droj*  of  liquids  in  conical  tubes,  241. 
livy  piles,  873.  . 
Drying  machine  for  laundries,  53. 


Duboscq'j  electric  lantern,  884. 

Dub's  laws  of  electro-magnetism,  915. 

Ductility,  175. 

Duration  of  visual  impressions.  487. 

Dwellings,  supply  of  fresh  air,  726. 

Dynamical  electricity,  862 ;  theory  of  heat.  762. 

Dynamics,  39;  Dynamometers,  37. 

EAR,  393;  sensibility  of,  378;  trumpet,  359. 

Earth  circuit,  922. 

Earth's  rotation,  effect  of,  upon  gravity,  94 ; 
demonstrated  by  the  pendulum,  86. 

Ebullition,  675. 

Echo,  353;  tone  changed  by,  355. 

Echoes  repeated,  354. 

Effects  of  centrifugal  force,  53. 

Elastic  balls  transmit  shock,  185 ;  bodies,  im- 
pact of,  182 ;  fluids,  252. 

Elasticity,  limit  of,  168  ;  modulus  of,  183 ;  of 
flexure,  162 ;  of  liquids.  188 ;  of  metals,  table, 
161 ;  of  solids,  159 ;  coefficient  of,  161 ;  of  ten- 
sion and  compression,  160;  of  torsion,  165. 

Electric  battery,  849. 

Electric  currents,  induced,  929;  light  in  a 
vacuum,  935 ;  mutual  action,  909. 

Electric  discharge,  effects  of,  853  ;  in  vacuum. 
852. 

Electric  light,  properties  of,  885;  regulators  of, 
884;  rotation  about  a  magnet,  936. 

Electric  spark,  color  of,  852. 

Electric  telegraph,  history  of.  921 ;  Morse's  re- 
cording, 924;  varieties  of,  923. 

Electricity,  atmospheric,  860,  861;  chemical 
effects,  858 ;  chemical  union  by,  856.;  classi- 
fication, 773;  conductors  of.  8i4 ;  disrnarge 
in  cascade,  850;  disguised,  843;  distribution 
of,  825;  dynamical,  862;  dynamical  con- 
verted into  statical,  933 ;  earth  a  reservoir 
of,  815;  floating  Current,  909;  from  all 
sources  identical,  939;  from  steam,  839;  loss 
of,  in  excited  bodies.  827;  magnetic,  774; 
mechanical  effects,  857 ;  only  on  outer  sur- 
face, 824;  of  plants,  945;  positive  and  nega- 
tive, 813;  of  the  air,  987;  physiological 
effects,  854;  theories  of,  816;  theory  of 
voltaic,  863;  universal  discharger  of,  851; 
velocity  of,  818 ;  vitreous  and  resinous,  813. 

Electrical  amusements.  840;  animals,  944; 
attraction  and  repulsion,  812;  bells,  842; 
blasting,  937  ;  cascade  in  vacuo.  935 ;  clocks, 
928;  condenser,  discharge  of,  845;  effects, 
811 ;  egg.  852. 

Electrical  excitement,  sources,  810;  univer- 
sality of,  940 ;  various  sources,  840. 

Electrical  fire  alarm,  928;  hail-storm,  842: 
helix,  910 ;  induction,  828 ;  lamp. Yolta's,  856. 

Electrical  machines,  834-838;  care  of,  838; 
theory  of,  841. 

Electrical  nomenclature,  882 ;  pendulum,  812; 
phenomena,  987 ;  power  of  points,  826 ;  re- 
tardation, 880;  wheel,  842;  tension  and  cur- 
rents, 817. 

Electro-chemical  telegraph,  926. 
Jiiectrode.  electrolyte.  882. 

Electro-dynamic  spiral,  910. 

Electro-dynamics,  general  laws.  902. 

Electrolysis,  laws  of,  890;  of 'salts,  891;  of 
water,  889. 

Electro-magnetic  currents,  motion  of,  904 

Electro-magnetic  motion.  917. 

Electro-magnets,  913;  Page's  revolving,  914; 
power  of,  915. 

Electrometers,  832. 


JNDtX 


Electrometer,  gold  leaf,  846;  torsion,  320. 

Electrophorus,  833. 

Electro-positive  and  electro-negative.  867. 

Electro-printing  telegraph,  925. 

Electroscopes,  813,  842. 

Electroscope,  Bohnenberger's,  873;  Volta's 
cojQilensiug,  846. 

Electrotype,  892. 

Emerson's  ventilators,  725. 

Emissive  power  for  heat,  638. 

Elements  are  simple  bodies,  1 

Endless  screw,  129. 

Endosmose,  244 ;  of  gases,  250 ;  theories  of,  251. 

Eudosmometer,  245, 

English  and  American  weights,  101. 

English  units  of  length,  17. 

Eolipile,  704. 

Epipolic  dispersion,  533. 

Equatorial  telescope,  505;  Cambridge,  506. 

Equilibrium,  38;  conditions  of,  in  liquids.  199; 
neutral,  unstable,  and  stable,  207  ;  of  bodies 
supported  in  more  than  one  point,  69;  of 
machines.  107. 

Equilibrium  of  liquids,  between  laminae,  240; 
free  from  gravity.  200;  in  communicating 
vessels,  201 ;  of  different  densities,  202. 

Equilibrium  of  solids  placed  upon  a  horizontal 
surface,  67 ;  supported  by  an  axis,  66. 

Equilibrium  of  the  lever,  114. 

Errors  of  barometer,  causes  of,  269. 

Escape  of  compressed  gases,  283;  of  liquids 
through  tubes,  223,  224. 

Essential  properties  of  matter,  12. 

Estimation  of  high  temperatures,  586. 

Eustachian  tube,  393. 

Evaporating  power  of  fuel,  715. 

Evaporation,  causes  influencing,  673;  cold  by, 
681 ;  mechanical  force  of.  684. 

Examples  of  compound  levers,  115. 

Exosmose,  244. 

Expansibility  and  compressibility,  610. 

Expansibility,  22. 

Expansion,  amount  of,  in  solids.  591 ;  apparent 
and  absolute,  598 ;  coefficient  of.  591 ;  cubical. 
590 ;  curve  of,  for  liquids,  602 ;  force  exerted 
by,  593;  increases  with  temperature,  592; 
linear,  589;  of  crystals,  590. 

Expansion  of  gases,  253,  605 ;  Reguault's  re- 
sults,  607. 

Expansion  of  liquids,  597;  above  boiling,  602; 
amount  of,  601. 

Expansion  apparent  of  mercury,  600 ;  of  mer- 
cury, coefficient,  598 ;  of  solids,  589 ;  of  water, 
604;  phenomena  of,  594;  unequal,  of  solids, 
595. 

Experiment  a  source  of  knowledge,  2;  hydro- 
static pressure,  194. 

Experiments  of  Despretz,  275 ;  of  Pascal,  194, 
262;  of  Plateau.  200;  of  Regnault,  276. 

Experiments  on  density  of  the  earth,  102;  on 
liquid  surfaces,  235. 

Explosions,  cause  of,  701. 

Extension.  13. 

Extremes  of  temperature.  744. 

Eye,  action  of,  on  light,  469;  adaptation  to 
distance,  480 ;  a  polariscope,  562 ;  structure 
of.  468. 

Eye-piece,  Tolles'  solid,  512. 

Eye-pieces,  500. 

FACTS  (in  interference)  versus  theory.  528. 
Fahrenheit  s  hydrometer,  212;  thermometer, 
570. 


Fairbanks'  scales.  115. 

Falling  bodies,  laws  of.  71. 

Falling  body,  action  and  reaction  of,  77 ;  space 

described  by,  71. 
Faraday's  nomenclature,  882. 
Faraday  on  liquefaction  of  gases,  689. 
Fire-alarm,  electrical,  928. 
Fire  engine.  294. 
Fire  regulators.  594. 
Fixed  lines  in  spectra,  461,  462. 
Fixed  pulley,  118. 
Flexure  of  beams,  162. 
Floating  bodies,  206;  equilibrium  of,  207. 
Floating  current,  909. 
Floating  docks,  206. 
Flow  from  capillary  tubes,  243. 
Flow  of  liquids,  218. 
Flow,  theoretical  and  actual,  216. 
Fluids,  186;  resistance  of,  143. 
Fluorecsence,  533. 

Foci  of  lenses,  compound,  450;  concave.  448; 
convex,  447 ;  principles.  445  ;  rules  for,  449. 
Fog-bows,  537. 
Fogs,  or  mists,  974. 
Foot-pound  a  measure  of  heat,  759. 
Force  and  heat,  relations,  758. 
Force,  chemical  or  physical,  5;  definition  of, 
35;  developed  by  evaporation,  684 ;  direction 
of,  40;  of  expansion,  593,  603;  of  gravity, 
58;  unit  of,  37. 

Forces  are  definite  quantities,  36. 
Forces,  centrifugal  and  centripetal,  52;  cor- 
relation of,  758;  not  parallel  applied  at  dif- 
ferent points.  49  ;  measure  of.  41 ;  parallelo- 
gram of,  45;  propositions  in  regard  to.  42; 
resolution  of,  50;  statical  and  dynamical, 
39 ;  system  of,  44. 
Forcing  pump,  292. 
Forms  of  crystals,  153;  of  mirrors,  417;  of 

vibrations,  307. 
Formulas,  achromatism,  467. 

"          altitudes  by  barometer,  272. 

"          apparent  expansion  of  mercur$-.600. 

"          central  forces,  54. 

"          change  of  volume  in  gases,  608. 

"          compensating  pendulum,  596. 

"          compound  lenses.  450. 

"          concave  lenses,  448. 

"          concave  mirrors,  428. 

"          convex  lens,  447. 

"          convex  mirrors,  432. 

"          correction  of  barometric  height,  599. 

"          electric  piles,  881. 

"          endless  screw,  129. 

"          escape  of  liquids,  223,  224. 

"          expansion  of  liquids,  598. 

"          expansion  of  solids,  591. 

"          flexure  of  beams.  162. 

«          flow  of  liquids,  216. 

"          inclined  plane,  122-124. 

"          index  of  refraction,  440. 

"          light  twice  reflected.  423. 

"          magnifying  power  of  lenses,  494. 

"          microscopes,  513. 

"          motion  of  projectiles,  103. 

"  Newton's,  for  velocity  of  sound,  653 

"  optical  centre  of  lenses,  452. 

"          pencils  of  light  refracted  at  plane 
surfaces,  443. 

"          pencils    of   light    transmitted    by 
plane  glass.  444. 

"          pendulum,  81,  82. 

"          penetrating  power  of  telescopes,507. 


INDEX, 


708 


Formulas,  pulley,  119,  120. 

"          refraction  at  spherical  surfaces,  445. 

"          refraction  by  parallel  media,  442. 

"          relation   of  volume,  temperature, 
and  pressure  in  gases,  609. 

"          screw.  127. 

«          specific  gravity.  210,  211. 

"          specific  heat,  653. 

"          spherical  aberration  of  lenses,  454. 

"          standard  thermometer,  577. 

"          strength  of  beams,  172. 

'•  uniform  motion,  30. 

"          variable  motion,  32. 

"          variation  of  gravity  by  rotation  of 
the  earth,  94. 

"          variation  of  gravity  in  altitude,  95. 

"          variation  of  gravity  in  latitude,  90. 

"          velocity  after  impact,  184. 

"          velocity  of  discharge,  220. 

"          velocity  of  light,  404. 

"          velocity  of  winds,  961. 

•'          vibration  of  air  in  tubes,  384. 

"          visual  power  of  telescopes,  507. 
Fnrtin's  barometer,  266 
foncault's  apparatus,  404. 
Franklin's  kite,  860 ;  pulse  glass,  677. 
Fraunhofe.r 's  dark  lines,  461. 
Freezing  in  red-hot  crucibles,  699. 
Freezing  mixtures,  657. 
Freezing  point,  569. 
Fresh  air  in  dwellings,  726. 
Fresnel  lens,  521. 

French  system  of  measures,  18 ;  weights,  100. 
Friction,  advantage  from,  141 ;  during  motion, 
138;  heat  from,  735.  736;  sliding,  137;  start- 
ing, 138. 

Frictional  electricity,  809. 
Frost,  977. 
Fuel,  evaporating  power,  715 ;  relative  value 

of,  753. 

Functions  of  the  ear,  394. 
Furnace  blowers,  282. 
Furnaces  for  hot  air,  729. 
Fusion,  laws   and  heat  of,  658;   peculiar  in 
some  solids,  659. 

GALVANIC  battery  a  misnomer,  864. 

Galvanic  current.  943. 

Galvanism,  discovery  of,  862;  contact  theory, 
863. 

Galvanometer,  905  ;  sine  compass,  906. 

Gamut  366. 

Gas  illumination,  products  of,  721. 

Gas  jet,  musical  note,  382. 

Gases,  252;  and  vapors,  identity  of,  688;  com- 
pressibility of,  274-277  ;  conductibility  for 
heat,  620 ;  density  of,  611 ;  expansion  of,  253 ; 
expansion  by  heat,  605 ;  laws  of  expansion, 
606;  liquid  and  solid,  properties  of,  691; 
mechanical  condition  of,  254;  transmit 
pressure,  255 ;  relation  of  volume,  tempera- 
ture, and  pressure,  609;  reduced  to  liquids, 
689 ;  specific  heat  of,  652,  653 ;  volume  of,  608. 

Gassiot's  cascade,  935. 

Gay  Lussac's  barometer,  267;  hydrometer, 
212;  laws  for  expansion  of  gases,  606. 

Glass,  temper  of,  178. 

Glottis,  388. 

Gold's  steam  heaters.  732. 

Graduation  of  thermometers,  569. 

GraJiam's  compensating  pendulum,  596. 

Gravity,  58 ;  a  source  of  motion,  70 ;  affected 
by  the  earth's  rotation,  94 ;  influenced  by 

61 


the  earth's  figure,  91 ;  intensity  varies  with 
latitude,  90 ;  measured  by  the  pendulum, 
88 ;  varied  by  altitude,  95. 

Gridiron  pendulum,  59t>. 

Grove's  battery,  875. 

Gyrascope,  57. 

HADLEY'S  sextant,  425. 

Hail,  986. 

Halos,  537. 

Hammering,  179. 

Hardening,  178. 

Hardness,  176. 

Hare's  calorimotor,  870;  deflagrator,  870; 
electrometer,  846. 

Harmony,  melody,  365. 

Harrison's  compensating  pendulum,  596. 

Hearing,  341 ;  of  animals,  396. 

Heat,  action  of,  on  matter,  566;  amount  by 
chemical  action,  751 ;  and  force,  relations 
of,  758;  and  light,  analogy  of, '765:  and 
light,  by  chemical  and  mechanical  action, 
768 ;  cause  of,  in  animals,  756;  causes  which 
modify  emissive,  absorbent,  and  reflective 
power,  639;  change  of  state  in  bodies,  764; 
coloration,  646;  conclusions,  772;  conduc- 
tion of,  613;  convection  of,  626;  developed 
by  solidification,  663;  diffraction  and  inter- 
ference, 649;  dynamical  theory,  762;  expan- 
sion of  gases  by,  606 ;  expansion  of  liquids 
by,  597  ;  expansion  of  solids  by,  589 ;  from 
magnetism,  918;  latent,  655;  mechanical 
equivalent,  758,  760;  mechanical  unit  of 
measurement,  759;  nature  of.  564;  of  com- 
bustion. 749 ;  modes  of  communication,  612, 
of  capillarity,  741;  of  chemical  action,  748; 
of  compression,  739;  of  friction,  735-738; 
effusion,  658;  of  humid  combinations,  754; 
of  percussion,  740;  of  voltaic  arch,  886;  of 
voltaic  currents,  887 ;  origin  of  terrestrial, 
746;  polarization  of,  649;  quantity  and  in- 
tensity, 771;  quantity  developed  by  fric- 
tion, 736;  quality  of,  how  changed,  770; 
radiation  of,  629 ;  reflection  of,  fi35 ;  refrac- 
tion of,  648 ;  relation  to  cold,  565 ;  specific, 
651;  transmission  of  radiant,  641 ;  unit  of, 
650 ;  universal  radiation,  633. 

Heating  by  hot  water,  730. 

Height  measured  by  barometer,  272. 

Heights  measured  by  boiling  water,  679. 

Helix,  electrical,  910. 

Hiero's  fountain.  295. 

High-pressure  engine,  711. 

High-pressure  steam,  680. 

Horse-power,  714. 

Horse-power  machines,  132, 

Hot  air  furnaces,  729. 

Hot  water  apparatus,  731. 

House's  telegraph,  925. 

Humidity  of  the  air,  972. 

Hurricanes,  968. 

Hydraulic  ram.  296. 

Hydraulics,  213. 

Hydrodynamics,  186. 

Hydrometers,  212. 

Hydrostatic  paradox.  195. 

Hydrostatic  press,  190. 

Hydrostatics,  186. 

Hygrometers,  973. 

Hypothesis  defined,  3. 

Hypsometer,  679. 

ICE,  currents  produced  by,  724. 


704 


INDEX. 


Ice  machine,  Twining's,  681. 

Illumination  of  railways,  520. 

Illumination,  products  of,  721. 

Illumination,  sufficiency  of,  477. 

Illustration  of  vis  viva,  111. 

Images,  by  concave  mirrors.  433:  by  convex 
mirrors,  435 ;  by  plane  mirrors,  419 ;  by 
small  apertures,  412 ;  by  inclined  mirrors, 
422 ;  by  two  plane  mirrors,  421 ;  distortion 
of,  455;  formed  by  lenses,  453;  in  the  eye, 
inverted,  470 ;  multiplied  by  two  surfaces, 
420 ;  virtual,  434. 

Impact  and  its  results,  112 ;  as  related  to  vis 
viva,  112;  in  relation  to  momentum,  112;  j 
of  elastic  bodies,  182. 

Impenetrability,  14. 

Impenetrability  of  air,  259. 

Imponderables,  11. 

Impressions  of  light  and  heat,  766. 

Incandescence,  767. 

Inch  of  water.  221. 

Inclination  map,  isoclinal  lines,  794. 

Inclined  plane,  121-124. 

Index  of  refraction,  440. 

Induced  currents,  different  orders,  930. 

Induced  currents  from  earth's  magnetism, 
932. 

Induction  an  act  of  contiguous  particles  830. 

Induction  coil  of  Ruhmkorff,  933;  effects  of, 
934. 

Induction,  electro-dynamic,  929:  of  a  current 
on  itself,  930;  of  electricity,  828 ;  of  magnet 
ism,  783. 

Inductive  philosophy,  4. 

Inductive  power  of  earth's  magnetism,  797. 

Inertia,  26;  of  air,  260. 

Inilammation  by  electricity,  855. 

Influence  of  the  earth's  figure  upon  gravity,  91. 

Intensity  of  aerial  waves.  332;  of  light,  413; 
of  luminous,  calorific,  and  chemical  rays, 
-40:5 ;  of  many  couples,  881 ;  of  radiant  heat, 
631. 

Interference  colors,  529;  of  light,  527;  of 
sound,  349;  of  waves.  327,  328. 

Intermittent  fountain,  286;  springs,  286;  sy- 
phon, 285. 

Internal  ear.  393. 

Internal  reflection  of  light,  408. 

Interval  in  music,  371. 

Ions,  882. 

Irregular  reflection  of  light,  410. 

Isochronism  of  the  pendulum,  80. 

Isochronous  vibrations,  303. 

Isodynamic  lines,  796. 

Isogonal  lines,  789. 

Isothermal  lines,  956. 

JETS  of  water,  225. 

Johnson  on  strength  of  materials,  170. 

Joule's  experiments  on  heat,  760,  761. 

K  ALKIDOSCOPE,  424. 

Kaly chromatics,  464. 
Koy-note  of  nature,  335. 
Kilometre,  18. 

LARYNX,  388. 

Latent  electricity,  843. 

Latent  heat,  655. 

Latent  heat  of  fusion,  658;  of  steam,  682. 

Lateral  strength  of  beams,  172. 

Latour's  law  for  vapors,  692. 

Law,  definition  of,  3. 


Law  of  cooling  by  radiation,  632;  of  Latouiv 
692;  of  universal  gravitation,  59. 

Laws  of  acoustics  determine  specific  heat,  053. 

Laws  of  Bernoulli,  384;  of  capillarity,  237: 
of  capillarity  between  lamina*,  240 ;  of  ele& 
trical  attraction  and  repulsion.  819-822 ;  of 
electrical  induction,  829 ;  of  electricity  and 
chemical  action,  898;  of  electrolysis,  890; 
of  electro-dynamics,  902;  of  electro-magnet- 
ism, 915;  of  falling  bodies.  71;  application, 
73;  verification,  72;  of  fusion,  658;  of 
Ohm,  880;  of  solidification,  662;  of  storms, 
971;  of  tenacity,  170 ;  of  torsion,  166. 

Length  of  luminous  waves,  531. 

Lenses,  438;  compound,  450;  concave.  448; 
convex,  447 ;  images  formed  by.  453  ;  optical 
centre  of.  452;  refraction  of  oblique  pencils 
by.  451 ;  'rules  for  foci,  449. 

Le,  Hoy's  dynamometer,  37. 

Lever,  113;  application  of,  115;  equilibrium 
of,  114. 

Leyden  jar.  847 ;  electricity  in,  848. 

Life  an  unknown  power,  10. 

Light,  action  of  eye  upon,  469 ;  amount  .re- 
flected, 407  ;  and  heat,  analogy  of,  765  ;  and 
heat  by  chemical  and  mechanical  action, 
768  ;  changed  by  polarization,  543;  color  of, 
depends  on  temperature,  768 ;  diffused,  410 ; 
direction  of  vibrations,  541 ;  heat  and  elec- 
tricity are  forces  in  nature,  11;  in  a  homo- 
geneous medium,  403  ;  influenced  by  mag- 
netism, 919;  internal  reflection,  408 ;  irregu- 
lar reflection,  410 :  length  of  vibrations,  531 ; 
nature  of,  398 ;  pencils  of,  passing  through 
plane  glass,  444 ;  pencils  of,  refracted  at 
plane  surfaces,  443 ;  polarized  by  absorption, 
545;  polarized  by  reflection,  546;  polarized 
by  refraction,  547,  548;  properties  of,  406; 
total  reflection  of,  409 ;  rays,  pencils,  beams, 
401;  refracted  by  parallel  strata,  412;  rela- 
tion of  bodies  to,  400 ;  sources  of,  399 ;  trans- 
mission of  vibrations,  542 ;  velocity  of,  404. 

Light-houses,  522,  523. 

Lightning,  990 ;  classes  of,  991 ;  return  stroke, 

QQ2 

Lightning-rods,  993. 

Limits  of  elasticity,  168;  of  magnitude,  173. 

Linear  expansion,  589. 

Liquid  surfaces,  cause  of  curve,  234. 

Liquid  veins,  constitution  of.  222. 

Liquids,  186;  amount  of  expansion,  601; 
ascent  in  capillary  tubes,  239 ;  conditions  of 
equilibrium,  199 ;  conductibility  for  heat, 
619 ;  convection  of  heat  in,  627 ;  curve  of  ex- 
pansion, 602;  downward  pressure  of,  191; 
elasticity  of,  188;  equilibrium  of,  199,  200; 
equilibrium  of,  in  communicating  vessels. 
201,  202;  expansion  of,  597;  expansion 
above  boiling,  602;  force  of  expansion,  (503; 
lateral  pressure,  193;  mechanical  condition, 
187;  repelled  by  heated  surface,  697;  spher- 
oidal state.  694 ;  transmit  pressure,  1S9 ;  nji 
ward  pressure,  192. 

Liquefaction  and  solidification,  655;  gradual, 
656. 

Liquefaction  of  gases,  theory,  688 ;  of  vapors, 
685. 

Lister's  aplanatic  foci,  509. 

Litre,  18. 

Living  force,  111. 

Lodestone,  774. 

Looming,  539. 

Long-sightedness,  486. 


INDEX. 


705 


I.  nv  pressure  engines,  710. 

MACHINE  power  and  weight,  106. 

Machines,  105;  eqxiilibrium  of,  107. 

Magic  lantern,  515  ;  squares,  852. 

Magnetic  attraction  and  repulsion,  780 ;  curve.", 
777;  dip  of  needle,  791;  electricity,  774; 
figures,  778;  force,  distribution,  776;  force, 
lines  of,  799 ;  induction,  783  ;  intensity,  795 ; 
meridian,  788;  needle,  775,  787;  observa- 
tions, 798;  phantom,  777.;  polarity,  776; 
rotary  polarization,  560. 

Magnetism,  action  upon  light,  919;  atmos- 
pheric, 800;  coercitive  force,  786;  by  contact, 
781;  conversion  into  heat,  918;  different 
bodies,  782 ;  of  steel  by  solar  rays,  807 ;  of 
the  earth,  action  of,  on  dipping  needle,  792; 
origin  of  the  earth's.  801;  terrestrial,  787; 
theories,  784,  785. 

Magnetizing  by  the  helix,  912. 

Magneto-electric  apparatus,  938. 

Magneto-electricity,  938. 

Magnets,  anomalous,  779;  artificial.  775:  by 
electro-magnetism,  80;");  by  touch,  803;  com- 
pound, 806;  deprived  of  power,  808;  direc- 
tive tendency  of,  787 ;  horse-shoe.  804 ;  natu- 
ral, 774 ;  production  of,  802 ;  value  how- 
varied,  802. 

Magnifying  glasses,  493. 

Magnifying  power  of  lenses,  494. 

Magnitude,  13;  limits  of,  173. 

Malleability,  174. 

Manometers,  278 ;  with  compressed  air,  280 ; 
with  free  air,  279. 

Map  of  isoclinal  lines,  794. 

Mariner's  compass,  787. 

Mariotte's  law,  274. 

Martin's  compensating  pendulum,  596. 

Mathematical  pendulum.  78. 

Matter,!;  accessory  properties,  19;  changes 
in,  7 ;  essential  properties,  12 ;  general  pro- 
perties, 6;  three  states  of,  15;  properties  of, 
physical  or  chemical,  8. 

Mass,  41,  96. 

Maximum  and  minimum  thermometers,  578. 

Maximum  density  of  aqueous  solutions,  604; 
of  water,  604. 

Mean  temperature,  950. 

Measure  offerees,  41. 

Measures  of  capacity,  17,  101. 

Mechanical  condition  of  gases.  254;  efficiency 
of  the  screw,  128;  equivalent  of  heat,  758; 
force  of  evaporation,  684;  illustration  of 
vibrations,  301 ;  sources  of  heat,  735. 

Mechanism  of  the  voice,  389. 

MeJIoni's  apparatus.  642. 

Mdloni's  thermo-rnultiplier,  942. 

Melody,  harmony,  365. 

Membranes,  vibration  of.  318. 

Men,  strength  of,  131. 

Mercurial  rain,  24. 

Mercurial  thermometer,  568;  limits  of,  574; 
defects  of,  576. 

Mercury,  depression  of,  in  tubes,  238. 

Meridian  measurements.  91. 

Metacentre,  208. 

Metallic  barometer,  163. 

Metallic  thermometers,  580. 

Metals,  change  of  properties,  180;  change  of 
structure,  180,  conduct  heat,  615. 

Metastatic  thermometer,  579. 

Meteorological  observations,  949. 

Meteorology,  946. 

62 


Metre,  18. 

Microscope,  achromatic,  angular  aperture,  de- 
fining power,  illuminating  power,  magnify- 
ing power,  penetrating  power,  visual  power, 
513;  compound,  496;  object-glasses,  508; 
Raspail's  dissecting,  495;  simple,  495;  solar, 
516:  stand,  514. 

Millimetre,  18. 

Minute  division,  19. 

Mirage,  540. 

Mirrors,  415  ;  forms  of,  417. 

Mobility,  25. 

Modified  forms  of  crystals,  155. 

Modulus  of  elasticity,  183. 

Molecular  motion,  in  heat,  763. 

Molecules,  20. 

Momentum,  43. 

Monochord,  367. 

Monthly  variations  in  temperature,  951. 

Morin's  apparatus,  72. 

Morse's  telegraph,  924. 

Motion  and  force,  composition  of,  examples,  45. 

Motion  communicated  by  collision,  181. 

Motion,  compound,  33;  curvilinear,  51;  of 
projectiles.  103;  uniform,  30;  uniformly 
varied,  32 ;  variable,  31 ;  varieties  of,  28. 

Mountings  for  telescopes,  505. 

Mouth-pipes,  380. 

Movable  pulley,  119. 

Movement  of  drops  in  tubes,  241. 

Music  halls,  362. 

Music,  theory  of,  363. 

Musical  instruments,  383. 

Musical  interval,  371. 

Musical  scale,  366;  new,  373. 

Musical  sounds,  335;  quality  of,  363. 

Musical  tones  from  magnetism,  916. 

NATURAL  diapason,  395. 

Natural  history,  10. 

Natural  philosophy,  9. 

Nature,  key-note  of,  335. 

Nearsigbtedness,  485. 

Negative  eye-piece,  500. 

Negretti  (£Zambra's  thermometer,  578. 

Neutral  equilibrium,  207. 

New  musical  scale,  373. 

Newton's  formulae  for  velocity  of  sound.  653 

Newton's  rings,  530. 

Nicholson's  hydrometer,  212. 

Nicol's  prism,  553. 

Night  glass,  498. 

Nitric  acid  battery,  875. 

Nobili's  galvanometer,  905. 

Nobili's  rings,  894. 

Nodal  figures,  317. 

Nodal  lines,  313;  how  delineated,  316;  posl 

tion  of,  314. 
Nodal  points,  305. 
Noise,  335. 
Nomenclature,  Faraday's  electrical,  882. 

OBJKCT-GLASSES  for  the  microscope,  508. 
Objectives  compound,  509. 
Oblique  pencils,  430. 
Oblique  pencils  refracted  by  lenses,  451. 
Observation  and  experiment,  2. 
Ocular  image,  brightness  of,  473. 
(Ersted's  discovery,  903. 
Ohm's  law  of  retarding  power.  880. 
Open  fire,  728. 
Opera-glass,  498. 
;  Optic  angle,  471. 


706 


INDEX. 


Optic  axis.  471. 
Optical  centre  of  a  lens,  452. 
Optical  instruments,  493. 
Optical  toys,  488. 
Optics,  397. 

Organ  of  Poole  and  Alley,  375. 
Organic  solutions,  osmose  iii,  248. 
Organs  of  hearing  in  animals,  396. 
Origin  of  terrestrial  heat,  746. 
Origin  of  undulations,  299. 
Oscillation,  centre  of,  83. 
Oscillation  denned.  78. 
Osmose,  244;  conditions  of,  246. 
)smose  of  inorganic  solutions,  249;  of  organic 

solutions,  248;  direction  of  current.,  247. 
Overshot  wheel,  229. 
Ozone,  859. 

PAGE'S  revolving  magnet,  914. 

Page's  vibrating  armature,  931. 

Parachute,  273. 

Parhelia,  537. 

Parallel  forces,  resultant  of,  46. 

Parallelogram  of  forces,  45 ;  of  rotations,  56 ; 
of  velocities,  34. 

Pascal's  experiments,  194,  262. 

Passive  resistance,  136. 

Paths  of  vibration,  311. 

Pencils  of  light,  401 ;  refracted  at  plane  sur- 
faces, 443 ;  at  spherical  surfaces,  446. 

Pendulum,  78;  applied  to  measure  time,  84; 
applied  to  study  of  gravity,  87 ;  ballistic. 
104;  compensating,  596;  cycloidal,  85;  de- 
monstrates rotation  of  the  earth,  86 ;  formu- 
lae for,  81;  isochronism  of,  80;  length  beat- 
ing seconds,  89;  physical  or  compound,  83; 
propositions  respecting,  82;  simple,  79;  used 
to  measure  force  of  gravity,  88. 

Penetrating  power  of  microscopes,  513;  of 
telescopes,  507. 

Penumbra,  411. 

Percussion  a  source  of  heat,  740. 

Perfect  concord,  372. 

Purlins'  apparatus,  731. 

Perpetual  motion,  135. 

Phases  of  undulations.  304. 

Phenomena  defined,  2;  of  expansion.  504. 

Philosophical  egg,  852. 

Phosphorescence,  399.  534. 

Photo-electric  lantern,  884. 

Photography,  519. 

Photometers,  414. 

Physical  force,  5 ;  pores,  2" ;  optics.  527 ; 
sources  of  heat,  742;  tables,  page  ;309; 
theory  of  music,  363. 

Physics  and  chemistry,  9. 

Physiological  effects  of  the  pile,  895. 

Piano  strings  friable,  180. 

Plane  glass,  refraction  by,  441. 

Plants,  electricity  of.  945. 

Plateau's  experiment,  200. 

Plates,  vibration  of,  312. 

Platform  balance,  115. 

Pneumatic  ink-bottle,  234. 

Pneumatics,  252. 

Polarity  of  compound  circuit,  878. 

Polarization  and  transfer  of  elements,  899. 

Polarization,  atmospheric,  561 ;  by  absorption, 
545;  by  beat  and  by  compression,  559;  by 
reflection,  546;  by  refraction,  547,  548; 
colored,  555;  of  heat,  649;  of  light,  541; 
partial,  649;  rotary,  556. 


Polari/ing  instn  (meats,  554. 

Poole's  musical  scale.  S73. 

Pores,  physical,  23;  sensible,  24. 

Porosity,  23. 

Positive  and  negative  crystals,  551. 

Positive  eye-piece,  500. 

PouilltVs  galvanometer,  906. 

Power  of  points,  electrical,  826. 

Power  of  steam,  714. 

Power,  adaptation  to  weight,  110. 

Power  and  weight,  106;  relation  of,  109. 

Press,  hydrostatic,  190. 

Pressure,  atmospheric,  257 ;  centre  of,  197 ;  of 
liquid  in  motion,  220 ;  of  liquid  downward, 
191 ;  of  liquid  on  side  of  vessel,  193 ;  of 
liquid  upon  containing  vessel.  214 ;  produced 
by  impact,  112 ;  transmitted  by  gases,  2;~>fi ; 
transmitted  by  liquids,  189;  varies  with 
Sp.  Gr.,  198. 

Primary  colors,  456. 

Prime  seventh,  373. 

Prince  Rupert's  drops,  178. 

Printing  telegraph,  925. 

Prisms  and  lenses,  438. 

Problems  on  acoustics,  page  289 ;  on  elasticity 
and  tenacity  of  solids,  page  146;  on  elec- 
tricity page  067  ;  on  gravitation,  page  73;  on 
heat,  page  506 ;  on  hydrodynamics,  page  199 ; 
on  laws  of  vibrations,  page  251;  on  theory  of 
machinery,  page  107;  on  optics,  page  392; 
on  pneumatics,  page  234 ;  on  weights,  mea- 
sures, and  motion,  page  37. 

Production  of  waves.  319. 

Products  of  combustion  and  respiration,  718. 

Progressive  undulations,  300;  in  liquids,  320. 

Properties  of  matter,  general  or  specific,  6 ; 
physical  or  chemical,  8. 

Properties  of  liquid  and  solid  gases,  691;  of 
solar  spectrum,  460;  of  solids.  149. 

Propositions  in  regard  to  forces,  42. 

Projectiles,  theory  and  laws  of,  103 

Proof  plane,  823. 

Pulley,  compound,  120 ;  fixed,  118 ;  movable. 
119. 

Pumps.  289-293. 

Pyrometers,  589. 

Pyrometer,  Daniell's,  584;  Draper's.  585;  Sax 
ton's  reflecting,  582;  Wedgewood's,  583. 

Pyrometrical  heating  effects,  752. 

QUALITY  of  musical  sounds.  363. 
Quantity  and  intensity  of  electricity,  865. 
Quantity  of  heat  from  friction,  736. 

RAIN.  980  ;  annual  depth  of,  983 ;  days  of,  982; 
distribution  of,  981. 

Radiant  heat,  intensity  of,  631;  partially  ab- 
sorbed, 630;  transmission  of,  641. 

Radiating  power  for  heat,  638. 

Radiation,  of  cold,  634 :  of  heat,  universal,  033  ; 
law  of  cooling  by,  632;  terrestrial,  745. 

Radiators,  steam,  732. 

Railway  illumination.  520. 

Rainbow.  536. 

Jf.amsden's  electrical  machine,  835. 

Range  of  human  voice,  390. 

Rays  of  light,  401. 

Reaction  of  escaping  liquids,  217. 

Reaumur's  thermometer,  570. 

Recomposition  of  white  light,  457. 

Reed  pipes,  381. 

Regulators  of  electric  light,  884 


INDEX. 


'07 


Reflecting  telescope,  501. 

Reflection  at  curved  surfaces,  426;  by  plane 

mirrors,  418;  by  regular  surfaces,  415;  of 

circular  waves,  326;  of  light,  406;  of  sound, 

352 :  of  waves,  323. 

Reflective  power,  how  determined,  636. 
Refractory  bodies.  660. 
Refraction  at  curved   surfaces,  445,  44(3 ;  at 

regular  surfaces.  438;  atmospheric,  538;  at 

plane    surfaces,   439;    by    lenses,   447-451; 

bv  plane  glass.  441 ;  by  prisms.  439;  of  heat, 

648;  of  light,  406;  of  pencils  of  light,  443; 

of  sound,  357. 
Refrigerators.  724. 
1-feynault's  experiments,  276. 
Rerjnault  on  expansion  of  gases  by  heat,  607. 
Relation  of  bodies  to  light,  400;  of  power  to 

weight,  109;   of  specific   heat  and   atomic 

weight,  654. 

Relative  value  of  fuel,  753. 
Repulsion,  146;  electrical,  812;  magnetic,  780. 
Repulsion  of  light  floating  bodies,  242. 
Repulsive  action  of  heated  surface.  C>97. 
Resistance  of  columns,  171;   of  fluids,  143; 

passive,  136. 

Kest,  absolute  and  relative.  25. 
Resultant  of  opposite  parallel  forces,  47;  of 

unequal  parallel  forces,  46. 
Results  of  impact,  112. 
Revolving  magnet,  914. 
Revolving  lights.  523. 
Rc.ynv'r's  dynamometer,  37. 
Rheostat,  907.     • 
Rigidity  of  ropes.  142. 
Ritchie's  electrical  machine.  837. 
Rolx'.rts1  oompensating  pendulum,  596. 
Rdberval's  balance,  115. 
Kods,  vibration  of,  310. 
Roqi-fs  oscillating  spiral,  909. 
Rolling  friction.  139. 
Ropes,  rigidity  of,  142. 
Rosstfs  telescope,  503. 
Rotascope,  57. 

Rotation  of  electric  light  about  a  magnet,  936. 
Rotation  of  the  earth  demonstrated  by  the 

pendulum,  86. 
Rotations,  parallelogram  of,  56 ;  right-handed 

or  left-handed,  56. 

Rotary  polarization,  556;  magnetic,  560. 
Rotary  pump.  293. 
Jiousseau's  hydrometer,  212. 
Ru/tmkorJF  coil,  933. 
Rule  for  position  of  images.  436. 
Jfumford's  photometer,  414:  tbermoscope,  587. 
Rutherford's  thermometer,  578. 

SAIGEY'S  table  of  length  of  pendulum,  90. 

Saturated  space,  669. 

Saturation.  661. 

Saitssitre's  hygrometer,  973. 

&nwt's  toothed  wheel,  361. 

S<m.O7/s  steam  engine.  706. 

Saxton's  deep-sea  thermometer.  581 ;  reflecting 

pyrometer,  582. 
Scale  beam,  115. 
Scintillating  tube,  852. 
Screens,  diathermanic  power  of,  643. 
Screw.  127 :  efficiency  of,  128 ;  endless.  129. 
Sea  lights.  522. 
Seasons.  947. 
Secondary  axes.  430. 
Seconds  pendulum,  89 ;  formulre  for,  90 ;  table 

of  lengths  in  different  latitudes,  90. 

61* 


:  Self-registering  thermometers,  578. 

Sensible  weight  varies  in  different  localities, 
j      93. 

j  Sensibility  of  the  ear,  378. 
'  Septum  required  for  osmose,  246. 

Series  of  elastic  balls.  185. 

Seventh,  harmony  of,  373. 

Sexlant,  lladlcy's,  425. 

Shock  transmitted  by  elastic  balls,  185. 
!  Silliman's  photometer,  414. 

Simple  microscope,  495. 

Simple  pendulum,  79. 

Simple  pendulum,  propositions  respecting,  82. 

Simple  vision  with  two  eyes,  482. 

Siren,  360. 

Sliding  friction,  137. 

Smee's  battery,  871. 

Snow,  984 ;  colored,  985 ;  limit  of  perpetual, 
955. 

Solar  microscope.  516. 

Solar  spectrum,  properties  of,  460. 

Solenoid.  910. 

Solid  eye-piece,  512. 

Solidification,  change  of  volume  by,  664. 

Solidification  liberates  heat,  663. 

Solidification  of  gases,  theory,  688. 

Solids,  characteristics  of,  149;  conduclibility 
for  heat,  614;  expansion  of,  589;  structure 
of.  150;  undulations  of,  306;  unequal  ex- 
pansion of.  595. 

Solution,  601. 

Sonometer,  367. 

Sonorous  tubes,  379. 

Sonorous  waves,  length  of.  370. 

Sound,  335;  distances  calculated  by,  346;  in 
all  elastic  bodies,  340;  interference  i-f.  349; 
not  instantaneous,  342;  not  propagated  in 
a  vacuum,  339;  propagated  by  waves,  337; 
reflected,  352;  refracted^  357;  velocity  in 
air,  344;  velocity  in  gases,  345;  velocity  in 
liquids,  347  ;  velocity  in  solids,  348. 

Sounds  of  birds,  392 ;  of  insects,  392 ;  produced 
by  animals,  392. 

Sounding  bodies  vibrate,  336. 

Source  of  heat  influencing  diathermancy,  644. 

Sources  of  heat  734-757. 

Sources  of  light.  399. 

Space  described  by  a  falling  body,  71. 

Speaking  trumpet,  358. 

Specific  gravity,  209. 

Specific  gravity  bottle,  211. 

Specific  gravity  by  balance,  210. 

Specific  heat,  651.    ' 

Specific  heat  and  atomic  weight  related.  654. 

Specific  heat  determined  by  laws  of  acoustics, 
653. 

Specific  heat  of  gases,  652. 

Specific  weight.  99. 

Spectrum,  456;  dark  lines  in,  461. 

Specula,  416. 

Spherical  aberration  of  lenses,  454;  of  mirrors, 
437. 

Spherical  mirrors,  426. 

Sphericity,  aberration  of,  455. 

Spheroidal  state,  694;  cause  of,  698;  can  so  of 
explosions,  701;  familiar  illustrations,  702; 
remarkable  phenomena,  700. 

Spirit  level,  203. 

Spirit  thermometers.  575. 

Spring  balance.  37. 

Springs  intermittent.  286. 

Stable  equilibrium,  207. 

Standard  thermometer,  577. 


'08 


INDEX. 


Starting  friction,  138. 

Statical  and  dynamical  forces,  39. 

Statical  electricity,  809. 

Statics  denned.  39. 

Stationary  undulations.  302. 

Stationary  waves,  321. 

Steam   boiler,  713;   explosions,   701;  Gold's, 

733. 

Steam  cylinder,  I'apin's.  707. 
Steam,  electricity  from,  839. 
Steam,  heat  latent  and  sensible  at  different 

temperatures,  683. 
Steam,  high  pressure,  680. 
Steam,  latent  heat  of,  6S2. 
Steam,  power  of.  714. 
Steam-engine.  703;  high  pressure.  711:   low 

pressure,"  710;    Newcomen's,   707;    AVtttt's. 

709. 

Steam-heaters,  732. 
Steam-power.  134. 
Steamboat,  the  first,  705. 
Steelyard,  115. 
Stere,  18. 

Stereomonoscope,  526. 
Stereoscope,  525. 
Stone's  ventilating  shaft.  723. 
Storms,  general  laws.  971. 
Stream  measurers,  227. 
Strength,  animal,  l:>0;  of  beams  and  tubes. 

172;  of  materials,  170;  of  men,  131. 
Structure  of  human  eye,  468. 
Structure  of  metals  changed,  180. 
Study  of  colors,  492. 
Stuttering,  391. 
Submarine  telegraphs.  927. 
Substance  defined,  I. 
Suction  and  lifting  pump,  2'Jl. 
Suction  pumps,  290. 
Sulphate  of  copper  battery.  872. 
Sun,  a  source  of  heat,  742 ;  influence  of,  948 ; 

quantity  of  heat  from.  743. 
Surface  of  discharging  liquid,  215. 
Syphon.  285. 
Syphon  barometer,  267. 
System  of  forces,  44. 
System  of  magnetic  observations,  798 
System  of  wheels,  117. 
Systems  of  crystals.  154. 

TABLES,  Ascent  of  liquids  in  tubes.  239. 

Absorptive  power  for  heat  from  dif- 
ferent sources,  App.  tab.  IX. 

"  Absorptive  power 'of  different  bodies, 
App.  tab.  VIII. 

"  Aqueous  vapor  in  a  cubic  foot  of  satu- 
rated air  at  different  temperatures, 
App.  tab.  XXI. 

"  Barometric  column  at  various  alti- 
tudes, 265. 

"        Boiling  point  of  liquids,   App.   tab. 

"  Boiling  point  of  water  at  different 
places,  App.  tab.  XVIII. 

"  Boiling  point  of  water  at  different 
pressures,  App.  tab.  XVI. 

"         Boiling  point  of  water  under  1,  2,  3, 

&c.,  atmospheres,  App.  tab.  XIX. 
Colors  of  tempered  steel,  178. 

"         Comparison  of  thermometers,  576. 

"        Compressibility  of  gases.  276. 

'•        Compressibility  of  liquids,  188. 

u  Conducting  power  of  metals  and  build- 
ing materials,  App.  tab.  VII. 


TABLES,  Decrease  of  temperature  from  eleva- 
tion, 954. 

"        Degree  of  elasticity,  183. 
"        Depression  of  mercury  in  tubes.  238. 
,        '•        Diathermancy  lor  heat  from  diil'ment 

sources,  645. 
"        Di  itherinancy    of   different    liquids. 

App.  tab.  X. 
"        Diathermancy  of  different  solids.  Ann 

tab.  XIII. 

"        Elasticity  of  metals,  1G1. 
"        Expansion  of  gases,  607. 

Expansion  of  gases,  App.  tab.  V. 
Expansion  of  liquids,  App.  tab.  IV. 
Expansion  of  mercury,  598. 
Expansion  of  solids,  App.  tab.  III. 
"        Force  required  to  heat  a  pound  of 

water  1°  F ,  761. 

Freezing  mixtures,  App.  tab.  XII. 
"        French  decimal  measures  and  weights 
changed  to  English  measures  and 
weights,  App.  tab.  II. 
"        Frequency  ot  different  winds,  965. 
"        Frequency  of  auroras,  996. 
"        Friction,  138. 
"        Hardness,  176. 
'•'        Heat  of  combustion  in  air,  753. 
"        Heat  of  combustion  in  oxygen,  751. 
"        Hydrometer  decrees  and  specific  gra- 
vities, App.  tab.  XXV. 
"        Hydrostatic      pressure     at     variuus 

depths,  196. 
"         Latent  and   sensible  heat  of  steam, 

App.  tab.  XXII. 
"         Laws  of  falling  bodies,  71. 
"        Limits  of  perpetual  snow,  955. 
"        Liquefaction    and     solidification    of 

gasen,  App.  tab.  XX. 
"         Measures  and  weights.  App.  tab.  I. 
"        Melting  points  and   heat  of  fusion, 

App.  tab.  XV. 
"        Radiating  a-nd  absorbent   power   of 

bodies  for  heat,  638. 
"         Radiating  power,  App.  tab.  VI. 
"         Reflection  of  light,  407. 
"         Specific  gravity  of  solids  and  liquids, 

App.  tab.  XXIII. 
"        Specific  heat,  App  tab.  XI. 
"        Specific   heat  for  constant  pressure 

and  constant  volume.  653. 
"        Strength  of  men  and  animals,  133. 
"         Strength  of  materials.  170. 
"        Temperature  in  different  latitudes, 

953. 

"        Tension  of  vapors,  App.  tab.  XIV. 
"        Velocity  of  winds,  961. 
"         Volume  and  density  of  water,  App. 

tab.  XXIV. 
Telegraph,  921-928. 

Telescope,  497;   achromatic,  504;   equatorial, 
505;  Galileo's,  .408 ;  Lord   Ros.se's,  503;  re- 
flecting, 501;  Sir  William  Herschel's,  502. 
Telescopes,   penetrating   power,   507;    visual 

power  of,  507. 
Telestereoscope,  524. 
Temper,  178. 

Temperament  in  music,  375. 
1  Temperature,  565;   estimation  of  high.  oSfi; 
i      extremes    of,    744;    mean,    950;    monthly 
'      variations,   951;    of  vaporization,   672;   of 
vegetables,  757;  variations  in  altitude.  954- 
variations  in  latitude,  953. 
Tempered  steel,  colors,  178. 


INDEX. 


709 


Tenacity  of  different  substances,  170. 

Tenacity,  laws  of,  170. 

Tension,  252 ;  changes  density,  169;  maximum, 
of  vapors,  669;  of  vapors,  Dalton's  law,  (370  ; 
of  vapors  in  communicating  vessels,  671. 

Terrestrial  attraction,  direction  of,  60;  point 
of  application.  61. 

Turret-trial  eye-piece,  500;  beat,  origin  of,  746; 
magnetism,  787  ;  radiation,  745. 

Thauinatrope,  488. 

Theorem  of  Archimedes,  205;  of  Torricelli,  219. 

Theoretical  and  actual  flow,  216. 

Theories  of  endosmose,  251;  of  light,  398;  of 
light  unsatisfactory,  405. 

Theory  defined,  3;  of  liquefaction  and  solidifi- 
cation of  gases,  688  ;  of  undulations,  299. 

Therinochrosy,  646. 

Thermo-electricity,  941. 

Thermo-electric  motions,  941. 

Thermometers,  567;  air,  587;  Breguet's  metal- 
lic. 580;  Centigrade,  570;  comparison  of 
scales  of,  571;  construction  of,  568;  defects 
in  mercurial,  576 ;  Fahrenheit's,  570;  gradu- 
ation of,  569;  house,  572;  Howard's  differ- 
ential, 587;  Kinnersley's,  852;  Leslie's  dif- 
ferential, 587;  limits  of  mercurial,  574; 
metastatic,  579;  Negretti  &  Zatnbra's  maxi- 
mum, 578;  Reaumur's,  570;  Rutherford's 
maximum,  and  minimum,  578;  Saxton's 
deep  sea,  581 ;  self-registering.  578 ;  sensi- 
bility of,  572;  spirit,  575;  standard,  577; 
tests  of.  572;  Walferdiri's  maximum,  578. 

Thermometrid  scales  compared,  571. 

Thermo-multiplier,  588,  942. 

Thermoscopes,  587. 

Thilorier  and  J^ianchi's  apparatus,  690. 

Three  states  of  matter,  15. 

Thunder.  989. 

Thunder-storms,  988. 

Time  and  velocity,  29. 

Time  required  for  vision,  489. 

Tolas'  solid  eye  piece.  512. 

Tone,  363;  changed  by  echo,  355. 

Tornadoes,  909. 

Torricellian  theorem,  219;  demonstrated,  220. 

Torricellian  vacuum,  261. 

Torsion,  elasticity  of,  165;  electrometer,  820; 
laws  of,  166:  of  rigid  bars,  167. 

Total  hydrostatic  pressure.  196. 

Total  reflection,  409. 

Trains  of  wheel  work.  117. 

Transposition  in  music.  374. 

Transverse  strength.  172. 

Tubes,  strength  of.  172. 

Tubular  bridges,  172. 

Tuning  fork,  377. 

Turbine  wheel,  231. 

Twining' s  ice  machine.  681. 

Tvleriati  electrical  machine,  837 

Tympanum,  393. 

UMBRA,  411. 

Undershot  wheel,  230. 

Undulation  in  oceans.  &c.,  329;  of  elastic 
fluids,  330;  of  liquids,  319. 

Undulations  of  a  sphere  of  air.  331  :  of  solids. 
306 ;  origin  of,  299 ;  phases  of,  304 ;  progres- 
sive. 300;  progressive,  in  liquids,  320;  sta- 
tionary, 302. 

Uniform  motion,  30. 

Uniform  musical  pitch,  page  668. 

Unison,  36  i. 

Unit  of  force,  37. 


Units  of  measure,  16. 

Universal  discharger.  851 :  gravitation,  law  of, 

59;  radiation  of  heat,  033. 
Unstable  equilibrium,  207. 
Upward  pressure  of  liquids,  192. 

VACUUM,  Torricellian,  261 ;  vapors  formed  in, 
668. 

Value  of  fuel,  715. 

Value  of  g  in  pendulum  experiments,  89. 

Vaporization,  6U7. 

Vaporization,  temperature,  and  limits,  672. 

Vapors,  2.V2;  and  gases,  identity  of,  688; 
density  of,  693;  formed  in  a  vacuum,  668; 
from  the  body,  719;  Latour's  law,  692; 
liquefaction  of,  685;  maximum  tension,  6t9. 

Variable  motion,  31. 

Variation  chart,  789. 

Variations  of  barometric  height,  270;  of  mag- 
netic needle,  788;  annual,  daily,  790. 

Vegetables,  temperature  of,  757. 

Velocities,  actual  and  theoretical,  144;  par- 
allelogram of,  34. 

Velocity  after  impact,  184;  o^all  sounds  the 
same,  343;  of  all  sounds  not  the  same,  page 
668;  of  aerial  waves,  332;  of  electricity, 
818;  of  light.  404;  of  rivers  and  streams, 
227;  of  sound  in  air,  344;  of  sound  in  liquids, 
347 ;  in  solids,  348  ;  of  sound,  Kewtou's  for- 
mula, 653. 

Ventilation,  716-726;  a  practical  problem.  722; 
necessity  of,  718;  quantity  of  air  required, 
720. 

Ventilating  shaft,  723. 

Ventilators,  725. 

Ventriloquism,  391. 

Verification  of  laws  of  falling  bodies,  72. 

Vernier,  266. 

Vibrating  armature,  931. 

Vibrating  dams,  386. 

Vibration  of  air  in  tubes,  379,  384;  of  cords, 
308;  laws  of,  of  cords,  309;  of  rods,  310; 
of  membranes.  318;  of  plates,  312;  of  plates, 
laws  of,  315 ;  paths  of,  311. 

Vibrations,  299;  forms  of,  307;  from  magnet- 
ism. 916 ;  isochronous,  303 ,  of  different  notes, 
absolute,  369;  relative,  308;  of  heat  and 
light,  765:  of  light,  direction.  541 ;  of  light, 
length  of.  531 ;  of  light,  transmission  of,  542 ; 
of  light,  resolution  of.  544. 

Victoria  tubular  bridge,  172. 

Virtual  focus,  429 ;  images,  434 ;  velocities,  105. 

Visible  bodies,  402. 

Vision,  468 ;  conditions  of.  475  ;  binocular,  484 ; 
double,  483;  single,  482. 

Visual  angle,  472. 

Visual  impressions  require  time.  489. 

Visual  power  of  microscope,  513;  of  telescopes, 
507. 

Visual  rays  nearly  parallel,  479. 

Vis  viva,  111. 

Vitality,  10. 

Vocal  apparatus  of  man,  388. 

Voice  and  speech.  387. 

Voice,  mechanism  of.  389;  range  of  human, 
390. 

Volta-electric  induction.  929. 

Voltaic  arch,  heat  of.  886. 

Voltaic  batteries,  869-881;  effects  in  various 
forms,  881. 

Voltaic  circuit,  polarity  of,  878. 

Voltaic  couple.  866. 

Voltaic  currents,  heat  of,  887. 


62* 


3  A 


710 


INDEX. 


Voltaic  electricity,  quantity  and  intensity, 
805. 

Voltaic  pile  or  battery,  86-i;  chemical  theory, 
898;  grouping  elements,  879;  physical  ef- 
fects, 883 ;  physiological  effects,  S'J5 ;  mag- 
netic effects,  895 ;  theory  of,  89(5. 

Voltaic  spark  and  arch,  8S3. 

Voltaism  and  galvanism,  864. 

Vila's  contact  'theory,  803,  897. 

Volla's  discovery,  origin  of,  863. 

VoUa's  electrical  lamp,  856. 

Volta's  electroscope,  846. 

VoUa's  hail  storm,  842. 

Voltameter,  889. 

Volume  changed  l\y  solidification,  664. 

Volume  of  gases,  008. 

WALFEBDIX'S  thermometer,  578. 

Warming,  727. 

Watches,  balance  wheels  of,  596. 

Water  bellows,  195. 

Water,  effect  of  unequal  expansion,  604;  ex- 
pansion of  604:  freezing  of.  665;  maximum 
density,  604;  Volume  at  different  tempera- 
tures, 604. 

Water  pumps,'  2S:>. 

Waterspouts,  970. 

Water- wheels,  2'.s. 

Watt's  steam  engine,  709. 

Waves,  depth  of.  322;  from  foci  of  ellipse,  324; 
from  focus  of  parabola,  325;  of  air  velocity 
and  intensity  of.  332:  of  condensation  illus- 
trated, 331 ;  of  11  ir  expanding  freely,  334;  of 


air,  interference  of,  333;  of  condensation, 

3:;0;  production  of,  319;  reflection  of,  323; 

stationary.  321. 

Weather  indicated  by  barometer,  271. 
Wedge,  125 ;  application  of.  120. 
Weighing  machine,  115. 
Wells,  artesian,  204. 
Weight,  37,  97,  106;  definition  of,  58. 
Weights,  French  system,  100. 
Weight,  specific,  99. 

Weight  varies  in  different  localities,  93. 
Wheel  and  axle,  116. 
Wheel  barometer.  268. 
Wheel,  breast,  230;   overshot,  229;  turbine. 

231 ;  undershot,  230. 
Wht-elwork.  trams  of.  117. 
Whirlwinds,  969. 
Whispering  galleries.  ">56. 
White  light,  composition  of,  457. 
Winds,  cyclones,  and  hurricanes,  968. 
Winds,  general  consideration  of,  957  ;  general 

direction  of,  965;   hot.  9G7  :  periodical,  963; 

propagation  of.  958 ;  regular,  962;  variable, 

964;  velocity  of,  901. 
W'.'llaston's  camera  lucid  a,  518. 
Wood  conducts  heat,  017. 

YARD,  17. 

ZAMBONI  &  DE  Luc,  dry  piles,  873. 

Zero  point  of  thermometer,  570 :  'li-p!;icenv'nt 

of,  573. 
Zero,  absolute,  666. 


END 


